Sampling Amazonian forest with clusters to measure tree species diversity: dissociating the effect of cluster size and sample size

Sampling Amazonian forest with clusters to measure tree species diversity: dissociating the effect of cluster size and sample size | 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 Sampling Amazonian forest with clusters to measure tree species diversity: dissociating the effect of cluster size and sample size Angelo Augusto EBLING, Alexandre BEHLING, Edberto Moura LIMA, and 2 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7328739/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 A mature forest remnant in the Amazon was sampled with 22 0.4-ha clusters, which means a sampling effort of 8.8 ha. From this complete sample, nine subdatasets reduced in cluster size and other nine reduced in sample size were created, totaling thus 18 subdatasets. The aim of this study was to dissociate the effects of sample size and cluster size on Hill’s numbers. A cluster consisted of a sample unit composed by four crosswise sub-units of 1,000 m² (20m×50m) each. The 18 subdatasets were aggregated into nine pairs equivalent in sampled area (SA), which decreased from 8.8 ha (complete sample) to successive reductions from 4.4 ha (first pair of subdataset) to 0.8 ha (nineth pair). Hill’s numbers were calculated for every subdataset and then sample-based rarefaction curves were constructed to generate diversity profiles. As a result, species richness was abruptly underestimated in approx. 40% for the first reduction in sample size (SA = 4.4 ha). Significant underestimation of species richness occurred when the SA is below 2.4 ha, and accuracy of the other diversity profiles was severely compromised below 1.6 ha. We concluded that species richness is more sensitive to reductions in SA than Shannon diversity and Pielou’s evenness indices. For a same sampling effort, the choice in installing more small units demonstrated to better capturate the diversity profiles than installing less large units, especially when estimating species richness. Although the patterns of under or overestimates of the other diversity profiles were not exactly clear, the accuracy is substantially hampered when the SA is less than 1.6 ha. Rarefaction. Diversity profile. Sensitivity analysis. Sampling intensity. National forest inventory Figures Figure 1 Figure 2 Figure 3 Figure 4 INTRODUCTION The Amazon’s forests hold a relevant portion of the world’s species diversity (Myers et al., 2000 ). Considering trees only, research estimates the occurrence of ~ 16,000 species throughout the Amazon region; 227 of them are hyper-dominant species (Steege, 2013). The within-community species diversity is referred to as the diversity alpha (α), whereas that among communities concerns the diversity beta (β). Among the several indices of diversity, Shannon, Pielou, and Simpson are perhaps the most widely used to measure diversity α (Magurran, 2013 ; Pielou, 2014 ). Forest inventories are an important source of data for biodiversity purposes. In the classical book by Loetsch et al. ( 1973 ), forest inventories are classified either as the ‘census’ – a complete inventory that totally covers the forest, requiring that every single tree be sampled – or as the ‘sampling inventories’ – an incomplete inventory in which only a sub-sample of the forest is measured. The sampling designs applied to incomplete inventories take into account, overall, arrangement of the sample unit (SU) distribution along the forest, as well as shape, size, and number of SUs, in which these last two determine the sampling intensity (SI). The larger the size and number of SUs, the higher the SI. The variance along the forest increases proportionally to the number of SUs required in the sampling (Loetsch et al., 1973 ). Given that the Amazon’s forests are typically rich in tree species, it is intuitive to think that to accurately estimate tree species diversity, a larger SI would be required, thus requiring allocation of more and/or larger SUs along the sampled forest. Cochran ( 1977 ) argues that smaller SUs usually provide precise estimates; however, to measure diversity, this general rule may not be as efficient in highly variable environments (e.g., tropical forests) as in those more homogeneous ones (e.g., boreal forests) (Yang et al., 2017 ; Saarinen et al., 2018 ). Incomplete inventories are, in general, the most preferable because they offer a cheaper and faster estimate of the mean. The challenge in opting for incomplete inventories (i.e., prioritizing the cost reduction) is that cost and sampling error share an inverse relationship, so that, in theory, the lower the sampling error, the more SUs are needed (Cochran, 1977 ). National Forest Inventories (NFIs) are a type of incomplete, large-scale inventory, being also the main data source used in national-level estimates of biodiversity in various countries around the world (Chirici et al., 2012 ; Corona et al., 2011 ). The NFI SU is generally a cluster-shaped field plot split into smaller units called the sub-units (Lawrence et al., 