A virtual species study to establish baseline for assessing the predicted current and future distribution ranges of real species in mountainous areas

A virtual species study to establish baseline for assessing the predicted current and future distribution ranges of real species in mountainous areas | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article A virtual species study to establish baseline for assessing the predicted current and future distribution ranges of real species in mountainous areas Chi-Cheng LIAO, Yi-Huey CHEN, Huan-Yu LIN This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4443811/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Simulation and model prediction of virtual species aim to establish baseline for assessing the projected contemporary and future distribution ranges of real species in mountainous areas. Fundamental niches and geographic ranges of 5 virtual species were defined in the diagram of principal components analysis based on a high-resolution climate dataset generated from meteorological data. Heterogeneity of the climate dataset had been validated to influence the relationships between species responses and suitable environments, consequently affecting the geographical distributions of virtual species. The performances of 11 algorithms were evaluated by the extracted fraction of shared presences (ESP), instead of TSS and AUC. ESP calculates the overlap between simulated suitable ranges and predicted current potential ranges of virtual species. According to ESP, ensemble modeling outperformed the 11 algorithms. A small sample size has significant effects on model performance due to the extremely low value of ESP, and the presence of only 5 sample points was evidently a limitation of model predictions. Furthermore, geographical distance among sample points provide signals of niches that will be identified through accurate predictions of ensemble modeling in our analyses. By the 2050s and 2090s, climate change may drive the range expansion of real species currently distributed in inland areas or on leeward slopes, while causing range restriction or local extinction of real species in coastal areas or on windward slopes. Our study can inform application of species distribution models to provide scientific support for conservation planning in mountainous areas and forecasts of species distributions under climate change. commission error ensemble modeling expected fraction of shared presences (ESP) omission error species distribution model Taiwan virtual species Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Introduction Species distribution models (SDMs) are powerful tools for exploring the habitat characteristics associated with occurrence patterns of species (Chambers et al. 2013 ; El-Gabbas & Dormann 2018 ; Qazi et al. 2022 ; Zimmer et al. 2023 ). SDMs correlate either presence-only or presence/absence data of species with relevant environmental variables and subsequently generate a geographical map indicating the potential distribution ranges of species (Peterson et al. 2011 ). Accurate distribution ranges projected by SDMs are crucial for making informed assessments and are particularly important for improving conservation management of rare or endangered species (Guillera‐Arroita et al. 2015; Hama & Khwarahm 2023 ; HamadAmin & Khwarahm 2023 ; Lannuzel et al. 2021 ; Zurell et al. 2023 ). Accuracy of SDMs largely depends on the sample size and unbiased sampling of spatial data (Bean et al. 2012 ; El‐Gabbas & Dormann 2018; Elith et al. 2011 ; Guisan et al. 2007 ; Inman et al. 2021 ; Kadmon et al. 2003 ). However, a large sample size and unbiased sampling of spatial data are great challenges for rare or endangered species (Laskey et al. 2020 ). Particularly in mountainous areas, complex topography, habitat fragmentation, as well as steep climate gradients along mountain slopes usually result in small populations and biased distribution of rare or endanger species. Small population size, fragmented or biased distribution of rare or endangered species are critical issues in model predictions (Lannuzel et al. 2021 ; Liao & Chen 2021 ). SDMs are seldom applied in mountainous areas not only because of the sample size of species, but also because of the resolution of climate dataset. Global climate datasets with 30-arc resolution, such as WorldClim (Fick & Hijmans 2017 ) or Chelsa (Karger et al. 2017 ), do not precisely reflect the heterogeneous climate environments in mountainous areas (Fick & Hijmans 2017 ), even when the climate dataset is downscaled to finer resolutions (Dobrowski 2011 ; Pradervand et al. 2014 ; Wang et al. 2016 ). Recently, a statistical method to generate high resolution climate datasets in mountainous areas was developed to improve the performances of SDMs (Liao & Chen 2021 ; Liao et al. 2023 ). The high resolution climate dataset of Liao et al. ( 2023 ) precisely reflected the heterogeneous climate environments in mountainous areas, and SDMs accurately projected potential distribution ranges of grassland when using this climate dataset (Liao et al. 2023 ). However, this high resolution climate dataset has not been directly validated by modeling rare or endangered species, and it may not be optimal for predicting species distributions in mountainous areas, potentially limiting its application. Before being used in modeling studies, the high resolution climate dataset needed to be assessed. Virtual species are increasingly used in SDMs mostly because they allow the separation of the effects of individual features in complex models (De Marco & Nóbrega 2018 ). In this study, virtual species were simulated to assess whether the high-resolution climate dataset had reflected the heterogeneity of climate environments in mountainous areas. A virtual species was generated by resembling real species to create a simulated ecological niche in an n-dimensional environmental space (Duan et al. 2015 ; Hirzel et al. 2001; Leroy et al. 2016 ; Qiao et al. 2016 ). The high-resolution climate dataset generated by Liao et al. ( 2023 ) was used to simulate virtual species in the principal components analysis (PCA) by estimating the probability of each cell belonging to the climate niche (Leroy et al. 2016 ). Subsequently, the gridded cells that were categorized as presence were mapped to show the suitable or geographical ranges in the study area. Different virtual species were simulated in different areas of the PCA diagram, and they were assumed to have distinct geographical distributions due to the heterogeneous climate environments in the study area. SDMs were then employed to project the potential distribution ranges of the virtual species. Virtual species have become increasingly popular for testing SDMs because simulated virtual species offer known distribution ranges, which support a comprehensive understanding of species-environment relationships (De Marco & Nóbrega 2018 ; Hirzel et al. 2001; Meynard & Kaplan 2013 ). Virtual species can provide controlled, unbiased presence and absence data, which are unavailable to field ecologists (Hirzel et al. 2001; Meynard et al. 2019 ). The “true” presence and absence data of virtual species are more appropriate for assessing model performance and overcoming the effects of biased samples of spatial points (Bombi & D’Amen 2012 ; Hirzel et al. 2001; Leroy et al. 2016 ; Qiao et al. 2019 ; Qiao et al. 2016 ). In addition to the predicting current distribution range, SDMs were also employed to project the future distribution range under future climate scenarios in this study. Climate change is a strong force that can cause shifts or expansion in species ranges and significantly increases the risk of extinction for rare or endangered species (Jiang et al. 2022 ; Qazi et al. 2022 ; Zurell et al. 2023 ). Rare or endangered species, which are characterized by small population sizes, are especially threatened by climate change (IUCN 2014 ). SDMs accurately predicting current distribution ranges and evaluating future range shifts are urgently necessary for the effective design of conservation strategies for rare or endangered species (Ali et al. 2023 ; Jiang et al. 2022 ; Ning et al. 2021 ; Wan et al. 2021 ; Zimmer et al. 2023 ; Zurell et al. 2023 ). Therefore, future climate datasets are crucual for SDMs to assess the vulnerability of species to climate change (HamadAmin & Khwarahm 2023 ; Zurell et al. 2023 ). If the current climate dataset generated by Liao et al. ( 2023 ) accurately reflects climate heterogeneity in mountainous areas, it enables the generation of future climate datasets. The generation of future climate datasets was based on the methodology of Liao et al. ( 2023 ), which was applied for SDMs to project range shifts of both virtual and real species in the study area. This study aims to generate high-resolution current and future climate datasets in a mountainous area expected to adequately capture the heterogeneous climate characteristics both in the current state and in future climate changes. In this study, five virtual species were simulated to validate the heterogeneity of climate datasets. Several question were addressed. (1) The characteristics of the current climate dataset were hypothesized to influence the relationship between species response (presence) and environments (habitat suitability), referred to as the species-environment relationship. (2) Various virtual species, simulated using the high-resolution climate dataset to determine habitat suitability, were assumed to have distinct geographical distribution ranges in the mountainous area. (3) SDMs were conducted to explore the current and future distribution ranges of virtual species in a mountainous area, aimed to examine the extent of range expansion, restriction, shift or local extinctions under climate change. (4) Real species were then applied for algorithms to predict both the current potential range and future distribution ranges under climate change. These predictions aim to inform applications for conservation management. Materials and Methods Study area Taiwan is a subtropical island located at the western edge of the Pacific Ocean, with coordinates ranging from 21° 55’ to 25° 20’ N and 119° 30’ to 122° 00’ E (Fig. 1 ). The subtropical island is located 150 km off the southeast coast of Mainland China and is characterized by a monsoon climate (Chen & Tsai 1983 ; Su 1984 ). The northeast monsoon during winter and the southwest monsoon during summer influence the weather conditions of Taiwan Island. Particularly, the northeast monsoon during winter prevails in Taiwan for six months, bringing heavy rainfall and strong winds to the northern and eastern slopes of the Central Mountain Range. In northern Taiwan (NTWN), a steep precipitation gradient extends from coast to inland areas that is significantly influencing the distribution of plant species (Liao & Chen 2022 ; Liao et al. 2023 ). The annual precipitation decreased from more than 6,000 mm at the northeastern slope to 1,900 mm at the southwestern slope of the mountain ridge in NTWN (Liao et al. 2023 ). The mean monthly temperatures at the mountain ridge range from 11.3 ℃ in winter to 20.5 ℃ in summer, while those at the coastal area range from 17.9 ℃ in winter to 26.6 ℃ in summer (Liao & Chen 2022 ; Liao et al. 2023 ). The study area in NTWN ranges from 24° 57’ to 25° 17’ N and 121° 24’ to 122° 00’ E (Fig. 1 ), covering an area of approximately 1,031 square kilometers (103,100 hectares). The highest mountain peak in the study area is Qixingshan, which stands at an elevation of 1,120 meters above sea level (asl.). The major vegetation type in NTWN is evergreen broad-leaved forest (Hsieh et al. 1997 ; Li et al. 2013 ; Liao et al. 2012 ). The forests in NTWN are dominated by species such as Castanopsis , Cleyera , Cyclobalanopsis , Dendropanax , Elaeocarpus , Engelhardia , Gordonia , Helicia , Ilex , Keteleeria , Limlia , Litsea , Machilus , Meliosma , Michelia , Pinus , Schefflera , Symplocos , and Trochodendron (Li et al. 2013 ). The mean canopy height of these forests is approximately 15 meters. There is no deciduous forest in NTWN, while native deciduous tree species are scattered within the forests of the region. Natural grasslands are commonly found along the mountain ridges spanning from the coast to the inland regions within the NTWN, while the elevations of natural grassland vary across these ridges within the study area (Liao et al. 2023 ). The predominant species of natural grassland in these mountain areas are Miscanthus sinensis and Pseudosasa usawai (Liao et al. 2014 ; Liao et al. 2023 ). It is worth noting that the climatic niches of these two species are similar and may demonstrate convergence of climatic niches (Liao et al. 2023 ). Downscaling of the current climate dataset In this study, a gridded climate dataset with spatial resolution of 50 × 50 m² was created to present historical climate environments of the study area. This dataset was generated by utilizing daily meteorological data downloaded from the Central Weather Bureau’s website (CWB, https://e-service.cwa.gov.tw/HistoryDataQuery/index.jsp ). The 50 × 50 m² gridded climate dataset was adopted to accurately capture the heterogeneous climate environments along the mountain slopes. To construct this dataset, we downloaded daily meteorological data from CWB’s website. The detailed process of downscaling the historical climate dataset described in Liao et al. ( 2023 ) includes the following steps: (1) interpolation of the meteorological climate dataset to generate smooth climate variable surfaces; (2) creation of gridded cells, each with a spatial resolution of 50 × 50 m², to extract data from the smooth climate variable surfaces; (3) altitudinal adjustment of the extracted climate data. Climate data from 30 meteorological stations in and around the study area were downloaded from the CWB website. Mean monthly temperature and total monthly precipitation obtained from the 30 meteorological stations were imported into ArcInfo software (ESRI, Redlands, California, USA) to generate smooth surfaces of climate variables using the Kriging method, resulting in the generation of .tif files for the climate variables. Gridded cells with a spatial resolution of 50 × 50 m² were also created using ArcInfo software. A total of over 0.4 million gridded cells were generated within the study area. For each gridded cell, the longitude, latitude, and elevation data were extracted from a digital terrain model (DTM) developed by the Department of Geography, Chinese Culture University. The DTM had a resolution of 20 by 20 meters. The elevation data obtained from the DTM was named DElev. Subsequently, the 50 × 50 m 2 gridded cells were mapped and overlapped with the .tif files of the meteorological climate surfaces to extract climate data. The meteorological climate dataset with a spatial resolution of 50 × 50 m² was named MCD50. Furthermore, the elevations of the meteorological stations were also interpolated using the Kriging method in ArcInfo software, resulting in the generation of a smooth elevation surface named MElev. The gridded cells of MCD50 were overlapped with MElev to extract the elevation data. The differences between DElev and MElev were calculated for the altitudinal adjustment of MCD50. The altitudinal adjustment function is: AdjMCD50 = slope × (DElev – MElev) + MCD50. The abbreviation AdjMCD50 represents the altitudinally adjusted meteorological climate data with a spatial resolution of 50 × 50 m². The slope of the function, also known as the empirical lapse rate, was calculated as the slope of the linear correlation between the elevation and climate data of the nearest 12 meteorological stations. The linear regression model was implemented using the "stats" package within the R environment (Chambers & Hastie 1992). The detailed methodology for generating the current climate dataset followed the study conducted by Liao et al. ( 2023 ). The altitudinally adjusted climate data, AdjMCD50, was utilized as the historical climate dataset for modeling species distributions. The climate dataset was generated by considering the following nine variables: mean annual temperature (Tmean), mean maximum temperature of the warmest month (Twrm), mean minimum temperature of the coldest month (Tcld), mean temperature in summer (Tsmr) and winter (Twnt), temperature differences between warmest and coldest months (Tdif), annual total precipitation (Pann), total precipitation in summer (Psmr) and winter (Pwnt). Downscaling of future climate projections The history of the Intergovernmental Panel on Climate Change’s (IPCC) assessment reports covers several generations of emissions scenarios (IPCC 2013 , 2022 ; Pedersen et al. 2021 ). Emission scenarios are generally developed to describe different socio-economic and policy choices, allowing for the assessment of different potential futures and their implications for the long-term climate systems (Kebede et al. 2018 ). In 2022, the global Shared Socioeconomic Pathways (SSPs) were introduced in the Sixth Assessment Report (AR6) most recently published by the IPCC, integrating socioeconomic developments into future climate scenarios (IPCC 2022 ). There are five SSPs (SSP1 to SSP5), and these SSPs are used in conjunction with climate models to generate a range of possible future climate and environmental conditions based on different societal choices and policy directions (IPCC 2022 ; Pedersen et al. 2021 ). Among the five pathways, SSP1 is the most optimistic scenario and emphasizes sustainable development, while SSP2 represents a middle pathway (Pu et al. 2020 ). SSP3 and SSP4 are the most undesirable pathway, assuming unsustainable development trends. SSP5 assumes an energy intensive, fossil-fuel-based economy, but also relatively optimistic development (Pu et al. 2020 ). Regarding the future climate scenarios, the working group of Taiwan Climate Change Information and Adaptation Knowledge Platform (TCCIP) has generated 5 × 5 km 2 gridded climate datasets to present future climate projections for the Taiwan island (Wang et al. 2021 ). The future climate projections fort the Taiwan island were downscaled from 49 General Circulation models (GCMs) during the 6th phase of the Coupled Model Intercomparison Project (CMIP6). Among the 49 available GCMs, five climate system models were used in this study: ACCESS-CM2 (Meucci et al. 2023 ), FGOALS-g3 (Pu et al. 2020 ), GFDL-ESM4 (Dunne et al. 2020 ), MIROC6 (Kataoka et al. 2020 ), and TaiESM1 (Wang et al. 2021 ). The five GCMs were used to generate downscaled future climate datasets at 50 × 50 m 2 resolution for the study area under different climate scenarios. The TCCIP published 5 × 5 km 2 gridded climate datasets to present climate data from 1960 to 2100. Since the climate dataset of AdjMCD50 was at a spatial resolution of 50 × 50 m 2 , the gridded climate dataset projecting future climate at 50 × 50 m 2 was recalculated based on the relative changes observed in the TCCIP’s historical and future climate datasets. We selected three time periods of climate data from TCCIP’s climate datasets to present the climate datasets for the early (2000–2020), mid (2045–2055), and end (2091–2100) of the 21th century. The TCCIP’s climate datasets for the three time periods were used to calculate the mean monthly temperature and total monthly precipitation. Subsequently, differences in monthly temperature and total monthly precipitation between the early and mid, as well as the early and end, of the 21th century were calculated to generate relative changes in climate data. The relative changes in temperature and precipitation were also represented as 5 × 5 km 2 gridded data, which were used to generate .tif files of smooth climate surfaces using the Kriging method in ArcInfo software. The gridded cells with a spatial resolution of 50 × 50 m 2 were overlapped with the .tif files of smooth climate surfaces to extract the relative changes in climate data. The historical climate datasets, AdjMCD50, were overlapped with the relative changes in 50 × 50 m 2 gridded climate datasets to project future climates. Simulations of virtual species The gridded cells with historical climate data (2000–2020) were analyzed using principal components analysis (PCA). PCA was employed to diminish dimensionality and mitigate collinearity among environmental variables, enabling a clearer quantification of environmental overlap (Journé et al. 2020 ; Meynard et al. 2019 ; Qiao et al. 2016 ). Nine climate variables were initially included in the PCA. Notably, significant collinearity was observed among Pwnt and Pann, Tsmr and Twrm, and Twnt and Tcld. Thus, Pann, Twrm, and Tcld were excluded from the PCA. The remaining climate variables were Tmean, Tsmr, Twnt, Tdif, Psmr, and Pwnt. Retaining of the first two principal components (PC1 and PC2) explained a combined 84.1% of the overall variation. To create a range of spatial patterns in habitat suitability, the function “generateSpFromPCA” implemented by R package “virtualspecies” was employed to simulate virtual species (Leroy et al. 2016 ). When using the function, the parameter nb.points was set to 5000. The other two parameters, means and sds, were configured to simulate five virtual species located in various regions of the PCA diagram, representing distinct niches and suitable environments of different virtual species. The performance of the function resulted in distinct geographical distribution patterns in the study area (Fig. 1 and Supplement 1). The first virtual species was designed to be located at the center of the PCA diagram, resulting in a geographic distribution range covering the windward slopes near mountain ridge (Fig. 1 ). The other four virtual species were designed to be located at the lower, left, right, and upper sides of the PCA diagram (Supplement 1). The simulation of the five virtual species aims to ensure that they occupied different environments and that their geographical distribution ranges widely across the study area. Inventory of real species In this study, we selected eleven real plant species and grasslands for modeling analysis. Among them, five species are rarely observed in the study area: Maackia taiwanensis , Benthamidia japonica , Lilium speciosum , Rhododendron pseudochrysanthum , and Bretschneidera sinensis . Their rarity is attributed to their limited geographic range on this island, mainly confined to the mountainous regions of NTWN, wtih only a few occurrences of these species recorded in the fieldwork. The remaining seven species include four woody angiosperms: Rhododendron nakaharai , Euscaphis japonica , Ficus fistulosa , Saurauia tristyla var. oldhamii , as well as two fern species, Dipteris conjugata and Sphaeropteris lepifera . Occurrences of these eleven plant species and grasslands were collected along the roads and mountain trails within the study area. Coordination of occurrences collected in the fieldwork were spatially verified to delete duplicated occurrence records. Modelling technique In this study, 11 algorithms were employed to predict the potential distribution ranges of virtual and real species in mountainous areas. The 11 algorithms include artificial neural network (ANN), classification tree analysis (CTA), flexible discriminant analysis (FDA), generalized additive model (GAM), generalized boosting model (GBM, or usually called boosted regression trees), general linear model (GLM), multiple adaptive regression splines (MARS), Maximum Entropy (MAXENT), random forest (RF), surface range envelop (SRE, or usually called BIOCLIM), and extreme gradient boosting training (XGBOOST). In addition, ensemble modeling, which includes 11 algorithms, was employed to predict virtual and real species in mountainous areas. The 11 algorithms and ensemble modeling were implemented using the “biomod2” package in R software (Thuiller et al. 2016 ). For each virtual species, occurrence and background points were integrated to generate a modeling dataset. The coordinates of the occurrences and background points were used to extract climate data from the climate surfaces. The occurrences were randomly sampled from the geographic distribution range of the virtual species, as shown in Fig. 1 and Supplement 1. Various numbers of sample points were used in the model prediction to assess the impacts of sample size on the model performances. The numbers of sample points imported into the model predictions were 5, 20, 50, 100, and 200. The number of background points was 100 times the number of sample points randomly selected in the study area. When the sample and background points were used for the model predictions, a random set comprising 80% of the occurrence and background data was selected to train the model, and the remaining 20% was used for evaluation. Model performance To assess accuracy of algorithms and ensemble modeling, the training dataset was resampled and modeled 10 times to quantify uncertainties in predictions. True skill statistics (TSS) and the area under receiver operating characteristic curve (AUC) were commonly used to assess the accuracy of species distribution models (Fois et al. 2015 ; Lannuzel et al. 2021 ; Qiao et al. 2019 ; Xu et al. 2021 ). For creating the final ensemble models, only those models with a TSS score greater than 0.8 were used (Khan & Verma 2022 ). Notably, a previous document proposed that the error indices, such as TSS and AUC, do not imply accuracy of suitability, since these indices provide a single-number discrimination measure across all possible ranges of thresholds (Lobo et al. 2008 ). High values of TSS and AUC do not guarantee accurate model performance (Liao & Chen 2022 ). Thus, a similarity index called expected fraction of shared presences (ESP) was introduced to evaluate model performance in this study. The ESP was modified from the Sorenson similarity index to compare the similarity of potential ranges between two species (Godsoe 2014 ; Inman et al. 2021 ). In this study, the ESP was revised to compare the suitable range of a virtual species simulated by PCA with its potential ranges predicted by 11 algorithms and ensemble modeling. The function of the ESP is: $$\text{E}\text{S}\text{P}=\frac{{2{\Sigma }}_{1}^{j}{P}_{s\left(j\right)}{P}_{p\left(j\right)}}{{{\Sigma }}_{1}^{j}({P}_{s\left(j\right)}+ {P}_{p\left(j\right)})}$$ where P s(j) denotes the presence of suitable range at a given cell j , and P p(j) denotes the presence of potential range at a given cell j . Meanwhile, P s(j) P p(j) denotes that a given cell j is both presence of suitable range (P s(j) ) and potential range (P p(j) ). An ESP value of 1 indicates perfect agreement between the suitable and potential ranges of a virtual species, while a value of 0 indicates complete geographic separation (Godsoe 2014 ; Inman et al. 2021 ). Results Suitable ranges of virtual species Five virtual species were simulated by selecting gridded cells from different regions in the PCA diagram, each representing distinct suitable ranges of the five virtual species in the study area. The gridded cells at the center of the PCA (PCAC) diagram represented a distribution range on windward slopes near mountain ridges in the study area (Fig. 1 ). The gridded cells at the lower (PCAO), left (PCAL), right (PCAR), and upper (PCAU) sides of the PCA diagram represented distribution ranges in the coastal area, mountain ridge, inland area, and leeward slopes near mountain ridge, respectively (Supplement 1). We generate 5 virtual species with distinct climatic niche in PCA diagram and the 5 virtual species evidently presented distinct geographical distribution ranges in the study area. It is evident that heterogeneous climate environments can provide diverse suitable habitats for the growth of species. By simulating the virtual species, the high-resolution gridded climate dataset generated from meteorological data was validated to reflect the climate heterogeneity of mountainous areas. Performances of 11 algorithms The potential distribution ranges of the five virtual species were predicted by 11 algorithms to evaluate their performances, aiming to select appropriate algorithms for predicting the potential distribution ranges of real species in mountainous area. Calculations of the ESPs were then used in this study to estimate the degree of overlap between suitable ranges of virtual species simulated in the PCA diagram and potential ranges predicted by the algorithms (Fig. 2 ). FDA, GBM, GLM, MARS, MAXENT, and SRE have relatively higher mean ESP values. Relatively higher mean ESP values demonstrated greater overlap between the simulated suitable ranges and the projected potential ranges, indicating better performances of these 6 algorithms. In the virtual species approach, ESP associated with false presences and false absences can be used to detect algorithm characteristics. Lower ESP value indicates that the values of commission (false presence) and omission (false absence) errors are likely to be higher (Fig. 2 ). A high value of false presences and false absences indicates overestimation and underestimation of the potential ranges of virtual species, respectively. A small sample size uncovers the characteristics of various algorithms. When the number of sample points was 5, the predicted ranges of CTA, SRE and XGBOOST showed relatively lower values of false presence but very high values of false absences. CTA, SRE, and XGBOOST tend to have higher omission errors or underestimations of the species’ potential ranges. On the contrary, the predicted ranges of GLM and MAXENT showed relatively high values of false presences and slightly lower values of false absences. GLM and MAXENT tend to have higher commission errors or overestimations of the species’ potential ranges. Algorithms that either overestimated or underestimated potential ranges can serve as technological options to provide scientific support for designing conservation strategies. The potential ranges predicted by algorithms based on large sample size were highly overlapped with the simulated suitable ranges of virtual species. Our findings demonstrate that sample size is a significant factor affecting the model performances, particularly when the sample size is 5. Five sample points are evidently the limitation of model predictions, because the ESP values were consistently lower than 0.45 for all of the algorithms. In addition, the distinct geographical ranges of the five virtual species have, to some extent, affected the ESP values. The full range of ESP values is slightly narrower for the virtual species distributed at the coastal area (PCAO, the first diagram of Supplement 2). On the contrary, the full range of ESP values is slightly wider for the virtual species distributed at the leeward slopes near mountain ridge (PCAU, the lowest diagram of Supplement 2). In most of the previous studies, the TSS and AUC were calculated to assess predictive performance of algorithms. Higher TSS and AUC should indicate better model performance. However, high values of TSS and AUC did not guarantee better model performances in this study. When the ESP values were relatively higher, the TSS and AUC were not always higher and were somewhat contradictory to the ESP index. In addition, there is no specific trend in TSS and AUC values in this study (Fig. 3 and Supplement 3). Conclusively, the TSS and AUC were not appropriate indices for representing the predictive performance of the algorithms. This study also employs virtual species distributions to evaluate the predictive power of ensemble modeling. Ensemble modeling accurately represented the potential geographical ranges of the five virtual species (Fig. 4 and Supplement 4). Ensemble modeling performed better than the 11 algorithms, as the ESP values were mostly close to or higher than 0.8 when the sample points were greater than 5. Sample size and geographical distribution ranges have less effect on ensemble modeling. Even so, an extremely small sample size had robust effects on the projection results of ensemble modeling. When 5 sample points were applied for ensemble modeling, a low ESP value demonstrated poor model performance (Fig. 5 ). Ensemble modeling performed well when number of sample points was higher than 20. A large sample size caused a precise overlap between the simulated suitable range and the predicted potential range of virtual species. Since ensemble modeling precisely projected potential distribution ranges of virtual species, it is a good model for predicting species’ potential distribution ranges. All 5 virtual species can be accurately predicted by ensemble modeling, and this pattern does not depend on the ecological characteristics of the virtual species. Our results demonstrate that ensemble modeling produced reliable information on the potential ranges of species. Importance of predictors For the 5 virtual species, the relative importance of predictors varied among algorithms, with temperature being evidently more important than precipitation (Table 1 and Supplement 4). The study area possesses complex topography and elevation gradients that certainly affected species