2010 ). Among other reasons, the preference for clusters is that the variance among them is reduced, thus requiring a lesser amount of SUs in the sampling (Cochran, 1977 ). As NFIs are based on sub-samples, the use of their database for biodiversity purposes needs the construction of rarefaction curves (RCs), due to the sensitivity of species diversity to the sampling design and SI, i.e., size and number of SUs (Chao et al., 2016 ; Corona et al., 2011 ; Magnussen, 2011 ; Beck and Schwanghart, 2010 ). Most of the research on species diversity normally concerns the SI; however, little discussion is devoted to quantifying and dissociating its effect. By dissociating, we mean that for the same SI, it is possible to allocate more or fewer SUs by varying their size. For example, 100 SUs of 1,000 m² correspond to the same sampled area (i.e., SI) as 10 SUs of 10,000 m², but both cases differ by a factor of ten in the number of sampled spots. Corona et al. ( 2011 ) argue that more tree species would be observed when many small plots are sampled instead of few large plots. Corona et al.’s arguments make sense because of the presence of species mosaics that may fully encompass a large SU, meaning that a wider distribution of smaller SUs increases the coverage of the tree species along the forest. In addition, plant species generally have spatial distributions much more complex than a random pattern (Magnussen and Boyle, 1995 ). The question raised in this study was “how big is the effect of the size and number of clusters on the tree species diversity in an Amazonian forest?” This paper fills a gap in the current literature because NFIs have been increasingly used for diversity analysis, while the efficiency of NFI clusters has not been fairly assessed for this purpose. With data from clusters standardized as Brazil’s NFI, we aimed to dissociate the effect of cluster size from sample size on the floristic diversity in an Amazonian forest. MATERIAL AND METHODS Study area The research areas are situated in the Bom Futuro National Forest, state of Rondônia, Brazil (Fig. 1 ). This national forest is a protected area with sustainable use of natural resources (IUCN category VI), and it covers a total area of ~ 100 thousand hectares. The research was conducted on 83 thousand hectares of forest, which represents about 83% of the total area of the National Forest. The area is covered mainly by pristine sub-montane rainforests, with areas of Lowland Rainforests, Savannah, Alluvial Rainforest, and other Alluvial pioneer vegetation. The climate belongs to the tropical monsoon (Am), the most representative climate of the west of the Brazilian Amazonian region, with mean annual temperature around 25 ºC and mean annual precipitation around 2200 mm (Alvares, 2013). The local relief varies from flat to wavy and elevation is from 60–200 m above sea level. The parent material belongs to the Amazon craton, and it is composed of Precambrian granite and gneiss (Bettencourt, 1999 ). The most common soil types are alfisols, oxisols, ultisols, and alluvial soils Field measurements The forest in the study area was inventoried by following a two-stage sampling design with SUs structured as the Brazilian NFI guidance. In the first (systematic) stage, a regular grid with square cells measuring 0.625 x 0.625 km (~ 0.39 km²) was drawn over the forest to be inventoried. In the second (random) stage, we randomly selected 22 cells (7 in the pilot inventory plus 15 in the definitive one) to install one SU in the midpoint of each cell. The SU is a 4,000 m² cluster with four crosswise sub-units (1,000 m² each) that are divided into ten sub-plots of 100 m² (10 x 10 m), totaling 40 sub-plots by cluster. Further detail about the Brazilian NFI can be consulted in David et al. ( 2019 ). Figure 2 shows the NFI original cluster, as well as illustrations of the procedure we used to reduce the cluster size, which was necessary in our analysis (see next section). All trees with diameter at breast height (DBH) ≥ 10 cm were measured, and botanical material was collected and taken to a herbarium (at the Federal University of Rondônia) for species identification. Trees with broken crown or stem were also included in the data collection. We measured dead or living woody trees; therefore, palms and tree fern species were not the target of this study. Dissociating effects of the cluster size from the sample size From our original sample containing 22, 4,000 m² clusters, the analytical procedure consisted of creating nine subsets of samples successively reduced in sample sizes (from 22 to 2 clusters), plus nine sets with reductions in cluster size (from 2,000 m² to 400 m²). Our framework covered nine pairs of samples approximately equivalent in the sample area. The following sections describe the analytical procedure. Table 1 gives the main sampling information of the subsets of samples. Table 1 Subsets of samples representing variations in cluster and sample sizes. Pairing Subsets with sample size reduction Subsets with cluster size reduction* ∆ sampled area (ha) n Cluster size (m²) Sampled area (ha) n