distributions. Temperature is highly correlated with elevation gradient. Therefore, temperature is certainly important in predicting virtual species. On the other hand, precipitation significantly differs between windward and leeward slopes in the study area. There are two species, B. sinensis and B. japonica , mainly observed on the windward slopes, and the distributions of these two species were likely related to the high precipitation on the windward slope. However, the relationships between plant distribution and precipitation gradient in the study area were not significantly represented in the model predictions. Table 1 The importance values of predictors for 11 algorithms and ensemble modeling in predicting virtual species. The virtual species are located at the center of PCA diagram. Predictors ANN FDA CTA GAM GBM GLM MAXNET MARS SRE RF XGBOOST Ensemble Psmr 0.11 0.00 0.00 0.05 0.03 0.00 0.01 0.04 0.09 0.06 0.07 0.04 Pwnt 0.08 0.01 0.01 0.07 0.03 0.02 0.01 0.05 0.09 0.06 0.16 0.05 Tmean 0.30 0.31 0.00 0.18 0.02 0.15 0.00 0.10 0.20 0.21 0.04 0.14 Twnt 0.16 0.27 0.33 0.25 0.23 0.27 0.25 0.28 0.18 0.18 0.26 0.24 Tsmr 0.20 0.32 0.51 0.24 0.28 0.50 0.38 0.35 0.22 0.26 0.18 0.31 Tdif 0.15 0.09 0.15 0.21 0.42 0.05 0.35 0.18 0.22 0.23 0.30 0.21 Model evaluation of real species Since ensemble modeling performed well in predicting virtual species, it was employed to predict the potential distribution ranges of the 11 plant species and grassland (Fig. 6 ). The most significant factor affecting model performance is the sample sizes of occurrences. A large sample size of species is usually difficult to collect in mountainous areas, particularly when the target species is rare or endangered species. If the number of occurrences is fewer than 50 records, all occurrences of the species were used for ensemble modeling predictions. For some species, the number of occurrences is more than 50 records, and 50 sample points randomly selected from the occurrences were used for ensemble modeling predictions. Ensemble modeling successfully and reasonably projected potential distribution ranges of the 11 plant species and grassland (Fig. 6 ). A small sample size had a significantly effect on the potential distribution ranges of real species. The sample sizes of L. speciosum and M. taiwanensis are relatively small; they have 9 and 14 records of occurrences, respectively. However, the two species have dramatically different patterns of potential distribution ranges. A small sample size with a widely distribution range, such as L. speciosum , resulted in larger potential geographical ranges. On the contrary, occurrences and potential distribution ranges of M. taiwanensis are constrained within a small geographical range in the study area. Sample size is not the only factor that has an impact on the potential distribution ranges of species; geographical distances among occurrence points also have effects on the potential distribution range. Range shifts of virtual and real species under future climate change Virtual species with distinct contemporary distribution ranges markedly presented range shifts, restrictions, or expansions under climate change (Supplement 6). Virtual species distributed on the windward slope, mountain ridges, or coastal areas exhibited range shifts in the mid-century and range restrictions by the end of the century (Supplement 6.1, 6.2 and 6.3), particularly under SSP585 scenario of climate models. On the contrary, virtual species distributed in inland areas and on leeward slopes near inland areas exhibited range expansion in the mid and end of this century (Supplement 6.4 and 6.5). Ensemble modeling has also shown that the consequences of climate change may lead to different possible outcomes of the 11 plant species and grassland (Supplement 7). The predicted results of ensemble modeling demonstrate that climate change could lead to the local extinction of some rare species, such as M. taiwanensis (Supplement 7.8), R. nakaharai (Supplement 7.9), and R. pseudochrysanthum (Supplement 7.10). Surprisingly, rare species do not always exhibit range restriction or local extinction under climate change, as seen with L. speciosum , which is predicted to have range expansion in the mid and end of this century (Supplement 7.7). Several plant species exhibit range shifts in the mid and end of this century, including B. sinensis (Supplement 7.2), D. conjugata (Supplement 7.3), S. tristyla (Supplement 7.11), S. lepifera (Supplement 7.12). On the other hand, B. japonica (Supplement 7.1) and F. fistulosa (Supplement 7.5) exhibit range expansions in the mid and end of this century. The remaining species, E. japonica (Supplement 7.4), and grassland (Supplement 7.6) exhibited range restriction or local extinction based on different climate models. Discussion Simulation of virtual species The simulation of virtual species was suggested to test any new method in SDM studies before applying it to real data (Austin 2007 ; Austin et al. 2006 ). In previous studies, the simulation of virtual species had been used to assess the influence of environmental structures on SDM performances, data aggregation strategies, and resolution and scales (Hirzel et al. 2001; Meynard et al. 2019 ; Qiao et al. 2019 ). In this study, virtual species were simulated in a mountainous area to test the heterogeneity of climate datasets, characteristics of algorithms, effects of sample sizes, and range shifts and/or local extinctions under climate change. Heterogeneity of climate dataset The WorldClim dataset (Fick & Hijmans 2017 ) is a widely used for SDM studies. Despite the global coverage of WorldClim, there are still some uncertainties in the environmental data due to spatial interpolation in mountainous areas and in regions with few observation stations (Fick & Hijmans 2017 ). The variable from WorldClim had been downscaled to finer resolutions for SDM studies, but this may only retain the information from the original data source without increasing the spatial resolution of the variables (Peterson et al. 2011 ; Sillero & Barbosa 2021 ). In this study, high-resolution historical and future climate datasets were generated by using the proposed statistical method (Liao et al. 2023 ). The high-resolution climate datasets included horizontal variations of climate features due to the interpolation of meteorological data, while calculations of lapse rates to adjust climate data of gridded cells encompassed climate variations along elevation. The high-resolution climate dataset generated in this study evidently reflected the topographical and altitudinal variations of climate environments in mountainous areas. The simulation of virtual species successfully validated the heterogeneous climate environments in the study area. The high-resolution climate dataset is appropriate for addressing issues related to SDM studies. The spatial resolution of future climate datasets derived from GCMs was 5 × 5 km 2 , which is not accurate enough to capture the heterogeneous climate environments in mountainous areas. This study applied the statistical method developed by Liao et al. ( 2023 ) to downscale future climate datasets from 5 GCMs to a finer resolution. The downscaled future climate datasets, with a spatial resolution of 50 × 50 m 2 , are evidently reliable for predicting the future distribution ranges of the virtual species. This statistical method can confidently generate high-resolution historical and future climate datasets in other mountainous areas. Performances and characteristics of algorithms A virtual species approach can be used to explore the predictive accuracy of algorithms. The TSS and AUC, evaluated by split-sample validation, are commonly used to assess model accuracy. However, the estimated discrimination capacity of TSS and AUC was not available to reflect the actual predictive ability of SDMs. TSS and AUC tend to be over-optimistic compared to the real model performance, when predicted under current conditions and especially when projected to future conditions (Santini et al. 2021 ). In this study, the TSS and AUC of 11 algorithms were mostly close to or higher than 0.8, except when the sample size was 5 (Fig. 3 and Supplement 3). High values of TSS and AUC do not guarantee accurate predictions of species’ potential ranges. Practically, the TSS and AUC only slightly varied across algorithms in our analyses and were not appropriate for presenting model performances. This study suggests using the ESP value to assess model performance in SDM studies. The ESP, used as an index, clearly presented the predictive power of algorithms and is much better than TSS and AUC. Although the ESP is a good indicator of model performances, the ESP was significantly affected by a small sample size. In our analyses, five sample points are evidently the limitation of the model predictions, since the ESP value is consistently lower than 0.45 for all of the algorithms. Meanwhile, the ratios of false presence and false absence were particularly high when the sample size was 5. That is, a small sample size significantly resulted in low accuracy in algorithm performance. Future distribution range of species Our analysis revealed that climate change had distinct effects on climate environments in different areas and consequently caused different responses in the five virtual species. Climate environments in coastal areas are projected to shift to higher temperatures and lower precipitation by the middle or end of this century according to climate systems. The climate environments shifted in coastal areas will be similar to the current climate environments in inland areas. The virtual species currently distributed in inland area or on leeward slopes of the study area will expand or shift their distribution ranges toward coastal areas under climate change. Meanwhile, the virtual species currently distributed in coastal areas or on mountain ridges undergo range restriction or local extinction because they have almost no chance to track their suitable ranges in the study area under climate change. Therefore, the distinct responses of various virtual species under climate change evidently relate to their climatic demands. Different responses of virtual species under climate change provide a baseline for studying the fates of plant species. Many of our study species were under threat of local extinction, such as B. japonica , B. sinensis , E. japonica , M. taiwanensis , R. nakaharai , and R. pseudochrysanthum . The suitable ranges of these six species were at coastal areas or on windward slopes near mountain ridges. Some species, such as D. conjugata , Grassland, S. tristyla , S. lepifera undergo range restrictions by the middle or end of this century. The suitable range of grassland is widely distributed along mountain ridges, while the three species are widely distributed from leeward to windward slopes. Only two species will expand their distribution ranges under climate change: F. fistulosa , and L. speciosum . It is reasonable that the species F. fistulosa will expand its suitable range under climate change because it is widely distributed in the study area. However, it is surprising that L. speciosum will expand its suitable range under climate change. L. speciosum was once widely distributed in the lowlands of northern Taiwan, but the species had suffered from extensive collections for trade or cultivation since the last century. The population size of the species has greatly diminished in northern Taiwan, and only a few remnant individuals are currently scattered throughout the study area. Due to human influences, the present distribution of L. speciosum is mostly absent from the environmentally suitable areas and only occupies only a portion of its fundamental niche in the study area. It is evident that the signal of the absence caused by artificial factors will be found in the distribution of presence records and projected by the algorithms (Elith et al. 2011 ). In addition, the future range expansion of L. speciosum by the middle or end of this century indicates that if a rare or endangered species is not threatened by climate but by artificial factors, it may not go extinct under climate change. Niche study Recently, numerous studies have been proposed to correlate species occurrence data with important environmental dimensions, and researchers have developed algorithms to estimate ecological niches and explore potential distribution ranges (Peterson et al. 2011 ). In the virtualspecies package of R programming, users generate virtual species by defining suitability from a PCA to analyze ecological niches in both multivariate environmental and geographical spaces, effectively linking views of niche and distribution (Leroy et al. 2016 ; Qiao et al. 2016 ). This study focused on the niche from the climatic perspective to explain the geographical distribution and ecological characteristics of species. Our study can confidently define the fundamental niche of virtual species at the landscape scale and can be used to link climate demands and geographical distribution of species in mountainous areas. Conclusion This study demonstrates that virtual species study is a powerful tool for validating the heterogeneity of high-resolution climate datasets, evaluating the characteristic of algorithms, and providing baseline for assessing predicted potential distribution ranges and future range shifts of real species in mountainous area. (1) Using a real landscape to study virtual species has the advantage of correlating explanatory environmental variables with geographical distributions. In this study, the high-resolution climate dataset generated from meteorological data effectively reflected climate features in the mountainous area. This dataset is available for PCA to define fundamental niches of virtual species and correlate their geographical distribution ranges. (2) Virtual species simulated in PCA aim to evaluate performances of algorithms, with ensemble modeling performing better than the other 11 algorithms. Ensemble modeling effectively captures the processes linking climate demand and geographical distribution of virtual species and has practically predicted the potential range of rare or endangered species. (3) Algorithm performances were evaluated using the ESP. The ESP value calculates the degree of overlap between suitable ranges of virtual species simulated by PCA and their potential ranges predicted by algorithms. Therefore, the ESP, associated with false presence and false absence, is a better index than TSS and AUC. (4) In this study, rare or endangered species scattered or biasedly distributed in mountainous areas empirically caused either wide or narrow potential geographical ranges. Under these circumstances, virtual species study provides a baseline for assessing predicted contemporary and future distribution ranges of real species. (5) Rare or endangered species predicted by ensemble modeling based on high-resolution climate datasets can be confidently applied for designing conservation areas and management strategies in mountainous areas. (6) Our study can inform the applications of species distribution models to provide scientific support for conservation planning in mountainous areas and forecasts of species distributions under climate change. Declarations Author Contribution C.C. Liao conceived and designed the research method, data collection, conducted the analyses and wrote the manuscript. Y. H. Chen collected some data and some significant ideas for improving the quality of this manuscript. H. Y. Lin contributed some significant inputs to improve analytical methods, particularly the method of downscaling high-resolution historical and future climate datasets. Acknowledgement The authors would like to thank Mr. Shi-Chieh Kuo and several students from the Department of Life Science at Chinese Culture University, Taipei, Taiwan for their assistance in data collection. Particularly, Ms. Weng, Yu-Ting and Zhang, Qiao-Zhu gave the greatest help in the field works. The authors are grateful to Mr. Kai-Jie Yang from the Institute of Geography at Chinese Culture University, Taipei, Taiwan for providing technical supports for ArcGIS software. This work was partially supported by Yangmingshan National Park, Construction and Planning Agency, Ministry of the Interior, Executive Yuan, Taipei, Taiwan. Professor Hung-Yang Tseng from the Department of Atmospheric Sciences at Chinese Culture University assisted in coordinating with the Taiwan Climate Change Projection Information and Adaptation Knowledge Platform (TCCIP) to obtain climate model data. We would like to express our gratitude for his assistance. The authors also express their gratitude to TCCIP for providing gridded datasets on the magnitude of temperature and precipitation changes predicted by climate models for the 21st century. References Ali F., Khan N., Khan A.M., Ali K. and Abbas F. 2023. Species distribution modelling of Monotheca buxifolia (Falc.) A. 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Supplementary Files Sup1PCAandRange.pdf Sup2PCAOLRUESP.pdf Sup3BoxplotofTSSandAUC.pdf Sup4VspProjectionRange.pdf Sup5Importancevalue.pdf Sup6.1PCACFutureRange.pdf Sup6.2PCAOFutureRange.pdf Sup6.3PCALFutureRange.pdf Sup6.4PCARFutureRange.pdf Sup6.5PCAUFutureRange.pdf Sup7.01Benjap5GCMs.pdf Sup7.02Bresin5GCMs.pdf Sup7.03Dipcorn5GCMs.pdf Sup7.04Eusjap5GCMs.pdf Sup7.05Ficfis5GCMs.pdf Sup7.06Grsprs5GCMs.pdf Sup7.07Lilspe5GCMs.pdf Sup7.08Maatai5GCMs.pdf Sup7.09Rhonak5GCMs.pdf Sup7.10Rhopse5GCMs.pdf Sup7.11Sautri5GCMs.pdf Sup7.12Sphlep5GCMs.pdf Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-4443811","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":308267620,"identity":"9bc1e21c-0805-496b-ab36-98081decfafc","order_by":0,"name":"Chi-Cheng LIAO","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA5UlEQVRIiWNgGAWjYBACAziLnfkAA2MDcVqg6pjZEpC0JBClhceAOC3mErnHH3zcw5C44TDPN4mfO2zkGNgPH93A+OMwTi2WM/ISG2c8A2nh3SbZeybNmIEnLe0GQwJuLQY3cgybeQ5AtEjwth1ObJDgMQNquY1fyx+wFp5nkn+J1sIA0cImTZwtZ94Yzuw5wGA88zCbsbVsW5oxG8gvCWn/cWs5nmPw4ccBBtm+480Pb75ts5HjZz987MYHmzScWqDgv+OCAwwsEiAmG4hIIKQBCOzlGxiYPxChcBSMglEwCkYgAACRd1r2e96ITAAAAABJRU5ErkJggg==","orcid":"","institution":"Chinese Culture University","correspondingAuthor":true,"prefix":"","firstName":"Chi-Cheng","middleName":"","lastName":"LIAO","suffix":""},{"id":308267621,"identity":"6349e08b-37af-4d52-bded-31cc298560c7","order_by":1,"name":"Yi-Huey CHEN","email":"","orcid":"","institution":"Chinese Culture University","correspondingAuthor":false,"prefix":"","firstName":"Yi-Huey","middleName":"","lastName":"CHEN","suffix":""},{"id":308267622,"identity":"0e5f1e93-12b7-4c12-90ed-5cb19b3e0b5d","order_by":2,"name":"Huan-Yu LIN","email":"","orcid":"","institution":"National Ilan University","correspondingAuthor":false,"prefix":"","firstName":"Huan-Yu","middleName":"","lastName":"LIN","suffix":""}],"badges":[],"createdAt":"2024-05-19 09:53:27","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4443811/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4443811/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":57640080,"identity":"69fc0089-38a4-44f0-a04d-a22bd85d74e4","added_by":"auto","created_at":"2024-06-03 17:03:00","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":730908,"visible":true,"origin":"","legend":"\u003cp\u003eThe fundamental niche of the virtual species (left diagram) generated from the principal components analysis (PCA) and its geographical distribution range in northern Taiwan (right maps). The virtual species was generated using the ‘generateSpFromPCA’ function from the R package. By using this function, gridded cells with climate environments of the study area were quantified using PCA. Subsequently, suitable environments for the virtual species were displayed in the PCA diagram by determining two parameters in the function, means and standard deviation (SDs), showing a color gradient ranging from purple (high suitability) to yellow (low suitability) and grey (unsuitability). \u0026nbsp;The resulting geographic distribution range of the virtual species were shown in right map (white area with dark outline). The right maps also present the study area in northern Taiwan, the geographic locations of Taiwan, and neighboring countries.\u003c/p\u003e","description":"","filename":"floatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-4443811/v1/54f0e7f67add5ceb44f288a7.png"},{"id":57640084,"identity":"d1ace893-f8d1-4711-bee9-7c93b5265ab8","added_by":"auto","created_at":"2024-06-03 17:03:01","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":28719,"visible":true,"origin":"","legend":"\u003cp\u003eThe boxplot shows the index of the expected fraction of shared presence (ESP, grey box), false presence (cyan box), and false absence (pink box). The ESP was calculated by the degree of overlap between the suitable ranges of the virtual species at center of principal components analysis (PCA) diagram and the potential ranges predicted by 11 algorithms. A relatively high ESP value indicates better performance of the algorithms. False presence (commission error) and false absence (omission error) represent prediction errors of the 11 algorithms. The colored points in the boxplots represent the sample sizes used for predictions by the algorithms. The sample sizes are 5, 20, 50, 100, and 200 random points of occurrences, represented by green, blue, orange, red, and black colors, r Their interquartile range are shown by boxes and with whiskers for their full range.espectively. Their interquartile ranges are shown by boxes, with whiskers indicating their full range.\u003c/p\u003e","description":"","filename":"Onlinefloatimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-4443811/v1/1209f46648e8ae9e7f88562d.png"},{"id":57640423,"identity":"bd385882-b54d-4799-8c95-0ebf89e0d202","added_by":"auto","created_at":"2024-06-03 17:11:01","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":70313,"visible":true,"origin":"","legend":"\u003cp\u003eBoxplots show the values of two error indices, TSS and AUC, used to assess predictive performances of 11 algorithms. The 11 algorithms predicted potential ranges of the virtual species at the center of the principal components analysis (PCA) diagram. The colored points in the two boxplots represent sample sizes used for model predictions. The sample sizes are 5, 20, 50, 100, and 200 random points of occurrences, represented by red, blue, purple, yellow, and green colors, respectively.\u003c/p\u003e","description":"","filename":"floatimage3.png","url":"https://assets-eu.researchsquare.com/files/rs-4443811/v1/6f7077282ec4c49be743a141.png"},{"id":57640090,"identity":"ae5cbb45-b485-44b6-987c-9f9a59f7e160","added_by":"auto","created_at":"2024-06-03 17:03:01","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":2135533,"visible":true,"origin":"","legend":"\u003cp\u003eMaps show the geographical distribution ranges of virtual species (upper left map) generated from the principal components analysis (PCA) and the projected results by the ensemble modeling with different sample sizes of occurrences. \u0026nbsp;The virtual species is located at the center of the PCA diagram (Fig. 1). The gridded cells that were categorized by ensemble modeling as presence points are shown by colored points. The points with a color gradient from yellow to red represent the probability of presence. \u0026nbsp;Sample size had significant effects on the performance of ensemble modeling, while five sample points are evidently the limitation for the predictions of ensemble modeling.\u003c/p\u003e","description":"","filename":"floatimage4.png","url":"https://assets-eu.researchsquare.com/files/rs-4443811/v1/60564f23cd636404ac96ec0b.png"},{"id":57640424,"identity":"23b894ae-93ae-42b7-85c4-ef0f1c656686","added_by":"auto","created_at":"2024-06-03 17:11:01","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":35057,"visible":true,"origin":"","legend":"\u003cp\u003eBoxplots show index of expected fraction of shared presence (ESP, grey box), false presence (cyan box), and false absence (pink box). \u0026nbsp;The ESP value was calculated by degree of overlap between the suitable ranges of five virtual species generated from principal components analysis (PCA) and the potential ranges predicted by ensemble modeling. Relatively high ESP values indicate better performance of ensemble modeling. \u0026nbsp;The performance of ensemble modeling is better than that of the 11 algorithms (Fig. 2). The colored points in the boxplots represent the number of sample points used for predictions in ensemble modeling. The numbers of sample points are 5, 20, 50, 100, and 200 and the corresponding colors are green, blue, orange, red, and black, respectively. Their interquartile ranges are shown by boxes and their full ranges are depicted with whiskers.\u003c/p\u003e","description":"","filename":"floatimage5.png","url":"https://assets-eu.researchsquare.com/files/rs-4443811/v1/57e1c2e06ae0c78ef2c1819d.png"},{"id":57640098,"identity":"c01c7f34-2584-4a85-bc0f-1ae62644515c","added_by":"auto","created_at":"2024-06-03 17:03:02","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":162658,"visible":true,"origin":"","legend":"\u003cp\u003eThe maps show the occurrences of the 11 species and grassland in northern Taiwan (depicted as open dots) and their potential distribution ranges predicted by ensemble modeling. \u0026nbsp;The gridded cells categorized as presence are represented by colored points. \u0026nbsp;The points exhibit a color gradient from yellow to red, indicating the probability of presence.\u003c/p\u003e","description":"","filename":"Onlinefloatimage6.png","url":"https://assets-eu.researchsquare.com/files/rs-4443811/v1/1212529f1ab8f272699102d2.png"},{"id":57994121,"identity":"e51f4d85-88e9-415c-a12f-fd63c0de34fe","added_by":"auto","created_at":"2024-06-09 07:46:40","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":4115194,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4443811/v1/cd73728f-d4d4-4858-a34b-03699d2f1656.pdf"},{"id":57640095,"identity":"0e9fa3ef-651f-4df3-a792-3a2772b2daf6","added_by":"auto","created_at":"2024-06-03 17:03:02","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":1186040,"visible":true,"origin":"","legend":"","description":"","filename":"Sup1PCAandRange.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4443811/v1/78cf6a19d16d48489229d246.pdf"},{"id":57640422,"identity":"1e0c008b-7d84-4c84-a6e5-c2485c50b218","added_by":"auto","created_at":"2024-06-03 17:11:00","extension":"pdf","order_by":2,"title":"","display":"","copyAsset":false,"role":"supplement","size":697994,"visible":true,"origin":"","legend":"","description":"","filename":"Sup2PCAOLRUESP.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4443811/v1/8d79389ca05ddf95cbc698ac.pdf"},{"id":57640426,"identity":"b8170fbd-5e41-4749-a0cc-8e0896f70c89","added_by":"auto","created_at":"2024-06-03 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17:03:02","extension":"pdf","order_by":19,"title":"","display":"","copyAsset":false,"role":"supplement","size":6962821,"visible":true,"origin":"","legend":"","description":"","filename":"Sup7.09Rhonak5GCMs.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4443811/v1/081bf56465c1f0bf4743cb19.pdf"},{"id":57640099,"identity":"16d32cc5-4d86-4bd9-acb6-ed69f3c672db","added_by":"auto","created_at":"2024-06-03 17:03:02","extension":"pdf","order_by":20,"title":"","display":"","copyAsset":false,"role":"supplement","size":8432152,"visible":true,"origin":"","legend":"","description":"","filename":"Sup7.10Rhopse5GCMs.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4443811/v1/6ca65f51125d549000c30958.pdf"},{"id":57640102,"identity":"51f4cb3c-a1a0-4294-95ce-fc9f199c6666","added_by":"auto","created_at":"2024-06-03 17:03:02","extension":"pdf","order_by":21,"title":"","display":"","copyAsset":false,"role":"supplement","size":8892912,"visible":true,"origin":"","legend":"","description":"","filename":"Sup7.11Sautri5GCMs.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4443811/v1/6fe986387a0f7ea0f206b415.pdf"},{"id":57640106,"identity":"98b76f38-c84b-403f-b57f-b856b53423bf","added_by":"auto","created_at":"2024-06-03 17:03:03","extension":"pdf","order_by":22,"title":"","display":"","copyAsset":false,"role":"supplement","size":9753730,"visible":true,"origin":"","legend":"","description":"","filename":"Sup7.12Sphlep5GCMs.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4443811/v1/af6084d6a167f85ed484d138.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"A virtual species study to establish baseline for assessing the predicted current and future distribution ranges of real species in mountainous areas","fulltext":[{"header":"Introduction","content":"\u003cp\u003eSpecies distribution models (SDMs) are powerful tools for exploring the habitat characteristics associated with occurrence patterns of species (Chambers et al. \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2013\u003c/span\u003e; El-Gabbas \u0026amp; Dormann \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2018\u003c/span\u003e; Qazi et al. \u003cspan citationid=\"CR53\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Zimmer et al. \u003cspan citationid=\"CR64\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). SDMs correlate either presence-only or presence/absence data of species with relevant environmental variables and subsequently generate a geographical map indicating the potential distribution ranges of species (Peterson et al. \u003cspan citationid=\"CR50\" class=\"CitationRef\"\u003e2011\u003c/span\u003e). Accurate distribution ranges projected by SDMs are crucial for making informed assessments and are particularly important for improving conservation management of rare or endangered species (Guillera‐Arroita et al. 2015; Hama \u0026amp; Khwarahm \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; HamadAmin \u0026amp; Khwarahm \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Lannuzel et al. \u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; Zurell et al. \u003cspan citationid=\"CR65\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). Accuracy of SDMs largely depends on the sample size and unbiased sampling of spatial data (Bean et al. \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2012\u003c/span\u003e; El‐Gabbas \u0026amp; Dormann 2018; Elith et al. \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e2011\u003c/span\u003e; Guisan et al. \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e2007\u003c/span\u003e; Inman et al. \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; Kadmon et al. \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e2003\u003c/span\u003e). However, a large sample size and unbiased sampling of spatial data are great challenges for rare or endangered species (Laskey et al. \u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). Particularly in mountainous areas, complex topography, habitat fragmentation, as well as steep climate gradients along mountain slopes usually result in small populations and biased distribution of rare or endanger species. Small population size, fragmented or biased distribution of rare or endangered species are critical issues in model predictions (Lannuzel et al. \u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; Liao \u0026amp; Chen \u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e2021\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eSDMs are seldom applied in mountainous areas not only because of the sample size of species, but also because of the resolution of climate dataset. Global climate datasets with 30-arc resolution, such as WorldClim (Fick \u0026amp; Hijmans \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e2017\u003c/span\u003e) or Chelsa (Karger et al. \u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e2017\u003c/span\u003e), do not precisely reflect the heterogeneous climate environments in mountainous areas (Fick \u0026amp; Hijmans \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e2017\u003c/span\u003e), even when the climate dataset is downscaled to finer resolutions (Dobrowski \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2011\u003c/span\u003e; Pradervand et al. \u003cspan citationid=\"CR51\" class=\"CitationRef\"\u003e2014\u003c/span\u003e; Wang et al. \u003cspan citationid=\"CR61\" class=\"CitationRef\"\u003e2016\u003c/span\u003e). Recently, a statistical method to generate high resolution climate datasets in mountainous areas was developed to improve the performances of SDMs (Liao \u0026amp; Chen \u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; Liao et al. \u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). The high resolution climate dataset of Liao et al. (\u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e2023\u003c/span\u003e) precisely reflected the heterogeneous climate environments in mountainous areas, and SDMs accurately projected potential distribution ranges of grassland when using this climate dataset (Liao et al. \u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). However, this high resolution climate dataset has not been directly validated by modeling rare or endangered species, and it may not be optimal for predicting species distributions in mountainous areas, potentially limiting its application.