Cluster size (m²) Sampled area (ha) I 11 4,000 4.40 22 2,000 4.40 0.00 II 9 4,000 3.60 22 1,600 3.52 0.08 III 8 4,000 3.20 22 1,500 3.30 -0.10 IV 7 4,000 2.80 22 1,300 2.86 -0.06 V 6 4,000 2.40 22 1,100 2.42 -0.02 VI 5 4,000 2.00 22 900 1.98 0.02 VII 4 4,000 1.60 22 700 1.54 0.06 VIII 3 4,000 1.20 22 500 1.10 0.10 IX 2 4,000 0.80 22 400 0.88 -0.08 Total - - 22.00 - - 22.00 0.00 * refers to reductions from inner to outer and from outer to inner, as in Fig. 2 ; n : number of clusters. To dissociate the effect of cluster size from the sample size, we paired two subsets so that a framework with nine pairs was outlined, as shown in Table 1 . The pairing obeyed the following criteria. First, one subset was reduced in cluster size whereas its pair was reduced in sample size. Second, the paired subsets had equivalence in sampled area. For example, Row I in Table 1 describes the first pair of subsets, which has the equivalence of 4.4 ha of sampled area per subset. While outlining our framework, we noted that the equivalence in sampled area of subsets within a pair cannot be exact in all pairs, as indicated in ∆ of Table 1 . However, we ensured that the difference between sampled areas within a pair is at most ± 0.1 ha, and that the overall equivalence among the nine pairs is exact (i.e., overall ∆=0). Third, within a pair, the cluster size of a subset must be at least twice as big as the other subset. These three criteria ensured that a reasonable forest area is sampled in all subsets of sample, as well as that a subset has larger sample size and smaller cluster size than its paired subset but ensuring that both subsets can be compared in terms of sampling effort. Research such as Miguel et al. ( 2016 ) and Ferreira et al. ( 2010 ) have recommended a minimum sample area necessary for accurately estimating diversity profiles or index. However, the reader should consider that our focus lies more on comparing the reduced samples comprised in our framework than producing accurate diversity estimations. Cluster size variation. Figure 1 illustrates our procedure for cluster size variation, which consisted of reducing clusters of 2,000 m² (0.20 ha) by successively removing 100-m² sub-plots from the cluster subunits. In that case, the initial cluster size of 2,000 m², which is half of the original size of 4,000 m², had to be utilized for reaching the equivalence in sample area represented by ∆s shown in Table 1 . The procedure resulted in ten cluster sizes: 0.20 ha (first reduction), 0.16 ha (second reduction), 0.15 ha (third), 0.13 ha (fourth), 0.11 ha (fifth), 0.09 ha (sixth), 0.07 ha (seventh), 0.05 ha (eighth), and 0.04 ha (ninth reduction). In addition, we considered two directions for reducing the cluster size: from outer to inner (Fig. 1 b) and from inner to outer (Fig. 1 c). Note in Fig. 1 that these directions generate longer or shorter distances between the subunits’ midpoint, with the shorter distances produced by the ‘outer to inner’ reduction, and the longer ones by the ‘inner to outer’ reduction. The idea with applying two directions is to investigate whether the distance between sub-plots affects the species diversity. Sample size variation. From our original dataset with 22 clusters, the number of clusters (sample size) was successively reduced from 11 clusters (first reduction), next to nine (second), to eight (third), and so on, until the ninth reduction comprising two clusters (Table 1 ). The lower number of two clusters was set by a matter of sampling sufficiency. For each sample size required, clusters were randomly selected with replacement from the original dataset through a bootstrap approach with 1,000 replications. This procedure originated nine thousand bootstrap samples and was necessary because there are several combinations for selecting ≤ 11 clusters out of 22. The bootstrap approach then plays the role of mitigating biases while selecting clusters in only one random sample. Accounting plant Diversity For every tree species observed through the field collection, plant families were classified according to Angiosperm Phylogeny Group IV (APG IV 2016) and species nomenclature was based on the 2016 Species List of Brazil’s Flora ( http://floradobrasil.jbrj.gov.br/ ). We calculated Hill’s numbers [Eq. 1] for the 18 (nine pairs) subsets of clusters presented in Table 1 . We assumed that the subsets are free of autocorrelation due to the shortest distance between the clusters being greater than 4 km. For the subsets within a pair, we assembled a matrix containing abundance data. Next, we applied Hill’s series to the abundance matrix and compared the plant diversity through diversity profiles. The diversity profiles were graphically presented in nine plots (one by pair, Table 1 ) illustrating curves for the (i) sample size variation and for the ‘inner to outer’ (ii) and ‘outer to inner’ (iii) reductions of the cluster size. A fourth curve based on the full sample containing 22, 4,000 m² clusters was added to the plots. These curves will be helpful to better visualize differences in diversity profiles among the full and reduced