\u003c/p\u003e \u003cp\u003eBefore being used in modeling studies, the high resolution climate dataset needed to be assessed. Virtual species are increasingly used in SDMs mostly because they allow the separation of the effects of individual features in complex models (De Marco \u0026amp; N\u0026oacute;brega \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e2018\u003c/span\u003e). In this study, virtual species were simulated to assess whether the high-resolution climate dataset had reflected the heterogeneity of climate environments in mountainous areas. A virtual species was generated by resembling real species to create a simulated ecological niche in an n-dimensional environmental space (Duan et al. \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2015\u003c/span\u003e; Hirzel et al. 2001; Leroy et al. \u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e2016\u003c/span\u003e; Qiao et al. \u003cspan citationid=\"CR55\" class=\"CitationRef\"\u003e2016\u003c/span\u003e). The high-resolution climate dataset generated by Liao et al. (\u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e2023\u003c/span\u003e) was used to simulate virtual species in the principal components analysis (PCA) by estimating the probability of each cell belonging to the climate niche (Leroy et al. \u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e2016\u003c/span\u003e). Subsequently, the gridded cells that were categorized as presence were mapped to show the suitable or geographical ranges in the study area. Different virtual species were simulated in different areas of the PCA diagram, and they were assumed to have distinct geographical distributions due to the heterogeneous climate environments in the study area.\u003c/p\u003e \u003cp\u003eSDMs were then employed to project the potential distribution ranges of the virtual species. Virtual species have become increasingly popular for testing SDMs because simulated virtual species offer known distribution ranges, which support a comprehensive understanding of species-environment relationships (De Marco \u0026amp; N\u0026oacute;brega \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e2018\u003c/span\u003e; Hirzel et al. 2001; Meynard \u0026amp; Kaplan \u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e2013\u003c/span\u003e). Virtual species can provide controlled, unbiased presence and absence data, which are unavailable to field ecologists (Hirzel et al. 2001; Meynard et al. \u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e2019\u003c/span\u003e). The \u0026ldquo;true\u0026rdquo; presence and absence data of virtual species are more appropriate for assessing model performance and overcoming the effects of biased samples of spatial points (Bombi \u0026amp; D\u0026rsquo;Amen \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e2012\u003c/span\u003e; Hirzel et al. 2001; Leroy et al. \u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e2016\u003c/span\u003e; Qiao et al. \u003cspan citationid=\"CR54\" class=\"CitationRef\"\u003e2019\u003c/span\u003e; Qiao et al. \u003cspan citationid=\"CR55\" class=\"CitationRef\"\u003e2016\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eIn addition to the predicting current distribution range, SDMs were also employed to project the future distribution range under future climate scenarios in this study. Climate change is a strong force that can cause shifts or expansion in species ranges and significantly increases the risk of extinction for rare or endangered species (Jiang et al. \u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Qazi et al. \u003cspan citationid=\"CR53\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Zurell et al. \u003cspan citationid=\"CR65\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). Rare or endangered species, which are characterized by small population sizes, are especially threatened by climate change (IUCN \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e2014\u003c/span\u003e). SDMs accurately predicting current distribution ranges and evaluating future range shifts are urgently necessary for the effective design of conservation strategies for rare or endangered species (Ali et al. \u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Jiang et al. \u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Ning et al. \u003cspan citationid=\"CR48\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; Wan et al. \u003cspan citationid=\"CR60\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; Zimmer et al. \u003cspan citationid=\"CR64\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Zurell et al. \u003cspan citationid=\"CR65\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). Therefore, future climate datasets are crucual for SDMs to assess the vulnerability of species to climate change (HamadAmin \u0026amp; Khwarahm \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Zurell et al. \u003cspan citationid=\"CR65\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). If the current climate dataset generated by Liao et al. (\u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e2023\u003c/span\u003e) accurately reflects climate heterogeneity in mountainous areas, it enables the generation of future climate datasets. The generation of future climate datasets was based on the methodology of Liao et al. (\u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e2023\u003c/span\u003e), which was applied for SDMs to project range shifts of both virtual and real species in the study area.\u003c/p\u003e \u003cp\u003eThis study aims to generate high-resolution current and future climate datasets in a mountainous area expected to adequately capture the heterogeneous climate characteristics both in the current state and in future climate changes. In this study, five virtual species were simulated to validate the heterogeneity of climate datasets. Several question were addressed. (1) The characteristics of the current climate dataset were hypothesized to influence the relationship between species response (presence) and environments (habitat suitability), referred to as the species-environment relationship. (2) Various virtual species, simulated using the high-resolution climate dataset to determine habitat suitability, were assumed to have distinct geographical distribution ranges in the mountainous area. (3) SDMs were conducted to explore the current and future distribution ranges of virtual species in a mountainous area, aimed to examine the extent of range expansion, restriction, shift or local extinctions under climate change. (4) Real species were then applied for algorithms to predict both the current potential range and future distribution ranges under climate change. These predictions aim to inform applications for conservation management.\u003c/p\u003e"},{"header":"Materials and Methods","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003eStudy area\u003c/h2\u003e \u003cp\u003eTaiwan is a subtropical island located at the western edge of the Pacific Ocean, with coordinates ranging from 21\u0026deg; 55\u0026rsquo; to 25\u0026deg; 20\u0026rsquo; N and 119\u0026deg; 30\u0026rsquo; to 122\u0026deg; 00\u0026rsquo; E (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e). The subtropical island is located 150 km off the southeast coast of Mainland China and is characterized by a monsoon climate (Chen \u0026amp; Tsai \u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e1983\u003c/span\u003e; Su \u003cspan citationid=\"CR58\" class=\"CitationRef\"\u003e1984\u003c/span\u003e). The northeast monsoon during winter and the southwest monsoon during summer influence the weather conditions of Taiwan Island. Particularly, the northeast monsoon during winter prevails in Taiwan for six months, bringing heavy rainfall and strong winds to the northern and eastern slopes of the Central Mountain Range.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eIn northern Taiwan (NTWN), a steep precipitation gradient extends from coast to inland areas that is significantly influencing the distribution of plant species (Liao \u0026amp; Chen \u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Liao et al. \u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). The annual precipitation decreased from more than 6,000 mm at the northeastern slope to 1,900 mm at the southwestern slope of the mountain ridge in NTWN (Liao et al. \u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). The mean monthly temperatures at the mountain ridge range from 11.3 ℃ in winter to 20.5 ℃ in summer, while those at the coastal area range from 17.9 ℃ in winter to 26.6 ℃ in summer (Liao \u0026amp; Chen \u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Liao et al. \u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e2023\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eThe study area in NTWN ranges from 24\u0026deg; 57\u0026rsquo; to 25\u0026deg; 17\u0026rsquo; N and 121\u0026deg; 24\u0026rsquo; to 122\u0026deg; 00\u0026rsquo; E (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e), covering an area of approximately 1,031 square kilometers (103,100 hectares). The highest mountain peak in the study area is Qixingshan, which stands at an elevation of 1,120 meters above sea level (asl.). The major vegetation type in NTWN is evergreen broad-leaved forest (Hsieh et al. \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e1997\u003c/span\u003e; Li et al. \u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e2013\u003c/span\u003e; Liao et al. \u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e2012\u003c/span\u003e). The forests in NTWN are dominated by species such as \u003cem\u003eCastanopsis\u003c/em\u003e, \u003cem\u003eCleyera\u003c/em\u003e, \u003cem\u003eCyclobalanopsis\u003c/em\u003e, \u003cem\u003eDendropanax\u003c/em\u003e, \u003cem\u003eElaeocarpus\u003c/em\u003e, \u003cem\u003eEngelhardia\u003c/em\u003e, \u003cem\u003eGordonia\u003c/em\u003e, \u003cem\u003eHelicia\u003c/em\u003e, \u003cem\u003eIlex\u003c/em\u003e, \u003cem\u003eKeteleeria\u003c/em\u003e, \u003cem\u003eLimlia\u003c/em\u003e, \u003cem\u003eLitsea\u003c/em\u003e, \u003cem\u003eMachilus\u003c/em\u003e, \u003cem\u003eMeliosma\u003c/em\u003e, \u003cem\u003eMichelia\u003c/em\u003e, \u003cem\u003ePinus\u003c/em\u003e, \u003cem\u003eSchefflera\u003c/em\u003e, \u003cem\u003eSymplocos\u003c/em\u003e, and \u003cem\u003eTrochodendron\u003c/em\u003e (Li et al. \u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e2013\u003c/span\u003e). The mean canopy height of these forests is approximately 15 meters. There is no deciduous forest in NTWN, while native deciduous tree species are scattered within the forests of the region. Natural grasslands are commonly found along the mountain ridges spanning from the coast to the inland regions within the NTWN, while the elevations of natural grassland vary across these ridges within the study area (Liao et al. \u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). The predominant species of natural grassland in these mountain areas are \u003cem\u003eMiscanthus sinensis\u003c/em\u003e and \u003cem\u003ePseudosasa usawai\u003c/em\u003e (Liao et al. \u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e2014\u003c/span\u003e; Liao et al. \u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). It is worth noting that the climatic niches of these two species are similar and may demonstrate convergence of climatic niches (Liao et al. \u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e2023\u003c/span\u003e).\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003eDownscaling of the current climate dataset\u003c/h2\u003e \u003cp\u003eIn this study, a gridded climate dataset with spatial resolution of 50 \u0026times; 50 m\u0026sup2; was created to present historical climate environments of the study area. This dataset was generated by utilizing daily meteorological data downloaded from the Central Weather Bureau\u0026rsquo;s website (CWB, \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://e-service.cwa.gov.tw/HistoryDataQuery/index.jsp\u003c/span\u003e\u003cspan address=\"https://e-service.cwa.gov.tw/HistoryDataQuery/index.jsp\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e). The 50 \u0026times; 50 m\u0026sup2; gridded climate dataset was adopted to accurately capture the heterogeneous climate environments along the mountain slopes. To construct this dataset, we downloaded daily meteorological data from CWB\u0026rsquo;s website. The detailed process of downscaling the historical climate dataset described in Liao et al. (\u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e2023\u003c/span\u003e) includes the following steps: (1) interpolation of the meteorological climate dataset to generate smooth climate variable surfaces; (2) creation of gridded cells, each with a spatial resolution of 50 \u0026times; 50 m\u0026sup2;, to extract data from the smooth climate variable surfaces; (3) altitudinal adjustment of the extracted climate data.\u003c/p\u003e \u003cp\u003eClimate data from 30 meteorological stations in and around the study area were downloaded from the CWB website. Mean monthly temperature and total monthly precipitation obtained from the 30 meteorological stations were imported into ArcInfo software (ESRI, Redlands, California, USA) to generate smooth surfaces of climate variables using the Kriging method, resulting in the generation of .tif files for the climate variables. Gridded cells with a spatial resolution of 50 \u0026times; 50 m\u0026sup2; were also created using ArcInfo software. A total of over 0.4\u0026nbsp;million gridded cells were generated within the study area. For each gridded cell, the longitude, latitude, and elevation data were extracted from a digital terrain model (DTM) developed by the Department of Geography, Chinese Culture University. The DTM had a resolution of 20 by 20 meters. The elevation data obtained from the DTM was named DElev. Subsequently, the 50 \u0026times; 50 m\u003csup\u003e2\u003c/sup\u003e gridded cells were mapped and overlapped with the .tif files of the meteorological climate surfaces to extract climate data. The meteorological climate dataset with a spatial resolution of 50 \u0026times; 50 m\u0026sup2; was named MCD50. Furthermore, the elevations of the meteorological stations were also interpolated using the Kriging method in ArcInfo software, resulting in the generation of a smooth elevation surface named MElev. The gridded cells of MCD50 were overlapped with MElev to extract the elevation data. The differences between DElev and MElev were calculated for the altitudinal adjustment of MCD50. The altitudinal adjustment function is: AdjMCD50\u0026thinsp;=\u0026thinsp;slope \u0026times; (DElev \u0026ndash; MElev)\u0026thinsp;+\u0026thinsp;MCD50. The abbreviation AdjMCD50 represents the altitudinally adjusted meteorological climate data with a spatial resolution of 50 \u0026times; 50 m\u0026sup2;. The slope of the function, also known as the empirical lapse rate, was calculated as the slope of the linear correlation between the elevation and climate data of the nearest 12 meteorological stations. The linear regression model was implemented using the \"stats\" package within the R environment (Chambers \u0026amp; Hastie 1992). The detailed methodology for generating the current climate dataset followed the study conducted by Liao et al. (\u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e2023\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eThe altitudinally adjusted climate data, AdjMCD50, was utilized as the historical climate dataset for modeling species distributions. The climate dataset was generated by considering the following nine variables: mean annual temperature (Tmean), mean maximum temperature of the warmest month (Twrm), mean minimum temperature of the coldest month (Tcld), mean temperature in summer (Tsmr) and winter (Twnt), temperature differences between warmest and coldest months (Tdif), annual total precipitation (Pann), total precipitation in summer (Psmr) and winter (Pwnt).\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003eDownscaling of future climate projections\u003c/h2\u003e \u003cp\u003eThe history of the Intergovernmental Panel on Climate Change\u0026rsquo;s (IPCC) assessment reports covers several generations of emissions scenarios (IPCC \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e2013\u003c/span\u003e, \u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Pedersen et al. \u003cspan citationid=\"CR49\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). Emission scenarios are generally developed to describe different socio-economic and policy choices, allowing for the assessment of different potential futures and their implications for the long-term climate systems (Kebede et al. \u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e2018\u003c/span\u003e). In 2022, the global Shared Socioeconomic Pathways (SSPs) were introduced in the Sixth Assessment Report (AR6) most recently published by the IPCC, integrating socioeconomic developments into future climate scenarios (IPCC \u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). There are five SSPs (SSP1 to SSP5), and these SSPs are used in conjunction with climate models to generate a range of possible future climate and environmental conditions based on different societal choices and policy directions (IPCC \u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Pedersen et al. \u003cspan citationid=\"CR49\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). Among the five pathways, SSP1 is the most optimistic scenario and emphasizes sustainable development, while SSP2 represents a middle pathway (Pu et al. \u003cspan citationid=\"CR52\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). SSP3 and SSP4 are the most undesirable pathway, assuming unsustainable development trends. SSP5 assumes an energy intensive, fossil-fuel-based economy, but also relatively optimistic development (Pu et al. \u003cspan citationid=\"CR52\" class=\"CitationRef\"\u003e2020\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eRegarding the future climate scenarios, the working group of Taiwan Climate Change Information and Adaptation Knowledge Platform (TCCIP) has generated 5 \u0026times; 5 km\u003csup\u003e2\u003c/sup\u003e gridded climate datasets to present future climate projections for the Taiwan island (Wang et al. \u003cspan citationid=\"CR62\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). The future climate projections fort the Taiwan island were downscaled from 49 General Circulation models (GCMs) during the 6th phase of the Coupled Model Intercomparison Project (CMIP6). Among the 49 available GCMs, five climate system models were used in this study: ACCESS-CM2 (Meucci et al. \u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e2023\u003c/span\u003e), FGOALS-g3 (Pu et al. \u003cspan citationid=\"CR52\" class=\"CitationRef\"\u003e2020\u003c/span\u003e), GFDL-ESM4 (Dunne et al. \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e2020\u003c/span\u003e), MIROC6 (Kataoka et al. \u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e2020\u003c/span\u003e), and TaiESM1 (Wang et al. \u003cspan citationid=\"CR62\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). The five GCMs were used to generate downscaled future climate datasets at 50 \u0026times; 50 m\u003csup\u003e2\u003c/sup\u003e resolution for the study area under different climate scenarios.\u003c/p\u003e \u003cp\u003eThe TCCIP published 5 \u0026times; 5 km\u003csup\u003e2\u003c/sup\u003e gridded climate datasets to present climate data from 1960 to 2100. Since the climate dataset of AdjMCD50 was at a spatial resolution of 50 \u0026times; 50 m\u003csup\u003e2\u003c/sup\u003e, the gridded climate dataset projecting future climate at 50 \u0026times; 50 m\u003csup\u003e2\u003c/sup\u003e was recalculated based on the relative changes observed in the TCCIP\u0026rsquo;s historical and future climate datasets. We selected three time periods of climate data from TCCIP\u0026rsquo;s climate datasets to present the climate datasets for the early (2000\u0026ndash;2020), mid (2045\u0026ndash;2055), and end (2091\u0026ndash;2100) of the 21th century. The TCCIP\u0026rsquo;s climate datasets for the three time periods were used to calculate the mean monthly temperature and total monthly precipitation. Subsequently, differences in monthly temperature and total monthly precipitation between the early and mid, as well as the early and end, of the 21th century were calculated to generate relative changes in climate data. The relative changes in temperature and precipitation were also represented as 5 \u0026times; 5 km\u003csup\u003e2\u003c/sup\u003e gridded data, which were used to generate .tif files of smooth climate surfaces using the Kriging method in ArcInfo software. The gridded cells with a spatial resolution of 50 \u0026times; 50 m\u003csup\u003e2\u003c/sup\u003e were overlapped with the .tif files of smooth climate surfaces to extract the relative changes in climate data. The historical climate datasets, AdjMCD50, were overlapped with the relative changes in 50 \u0026times; 50 m\u003csup\u003e2\u003c/sup\u003e gridded climate datasets to project future climates.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec6\" class=\"Section2\"\u003e \u003ch2\u003eSimulations of virtual species\u003c/h2\u003e \u003cp\u003eThe gridded cells with historical climate data (2000\u0026ndash;2020) were analyzed using principal components analysis (PCA). PCA was employed to diminish dimensionality and mitigate collinearity among environmental variables, enabling a clearer quantification of environmental overlap (Journ\u0026eacute; et al. \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e2020\u003c/span\u003e; Meynard et al. \u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e2019\u003c/span\u003e; Qiao et al. \u003cspan citationid=\"CR55\" class=\"CitationRef\"\u003e2016\u003c/span\u003e). Nine climate variables were initially included in the PCA. Notably, significant collinearity was observed among Pwnt and Pann, Tsmr and Twrm, and Twnt and Tcld. Thus, Pann, Twrm, and Tcld were excluded from the PCA. The remaining climate variables were Tmean, Tsmr, Twnt, Tdif, Psmr, and Pwnt. Retaining of the first two principal components (PC1 and PC2) explained a combined 84.1% of the overall variation.\u003c/p\u003e \u003cp\u003eTo create a range of spatial patterns in habitat suitability, the function \u0026ldquo;generateSpFromPCA\u0026rdquo; implemented by R package \u0026ldquo;virtualspecies\u0026rdquo; was employed to simulate virtual species (Leroy et al. \u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e2016\u003c/span\u003e). When using the function, the parameter nb.points was set to 5000. The other two parameters, means and sds, were configured to simulate five virtual species located in various regions of the PCA diagram, representing distinct niches and suitable environments of different virtual species. The performance of the function resulted in distinct geographical distribution patterns in the study area (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e and Supplement 1). The first virtual species was designed to be located at the center of the PCA diagram, resulting in a geographic distribution range covering the windward slopes near mountain ridge (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e). The other four virtual species were designed to be located at the lower, left, right, and upper sides of the PCA diagram (Supplement 1). The simulation of the five virtual species aims to ensure that they occupied different environments and that their geographical distribution ranges widely across the study area.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec7\" class=\"Section2\"\u003e \u003ch2\u003eInventory of real species\u003c/h2\u003e \u003cp\u003eIn this study, we selected eleven real plant species and grasslands for modeling analysis. Among them, five species are rarely observed in the study area: \u003cem\u003eMaackia taiwanensis\u003c/em\u003e, \u003cem\u003eBenthamidia japonica\u003c/em\u003e, \u003cem\u003eLilium speciosum\u003c/em\u003e, \u003cem\u003eRhododendron pseudochrysanthum\u003c/em\u003e, and \u003cem\u003eBretschneidera sinensis\u003c/em\u003e. Their rarity is attributed to their limited geographic range on this island, mainly confined to the mountainous regions of NTWN, wtih only a few occurrences of these species recorded in the fieldwork. The remaining seven species include four woody angiosperms: \u003cem\u003eRhododendron nakaharai\u003c/em\u003e, \u003cem\u003eEuscaphis japonica\u003c/em\u003e, \u003cem\u003eFicus fistulosa\u003c/em\u003e, \u003cem\u003eSaurauia tristyla\u003c/em\u003e var. \u003cem\u003eoldhamii\u003c/em\u003e, as well as two fern species, \u003cem\u003eDipteris conjugata\u003c/em\u003e and \u003cem\u003eSphaeropteris lepifera\u003c/em\u003e. Occurrences of these eleven plant species and grasslands were collected along the roads and mountain trails within the study area. Coordination of occurrences collected in the fieldwork were spatially verified to delete duplicated occurrence records.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec8\" class=\"Section2\"\u003e \u003ch2\u003eModelling technique\u003c/h2\u003e \u003cp\u003eIn this study, 11 algorithms were employed to predict the potential distribution ranges of virtual and real species in mountainous areas. The 11 algorithms include artificial neural network (ANN), classification tree analysis (CTA), flexible discriminant analysis (FDA), generalized additive model (GAM), generalized boosting model (GBM, or usually called boosted regression trees), general linear model (GLM), multiple adaptive regression splines (MARS), Maximum Entropy (MAXENT), random forest (RF), surface range envelop (SRE, or usually called BIOCLIM), and extreme gradient boosting training (XGBOOST). In addition, ensemble modeling, which includes 11 algorithms, was employed to predict virtual and real species in mountainous areas. The 11 algorithms and ensemble modeling were implemented using the \u0026ldquo;biomod2\u0026rdquo; package in R software (Thuiller et al. \u003cspan citationid=\"CR59\" class=\"CitationRef\"\u003e2016\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eFor each virtual species, occurrence and background points were integrated to generate a modeling dataset. The coordinates of the occurrences and background points were used to extract climate data from the climate surfaces. The occurrences were randomly sampled from the geographic distribution range of the virtual species, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e and Supplement 1. Various numbers of sample points were used in the model prediction to assess the impacts of sample size on the model performances. The numbers of sample points imported into the model predictions were 5, 20, 50, 100, and 200. The number of background points was 100 times the number of sample points randomly selected in the study area. When the sample and background points were used for the model predictions, a random set comprising 80% of the occurrence and background data was selected to train the model, and the remaining 20% was used for evaluation.\u003c/p\u003e \u003cdiv id=\"Sec9\" class=\"Section3\"\u003e \u003ch2\u003eModel performance\u003c/h2\u003e \u003cp\u003eTo assess accuracy of algorithms and ensemble modeling, the training dataset was resampled and modeled 10 times to quantify uncertainties in predictions. True skill statistics (TSS) and the area under receiver operating characteristic curve (AUC) were commonly used to assess the accuracy of species distribution models (Fois et al. \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e2015\u003c/span\u003e; Lannuzel et al. \u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; Qiao et al. \u003cspan citationid=\"CR54\" class=\"CitationRef\"\u003e2019\u003c/span\u003e; Xu et al. \u003cspan citationid=\"CR63\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). For creating the final ensemble models, only those models with a TSS score greater than 0.8 were used (Khan \u0026amp; Verma \u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e2022\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eNotably, a previous document proposed that the error indices, such as TSS and AUC, do not imply accuracy of suitability, since these indices provide a single-number discrimination measure across all possible ranges of thresholds (Lobo et al. \u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e2008\u003c/span\u003e). High values of TSS and AUC do not guarantee accurate model performance (Liao \u0026amp; Chen \u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). Thus, a similarity index called expected fraction of shared presences (ESP) was introduced to evaluate model performance in this study. The ESP was modified from the Sorenson similarity index to compare the similarity of potential ranges between two species (Godsoe \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e2014\u003c/span\u003e; Inman et al. \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). In this study, the ESP was revised to compare the suitable range of a virtual species simulated by PCA with its potential ranges predicted by 11 algorithms and ensemble modeling. The function of the ESP is:\u003cdiv id=\"Equa\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equa\" name=\"EquationSource\"\u003e\n$$\\text{E}\\text{S}\\text{P}=\\frac{{2{\\Sigma }}_{1}^{j}{P}_{s\\left(j\\right)}{P}_{p\\left(j\\right)}}{{{\\Sigma }}_{1}^{j}({P}_{s\\left(j\\right)}+ {P}_{p\\left(j\\right)})}$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere P\u003csub\u003e\u003cem\u003es(j)\u003c/em\u003e\u003c/sub\u003e denotes the presence of suitable range at a given cell \u003cem\u003ej\u003c/em\u003e, and P\u003csub\u003e\u003cem\u003ep(j)\u003c/em\u003e\u003c/sub\u003e denotes the presence of potential range at a given cell \u003cem\u003ej\u003c/em\u003e. Meanwhile, P\u003csub\u003e\u003cem\u003es(j)\u003c/em\u003e\u003c/sub\u003eP\u003csub\u003e\u003cem\u003ep(j)\u003c/em\u003e\u003c/sub\u003e denotes that a given cell \u003cem\u003ej\u003c/em\u003e is both presence of suitable range (P\u003csub\u003e\u003cem\u003es(j)\u003c/em\u003e\u003c/sub\u003e) and potential range (P\u003csub\u003e\u003cem\u003ep(j)\u003c/em\u003e\u003c/sub\u003e). An ESP value of 1 indicates perfect agreement between the suitable and potential ranges of a virtual species, while a value of 0 indicates complete geographic separation (Godsoe \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e2014\u003c/span\u003e; Inman et al. \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e2021\u003c/span\u003e).\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e"},{"header":"Results","content":"\u003cdiv id=\"Sec11\" class=\"Section2\"\u003e \u003ch2\u003eSuitable ranges of virtual species\u003c/h2\u003e \u003cp\u003eFive virtual species were simulated by selecting gridded cells from different regions in the PCA diagram, each representing distinct suitable ranges of the five virtual species in the study area. The gridded cells at the center of the PCA (PCAC) diagram represented a distribution range on windward slopes near mountain ridges in the study area (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e). The gridded cells at the lower (PCAO), left (PCAL), right (PCAR), and upper (PCAU) sides of the PCA diagram represented distribution ranges in the coastal area, mountain ridge, inland area, and leeward slopes near mountain ridge, respectively (Supplement 1). We generate 5 virtual species with distinct climatic niche in PCA diagram and the 5 virtual species evidently presented distinct geographical distribution ranges in the study area. It is evident that heterogeneous climate environments can provide diverse suitable habitats for the growth of species. By simulating the virtual species, the high-resolution gridded climate dataset generated from meteorological data was validated to reflect the climate heterogeneity of mountainous areas.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec12\" class=\"Section2\"\u003e \u003ch2\u003ePerformances of 11 algorithms\u003c/h2\u003e \u003cp\u003eThe potential distribution ranges of the five virtual species were predicted by 11 algorithms to evaluate their performances, aiming to select appropriate algorithms for predicting the potential distribution ranges of real species in mountainous area. Calculations of the ESPs were then used in this study to estimate the degree of overlap between suitable ranges of virtual species simulated in the PCA diagram and potential ranges predicted by the algorithms (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e). FDA, GBM, GLM, MARS, MAXENT, and SRE have relatively higher mean ESP values. Relatively higher mean ESP values demonstrated greater overlap between the simulated suitable ranges and the projected potential ranges, indicating better performances of these 6 algorithms.