samples. All analyses were run in the R environment, version 4.0.2, using vegan (Oksanen et al., 2016 ) and BiodiversityR packages. We used a 5% significance level in all cases. \(\:{}^{q}D={\left(\sum\:_{i=1}^{S}{p}_{i}^{q}\right)}^{1/(1-q)}\text{f}\text{o}\text{r}\:q\ne\:1\) [1] $$\:{}^{q}D=\left(\sum\:_{i=1}^{S}{p}_{i}^{q}\right)\text{f}\text{o}\text{r}\:q=1$$ where, \(\:S\) : number of species in the assemblage; \(\:{p}_{i}\) : relative abundance; \(\:q\) : parameter that determines the sensitivity of the measure to the relative frequencies. When \(\:q=0\) results in species richness, \(\:q=1\) in Shannon’s index, \(\:q=2\) in Pielou’s index. RESULTS The complete (original) sample (22 4,000 m² clusters) included 4,386 trees, from which 188 tree species, 145 genera, and 33 families were identified. Figure 3 shows the Hill’s numbers for the nine pairings presented in Table 1 . The richness estimated from the full sample was 188 species, the Shannon index was H^' = 4.257 [= log(70.6)], and the Simpson index was 0.031 [= 1/32.3]. Recall that species richness equals the Hill’s numbers when q = 0 in Eq. (1), and the Shannon and Simpson indices are equivalent to, respectively, the Hill’s numbers when q = 1 and 2 in Eq. (1) Figure 3 graphically depicts the diversity profile calculated through Eq. 1 for the reduced sub-datasets (pairings I–IX) shown in Table 1 , including the full sample. While contrasting the full and reduced samples, three results shown in Fig. 3 are highlighted. First, species richness was much more sensitive to the reductions than the other indices. In addition, it was the only index underestimated in 100% of cases (all reductions and pairings, Table 1 ) in relation to the full sample. The sample with n = 22, 400 m² clusters reduced from outer to inner (Pairing IX, Table 1 , Fig. 3 ) provided the lowest richness of 73 species. This represents a 61% underestimation compared to the 188 species given by the full sample. In general, the reduction in cluster size underestimated species richness less for sampled areas from 4.4 ha to 2.4 ha (Pairing I to V, Table 1 ); for sampled areas less than 2.4 ha (Pairing VI to IX, Table 1 ), the reduction in cluster size underestimated more than the reduction in sample size. Second, the Shannon index was underestimated more than the Simpson index, compared to the full sample. Among the reductions and pairings outlined in Table 1 , the Shannon index was underestimated in 44% of cases, and the Simpson index in 22%. However, no clear trend in the underestimation was observed for either index. The sample size reduction underestimated the Shannon index in 56% of cases, and the Simpson index in 33%. The cluster size reduction ‘inner to outer’ underestimated the Shannon index in 44% of cases, more than the Simpson index, which was underestimated in 11% of cases. The reduction ‘outer to inner’, in turn, underestimated the Shannon index in 33% of cases, against 22% for the Simpson index. Third, the cluster size reductions ‘inner to outer’ produced different diversity profiles from the reductions ‘outer to inner’. The differences in species richness, Shannon, and Simpson indices were, on average, 3% (Pairing VI), 4% (Pairing I), 7% (Pairing IV), 8% (Pairings III and IX), 9% (Pairing II), 10% (Pairings VII and VIII), and 11% (Pairing V). One remark is that the degree of these differences was not affected by the sampled area, meaning that a 2,000 m² cluster reduced from inner to outer and another equal-sized cluster reduced from outer to inner are not necessarily more similar to each other than two smaller (e.g., 400 m²) clusters also reduced in both directions Figure 4 illustrates the confidence interval (CI) for the number of species for each reduced sub-dataset (pairings I–IX) shown in Table 1 . Notable narrowing of the CIs was observed as the sampling intensity was reduced. The CIs overlapped until pairing III, i.e., for sampled areas larger than 3.2 ha (Table 1 ). DISCUSSION The results emphasize the sensitivity of species richness to reductions in sample size within the Amazon forest. The study contrasts full and reduced samples, revealing that species richness is significantly more affected by reductions compared to other diversity indices. Notably, species richness was consistently underestimated in 100% of cases across all reductions and pairings, with sample size reduction leading to substantial underestimations. In Pairing IX, where a sample of n = 22, 400 m² clusters was reduced from outer to inner, the lowest richness of 73 species was observed, representing a 61% decrease compared to the 188 species identified in the full sample. The study further indicates that reductions in cluster size generally result in less underestimation of species richness for sampled areas from 4.4 ha to 2.4 ha (Pairing I to V). However, for sampled areas less than 2.4 ha (Pairing VI to IX), reductions in cluster size lead to greater underestimations compared to reductions in sample size. These findings align with previous research on Amazon forest diversity, highlighting the complex relationship between sample