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eIn the virtual species approach, ESP associated with false presences and false absences can be used to detect algorithm characteristics. Lower ESP value indicates that the values of commission (false presence) and omission (false absence) errors are likely to be higher (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e). A high value of false presences and false absences indicates overestimation and underestimation of the potential ranges of virtual species, respectively. A small sample size uncovers the characteristics of various algorithms. When the number of sample points was 5, the predicted ranges of CTA, SRE and XGBOOST showed relatively lower values of false presence but very high values of false absences. CTA, SRE, and XGBOOST tend to have higher omission errors or underestimations of the species\u0026rsquo; potential ranges. On the contrary, the predicted ranges of GLM and MAXENT showed relatively high values of false presences and slightly lower values of false absences. GLM and MAXENT tend to have higher commission errors or overestimations of the species\u0026rsquo; potential ranges. Algorithms that either overestimated or underestimated potential ranges can serve as technological options to provide scientific support for designing conservation strategies.\u003c/p\u003e \u003cp\u003eThe potential ranges predicted by algorithms based on large sample size were highly overlapped with the simulated suitable ranges of virtual species. Our findings demonstrate that sample size is a significant factor affecting the model performances, particularly when the sample size is 5. Five sample points are evidently the limitation of model predictions, because the ESP values were consistently lower than 0.45 for all of the algorithms.\u003c/p\u003e \u003cp\u003eIn addition, the distinct geographical ranges of the five virtual species have, to some extent, affected the ESP values. The full range of ESP values is slightly narrower for the virtual species distributed at the coastal area (PCAO, the first diagram of Supplement 2). On the contrary, the full range of ESP values is slightly wider for the virtual species distributed at the leeward slopes near mountain ridge (PCAU, the lowest diagram of Supplement 2).\u003c/p\u003e \u003cp\u003eIn most of the previous studies, the TSS and AUC were calculated to assess predictive performance of algorithms. Higher TSS and AUC should indicate better model performance. However, high values of TSS and AUC did not guarantee better model performances in this study. When the ESP values were relatively higher, the TSS and AUC were not always higher and were somewhat contradictory to the ESP index. In addition, there is no specific trend in TSS and AUC values in this study (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e and Supplement 3). Conclusively, the TSS and AUC were not appropriate indices for representing the predictive performance of the algorithms.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThis study also employs virtual species distributions to evaluate the predictive power of ensemble modeling. Ensemble modeling accurately represented the potential geographical ranges of the five virtual species (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e and Supplement 4). Ensemble modeling performed better than the 11 algorithms, as the ESP values were mostly close to or higher than 0.8 when the sample points were greater than 5. Sample size and geographical distribution ranges have less effect on ensemble modeling. Even so, an extremely small sample size had robust effects on the projection results of ensemble modeling. When 5 sample points were applied for ensemble modeling, a low ESP value demonstrated poor model performance (Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e). Ensemble modeling performed well when number of sample points was higher than 20. A large sample size caused a precise overlap between the simulated suitable range and the predicted potential range of virtual species. Since ensemble modeling precisely projected potential distribution ranges of virtual species, it is a good model for predicting species\u0026rsquo; potential distribution ranges. All 5 virtual species can be accurately predicted by ensemble modeling, and this pattern does not depend on the ecological characteristics of the virtual species. Our results demonstrate that ensemble modeling produced reliable information on the potential ranges of species.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec13\" class=\"Section2\"\u003e \u003ch2\u003eImportance of predictors\u003c/h2\u003e \u003cp\u003eFor the 5 virtual species, the relative importance of predictors varied among algorithms, with temperature being evidently more important than precipitation (Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e and Supplement 4). The study area possesses complex topography and elevation gradients that certainly affected species distributions. Temperature is highly correlated with elevation gradient. Therefore, temperature is certainly important in predicting virtual species. On the other hand, precipitation significantly differs between windward and leeward slopes in the study area. There are two species, \u003cem\u003eB. sinensis\u003c/em\u003e and \u003cem\u003eB. japonica\u003c/em\u003e, mainly observed on the windward slopes, and the distributions of these two species were likely related to the high precipitation on the windward slope. However, the relationships between plant distribution and precipitation gradient in the study area were not significantly represented in the model predictions.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eThe importance values of predictors for 11 algorithms and ensemble modeling in predicting virtual species. The virtual species are located at the center of PCA diagram.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"13\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c10\" colnum=\"10\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c11\" colnum=\"11\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c12\" colnum=\"12\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c13\" colnum=\"13\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePredictors\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eANN\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eFDA\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eCTA\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eGAM\u003c/p\u003e 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\u003c/th\u003e \u003cth align=\"left\" colname=\"c11\"\u003e \u003cp\u003e0.06\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c12\"\u003e \u003cp\u003e0.16\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c13\"\u003e \u003cp\u003e0.05\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eTmean\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003e0.30\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e\u003cb\u003e0.31\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e\u003cb\u003e0.00\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003e0.18\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e\u003cb\u003e0.02\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e\u003cb\u003e0.15\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e\u003cb\u003e0.00\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e\u003cb\u003e0.10\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e\u003cb\u003e0.20\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c11\"\u003e \u003cp\u003e\u003cb\u003e0.21\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c12\"\u003e \u003cp\u003e\u003cb\u003e0.04\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c13\"\u003e \u003cp\u003e\u003cb\u003e0.14\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eTwnt\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003e0.16\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e\u003cb\u003e0.27\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e\u003cb\u003e0.33\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003e0.25\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e\u003cb\u003e0.23\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e\u003cb\u003e0.27\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e\u003cb\u003e0.25\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e\u003cb\u003e0.28\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e\u003cb\u003e0.18\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c11\"\u003e \u003cp\u003e\u003cb\u003e0.18\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c12\"\u003e \u003cp\u003e\u003cb\u003e0.26\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c13\"\u003e \u003cp\u003e\u003cb\u003e0.24\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eTsmr\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003e0.20\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e\u003cb\u003e0.32\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e\u003cb\u003e0.51\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003e0.24\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e\u003cb\u003e0.28\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e\u003cb\u003e0.50\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e\u003cb\u003e0.38\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e\u003cb\u003e0.35\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e\u003cb\u003e0.22\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c11\"\u003e \u003cp\u003e\u003cb\u003e0.26\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c12\"\u003e \u003cp\u003e\u003cb\u003e0.18\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c13\"\u003e \u003cp\u003e\u003cb\u003e0.31\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eTdif\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003e0.15\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e\u003cb\u003e0.09\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e\u003cb\u003e0.15\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003e0.21\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e\u003cb\u003e0.42\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e\u003cb\u003e0.05\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e\u003cb\u003e0.35\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e\u003cb\u003e0.18\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e\u003cb\u003e0.22\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c11\"\u003e \u003cp\u003e\u003cb\u003e0.23\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c12\"\u003e \u003cp\u003e\u003cb\u003e0.30\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c13\"\u003e \u003cp\u003e\u003cb\u003e0.21\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec14\" class=\"Section2\"\u003e \u003ch2\u003eModel evaluation of real species\u003c/h2\u003e \u003cp\u003eSince ensemble modeling performed well in predicting virtual species, it was employed to predict the potential distribution ranges of the 11 plant species and grassland (Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e). The most significant factor affecting model performance is the sample sizes of occurrences. A large sample size of species is usually difficult to collect in mountainous areas, particularly when the target species is rare or endangered species. If the number of occurrences is fewer than 50 records, all occurrences of the species were used for ensemble modeling predictions. For some species, the number of occurrences is more than 50 records, and 50 sample points randomly selected from the occurrences were used for ensemble modeling predictions. Ensemble modeling successfully and reasonably projected potential distribution ranges of the 11 plant species and grassland (Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eA small sample size had a significantly effect on the potential distribution ranges of real species. The sample sizes of \u003cem\u003eL. speciosum\u003c/em\u003e and \u003cem\u003eM. taiwanensis\u003c/em\u003e are relatively small; they have 9 and 14 records of occurrences, respectively. However, the two species have dramatically different patterns of potential distribution ranges. A small sample size with a widely distribution range, such as \u003cem\u003eL. speciosum\u003c/em\u003e, resulted in larger potential geographical ranges. On the contrary, occurrences and potential distribution ranges of \u003cem\u003eM. taiwanensis\u003c/em\u003e are constrained within a small geographical range in the study area. Sample size is not the only factor that has an impact on the potential distribution ranges of species; geographical distances among occurrence points also have effects on the potential distribution range.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec15\" class=\"Section2\"\u003e \u003ch2\u003eRange shifts of virtual and real species under future climate change\u003c/h2\u003e \u003cp\u003eVirtual species with distinct contemporary distribution ranges markedly presented range shifts, restrictions, or expansions under climate change (Supplement 6). Virtual species distributed on the windward slope, mountain ridges, or coastal areas exhibited range shifts in the mid-century and range restrictions by the end of the century (Supplement 6.1, 6.2 and 6.3), particularly under SSP585 scenario of climate models. On the contrary, virtual species distributed in inland areas and on leeward slopes near inland areas exhibited range expansion in the mid and end of this century (Supplement 6.4 and 6.5).\u003c/p\u003e \u003cp\u003eEnsemble modeling has also shown that the consequences of climate change may lead to different possible outcomes of the 11 plant species and grassland (Supplement 7). The predicted results of ensemble modeling demonstrate that climate change could lead to the local extinction of some rare species, such as \u003cem\u003eM. taiwanensis\u003c/em\u003e (Supplement 7.8), \u003cem\u003eR. nakaharai\u003c/em\u003e (Supplement 7.9), and \u003cem\u003eR. pseudochrysanthum\u003c/em\u003e (Supplement 7.10). Surprisingly, rare species do not always exhibit range restriction or local extinction under climate change, as seen with \u003cem\u003eL. speciosum\u003c/em\u003e, which is predicted to have range expansion in the mid and end of this century (Supplement 7.7). Several plant species exhibit range shifts in the mid and end of this century, including \u003cem\u003eB. sinensis\u003c/em\u003e (Supplement 7.2), \u003cem\u003eD. conjugata\u003c/em\u003e (Supplement 7.3), \u003cem\u003eS. tristyla\u003c/em\u003e (Supplement 7.11), \u003cem\u003eS. lepifera\u003c/em\u003e (Supplement 7.12). On the other hand, \u003cem\u003eB. japonica\u003c/em\u003e (Supplement 7.1) and \u003cem\u003eF. fistulosa\u003c/em\u003e (Supplement 7.5) exhibit range expansions in the mid and end of this century. The remaining species, \u003cem\u003eE. japonica\u003c/em\u003e (Supplement 7.4), and grassland (Supplement 7.6) exhibited range restriction or local extinction based on different climate models.\u003c/p\u003e \u003c/div\u003e"},{"header":"Discussion","content":"\u003cdiv id=\"Sec17\" class=\"Section2\"\u003e \u003ch2\u003eSimulation of virtual species\u003c/h2\u003e \u003cp\u003eThe simulation of virtual species was suggested to test any new method in SDM studies before applying it to real data (Austin \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2007\u003c/span\u003e; Austin et al. \u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e2006\u003c/span\u003e). In previous studies, the simulation of virtual species had been used to assess the influence of environmental structures on SDM performances, data aggregation strategies, and resolution and scales (Hirzel et al. 2001; Meynard et al. \u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e2019\u003c/span\u003e; Qiao et al. \u003cspan citationid=\"CR54\" class=\"CitationRef\"\u003e2019\u003c/span\u003e). In this study, virtual species were simulated in a mountainous area to test the heterogeneity of climate datasets, characteristics of algorithms, effects of sample sizes, and range shifts and/or local extinctions under climate change.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec18\" class=\"Section2\"\u003e \u003ch2\u003eHeterogeneity of climate dataset\u003c/h2\u003e \u003cp\u003eThe WorldClim dataset (Fick \u0026amp; Hijmans \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e2017\u003c/span\u003e) is a widely used for SDM studies. Despite the global coverage of WorldClim, there are still some uncertainties in the environmental data due to spatial interpolation in mountainous areas and in regions with few observation stations (Fick \u0026amp; Hijmans \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e2017\u003c/span\u003e). The variable from WorldClim had been downscaled to finer resolutions for SDM studies, but this may only retain the information from the original data source without increasing the spatial resolution of the variables (Peterson et al. \u003cspan citationid=\"CR50\" class=\"CitationRef\"\u003e2011\u003c/span\u003e; Sillero \u0026amp; Barbosa \u003cspan citationid=\"CR57\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). In this study, high-resolution historical and future climate datasets were generated by using the proposed statistical method (Liao et al. \u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). The high-resolution climate datasets included horizontal variations of climate features due to the interpolation of meteorological data, while calculations of lapse rates to adjust climate data of gridded cells encompassed climate variations along elevation. The high-resolution climate dataset generated in this study evidently reflected the topographical and altitudinal variations of climate environments in mountainous areas. The simulation of virtual species successfully validated the heterogeneous climate environments in the study area. The high-resolution climate dataset is appropriate for addressing issues related to SDM studies.\u003c/p\u003e \u003cp\u003eThe spatial resolution of future climate datasets derived from GCMs was 5 \u0026times; 5 km\u003csup\u003e2\u003c/sup\u003e, which is not accurate enough to capture the heterogeneous climate environments in mountainous areas. This study applied the statistical method developed by Liao et al. (\u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e2023\u003c/span\u003e) to downscale future climate datasets from 5 GCMs to a finer resolution. The downscaled future climate datasets, with a spatial resolution of 50 \u0026times; 50 m\u003csup\u003e2\u003c/sup\u003e, are evidently reliable for predicting the future distribution ranges of the virtual species. This statistical method can confidently generate high-resolution historical and future climate datasets in other mountainous areas.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec19\" class=\"Section2\"\u003e \u003ch2\u003ePerformances and characteristics of algorithms\u003c/h2\u003e \u003cp\u003eA virtual species approach can be used to explore the predictive accuracy of algorithms. The TSS and AUC, evaluated by split-sample validation, are commonly used to assess model accuracy. However, the estimated discrimination capacity of TSS and AUC was not available to reflect the actual predictive ability of SDMs. TSS and AUC tend to be over-optimistic compared to the real model performance, when predicted under current conditions and especially when projected to future conditions (Santini et al. \u003cspan citationid=\"CR56\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). In this study, the TSS and AUC of 11 algorithms were mostly close to or higher than 0.8, except when the sample size was 5 (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e and Supplement 3). High values of TSS and AUC do not guarantee accurate predictions of species\u0026rsquo; potential ranges. Practically, the TSS and AUC only slightly varied across algorithms in our analyses and were not appropriate for presenting model performances.\u003c/p\u003e \u003cp\u003eThis study suggests using the ESP value to assess model performance in SDM studies. The ESP, used as an index, clearly presented the predictive power of algorithms and is much better than TSS and AUC. Although the ESP is a good indicator of model performances, the ESP was significantly affected by a small sample size. In our analyses, five sample points are evidently the limitation of the model predictions, since the ESP value is consistently lower than 0.45 for all of the algorithms. Meanwhile, the ratios of false presence and false absence were particularly high when the sample size was 5. That is, a small sample size significantly resulted in low accuracy in algorithm performance.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec20\" class=\"Section2\"\u003e \u003ch2\u003eFuture distribution range of species\u003c/h2\u003e \u003cp\u003eOur analysis revealed that climate change had distinct effects on climate environments in different areas and consequently caused different responses in the five virtual species. Climate environments in coastal areas are projected to shift to higher temperatures and lower precipitation by the middle or end of this century according to climate systems. The climate environments shifted in coastal areas will be similar to the current climate environments in inland areas. The virtual species currently distributed in inland area or on leeward slopes of the study area will expand or shift their distribution ranges toward coastal areas under climate change. Meanwhile, the virtual species currently distributed in coastal areas or on mountain ridges undergo range restriction or local extinction because they have almost no chance to track their suitable ranges in the study area under climate change. Therefore, the distinct responses of various virtual species under climate change evidently relate to their climatic demands.\u003c/p\u003e \u003cp\u003eDifferent responses of virtual species under climate change provide a baseline for studying the fates of plant species. Many of our study species were under threat of local extinction, such as \u003cem\u003eB. japonica\u003c/em\u003e, \u003cem\u003eB. sinensis\u003c/em\u003e, \u003cem\u003eE. japonica\u003c/em\u003e, \u003cem\u003eM. taiwanensis\u003c/em\u003e, \u003cem\u003eR. nakaharai\u003c/em\u003e, and \u003cem\u003eR. pseudochrysanthum\u003c/em\u003e. The suitable ranges of these six species were at coastal areas or on windward slopes near mountain ridges. Some species, such as \u003cem\u003eD. conjugata\u003c/em\u003e, Grassland, \u003cem\u003eS. tristyla\u003c/em\u003e, \u003cem\u003eS. lepifera\u003c/em\u003e undergo range restrictions by the middle or end of this century. The suitable range of grassland is widely distributed along mountain ridges, while the three species are widely distributed from leeward to windward slopes. Only two species will expand their distribution ranges under climate change: \u003cem\u003eF. fistulosa\u003c/em\u003e, and \u003cem\u003eL. speciosum\u003c/em\u003e. It is reasonable that the species \u003cem\u003eF. fistulosa\u003c/em\u003e will expand its suitable range under climate change because it is widely distributed in the study area. However, it is surprising that \u003cem\u003eL. speciosum\u003c/em\u003e will expand its suitable range under climate change. \u003cem\u003eL. speciosum\u003c/em\u003e was once widely distributed in the lowlands of northern Taiwan, but the species had suffered from extensive collections for trade or cultivation since the last century. The population size of the species has greatly diminished in northern Taiwan, and only a few remnant individuals are currently scattered throughout the study area. Due to human influences, the present distribution of \u003cem\u003eL. speciosum\u003c/em\u003e is mostly absent from the environmentally suitable areas and only occupies only a portion of its fundamental niche in the study area. It is evident that the signal of the absence caused by artificial factors will be found in the distribution of presence records and projected by the algorithms (Elith et al. \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e2011\u003c/span\u003e). In addition, the future range expansion of \u003cem\u003eL. speciosum\u003c/em\u003e by the middle or end of this century indicates that if a rare or endangered species is not threatened by climate but by artificial factors, it may not go extinct under climate change.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec21\" class=\"Section2\"\u003e \u003ch2\u003eNiche study\u003c/h2\u003e \u003cp\u003eRecently, numerous studies have been proposed to correlate species occurrence data with important environmental dimensions, and researchers have developed algorithms to estimate ecological niches and explore potential distribution ranges (Peterson et al. \u003cspan citationid=\"CR50\" class=\"CitationRef\"\u003e2011\u003c/span\u003e). In the virtualspecies package of R programming, users generate virtual species by defining suitability from a PCA to analyze ecological niches in both multivariate environmental and geographical spaces, effectively linking views of niche and distribution (Leroy et al. \u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e2016\u003c/span\u003e; Qiao et al. \u003cspan citationid=\"CR55\" class=\"CitationRef\"\u003e2016\u003c/span\u003e). This study focused on the niche from the climatic perspective to explain the geographical distribution and ecological characteristics of species. Our study can confidently define the fundamental niche of virtual species at the landscape scale and can be used to link climate demands and geographical distribution of species in mountainous areas.\u003c/p\u003e \u003c/div\u003e"},{"header":"Conclusion","content":"\u003cp\u003eThis study demonstrates that virtual species study is a powerful tool for validating the heterogeneity of high-resolution climate datasets, evaluating the characteristic of algorithms, and providing baseline for assessing predicted potential distribution ranges and future range shifts of real species in mountainous area. (1) Using a real landscape to study virtual species has the advantage of correlating explanatory environmental variables with geographical distributions. In this study, the high-resolution climate dataset generated from meteorological data effectively reflected climate features in the mountainous area. This dataset is available for PCA to define fundamental niches of virtual species and correlate their geographical distribution ranges. (2) Virtual species simulated in PCA aim to evaluate performances of algorithms, with ensemble modeling performing better than the other 11 algorithms. Ensemble modeling effectively captures the processes linking climate demand and geographical distribution of virtual species and has practically predicted the potential range of rare or endangered species. (3) Algorithm performances were evaluated using the ESP. The ESP value calculates the degree of overlap between suitable ranges of virtual species simulated by PCA and their potential ranges predicted by algorithms. Therefore, the ESP, associated with false presence and false absence, is a better index than TSS and AUC. (4) In this study, rare or endangered species scattered or biasedly distributed in mountainous areas empirically caused either wide or narrow potential geographical ranges. Under these circumstances, virtual species study provides a baseline for assessing predicted contemporary and future distribution ranges of real species. (5) Rare or endangered species predicted by ensemble modeling based on high-resolution climate datasets can be confidently applied for designing conservation areas and management strategies in mountainous areas. (6) Our study can inform the applications of species distribution models to provide scientific support for conservation planning in mountainous areas and forecasts of species distributions under climate change.\u003c/p\u003e"},{"header":"Declarations","content":"\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eC.C. Liao conceived and designed the research method, data collection, conducted the analyses and wrote the manuscript. Y. H. Chen collected some data and some significant ideas for improving the quality of this manuscript. H. Y. Lin contributed some significant inputs to improve analytical methods, particularly the method of downscaling high-resolution historical and future climate datasets.\u003c/p\u003e\u003ch2\u003eAcknowledgement\u003c/h2\u003e\u003cp\u003eThe authors would like to thank Mr. Shi-Chieh Kuo and several students from the Department of Life Science at Chinese Culture University, Taipei, Taiwan for their assistance in data collection. Particularly, Ms. Weng, Yu-Ting and Zhang, Qiao-Zhu gave the greatest help in the field works. The authors are grateful to Mr. Kai-Jie Yang from the Institute of Geography at Chinese Culture University, Taipei, Taiwan for providing technical supports for ArcGIS software. This work was partially supported by Yangmingshan National Park, Construction and Planning Agency, Ministry of the Interior, Executive Yuan, Taipei, Taiwan. Professor Hung-Yang Tseng from the Department of Atmospheric Sciences at Chinese Culture University assisted in coordinating with the Taiwan Climate Change Projection Information and Adaptation Knowledge Platform (TCCIP) to obtain climate model data. We would like to express our gratitude for his assistance. The authors also express their gratitude to TCCIP for providing gridded datasets on the magnitude of temperature and precipitation changes predicted by climate models for the 21st century.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eAli F., Khan N., Khan A.M., Ali K. and Abbas F. 2023. Species distribution modelling of Monotheca buxifolia (Falc.) A. DC.: Present distribution and impacts of potential climate change. Heliyon 9.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eAustin M. 2007. Species distribution models and ecological theory: a critical assessment and some possible new approaches. 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Cambridge Prisms: Extinction 1: e8.\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"commission error, ensemble modeling, expected fraction of shared presences (ESP), omission error, species distribution model, Taiwan, virtual species","lastPublishedDoi":"10.21203/rs.3.rs-4443811/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4443811/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eSimulation and model prediction of virtual species aim to establish baseline for assessing the projected contemporary and future distribution ranges of real species in mountainous areas. Fundamental niches and geographic ranges of 5 virtual species were defined in the diagram of principal components analysis based on a high-resolution climate dataset generated from meteorological data. Heterogeneity of the climate dataset had been validated to influence the relationships between species responses and suitable environments, consequently affecting the geographical distributions of virtual species. The performances of 11 algorithms were evaluated by the extracted fraction of shared presences (ESP), instead of TSS and AUC. ESP calculates the overlap between simulated suitable ranges and predicted current potential ranges of virtual species. According to ESP, ensemble modeling outperformed the 11 algorithms. A small sample size has significant effects on model performance due to the extremely low value of ESP, and the presence of only 5 sample points was evidently a limitation of model predictions. Furthermore, geographical distance among sample points provide signals of niches that will be identified through accurate predictions of ensemble modeling in our analyses. By the 2050s and 2090s, climate change may drive the range expansion of real species currently distributed in inland areas or on leeward slopes, while causing range restriction or local extinction of real species in coastal areas or on windward slopes. Our study can inform application of species distribution models to provide scientific support for conservation planning in mountainous areas and forecasts of species distributions under climate change.\u003c/p\u003e","manuscriptTitle":"A virtual species study to establish baseline for assessing the predicted current and future distribution ranges of real species in mountainous areas","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-06-03 17:02:54","doi":"10.21203/rs.3.rs-4443811/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"d916bf6b-8902-4f39-acdd-73647475f9db","owner":[],"postedDate":"June 3rd, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2024-06-09T07:38:30+00:00","versionOfRecord":[],"versionCreatedAt":"2024-06-03 17:02:54","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-4443811","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-4443811","identity":"rs-4443811","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}