size, cluster size, and accurate estimation of species richness. Studies have shown that the Amazon rainforest harbors unparalleled tree species richness, with estimates ranging from approximately 16,000 tree species (Fauset et al., 2015 ). The complexity of Amazonian tree diversity is further underscored by the presence of over 900 flood-tolerant tree species in varzea forests, highlighting the region's exceptional species richness (Wittmann et al., 2006 ). Moreover, the focus on underestimation of species richness due to reductions in sample and cluster sizes resonates with the broader discourse on the importance of accurate sampling strategies in assessing tree diversity. Understanding the nuances of species richness estimation in the Amazon forest is crucial for effective conservation and management practices aimed at preserving the region's rich biodiversity. Figure 3 shows that the distance between subunits within a cluster influences the capture of Hill numbers for pairings V–IX, leading to variations in species diversity. This variability is due to differences in subunit compositions within the clusters, particularly in pairings V–IX, where reduced clusters exhibit distinct subunit compositions. These fluctuations in species diversity are reflected in Hill numbers, with an average difference of 14% in Pairing IX. Similar patterns are observed in Pairings V to VIII, where clusters display diverse subunit compositions, resulting in species variability within the same cluster area. The variations in species diversity within clusters are linked to differences in subunit compositions across pairings. Pairings I–IV, characterized by smaller distances between cluster subunits, have minimal effects on species diversity, with an average difference of only 1–3%. This underscores the importance of subunit composition in influencing species variability within clusters. These findings are consistent with research on Amazon forest diversity, which identifies the region as having unparalleled tree species richness. Studies estimate the Amazon to be home to approximately 16,000 tree species, showcasing its exceptional biodiversity (Fauset et al., 2015 ). The complex interplay between environmental factors and tree diversity in the Amazon is further emphasized, with a focus on understanding diversity patterns in different regions of the Amazon basin (Lima, 2023 ; Zevallos et al., 2022 ). Furthermore, the text highlights the significance of subunit distances within clusters in shaping species diversity, echoing the importance of forest fragmentation and cluster shape on tree diversity as emphasized in previous studies (Hill & Curran, 2003 ). Management strategies that prioritize minimizing disturbance and maintaining forest structure are crucial for preserving high levels of tree diversity (Hill & Curran, 2003 ). The research indicated that the Shannon index was underestimated more frequently than the Simpson index when considering the full sample. Specifically, the Shannon index was underestimated in 44% of cases, while the Simpson index was underestimated in 22% of cases (Bhattarai et al., 2018 ). This discrepancy highlights a potential difference in their sensitivity or applicability within certain contexts of the Amazon forest ecosystem. We found that sample size reduction led to underestimation of the Shannon index in 56% of cases and the Simpson index in 33% of cases. Additionally, cluster size reductions from ‘inner to outer’ resulted in underestimation of the Shannon index in 44% of cases, which was more pronounced compared to the Simpson index, underestimated in only 11% of cases. Conversely, reductions from ‘outer to inner’ underestimated the Shannon index in 33% of cases and the Simpson index in 22% of cases (Bhattarai et al., 2018 ). These findings suggest that the direction and magnitude of reductions in sample and cluster sizes can differently influence the estimation of diversity indices, emphasizing the need for careful consideration of these factors in biodiversity assessments. Cluster size reductions from ‘inner to outer’ produced distinct diversity profiles compared to reductions from ‘outer to inner’. The percentage differences observed in species richness, Shannon index, and Simpson index ranged from 3–11% across different pairings (Bhattarai et al., 2018 ). Notably, the degree of these differences was consistent regardless of the sampled area, indicating that the direction of cluster size reduction played a significant role in shaping biodiversity profiles, independent of the specific area under consideration. This finding underscores the importance of considering the spatial arrangement and composition of clusters when evaluating biodiversity patterns in the Amazon forest. In the context of biodiversity assessments, the Shannon index and the Simpson index are commonly used metrics to quantify species diversity. The Shannon index considers both species richness and evenness, providing a more comprehensive measure of diversity, while the Simpson index focuses more on dominance within a community (Hill, 1973 ). Kardgar et al. ( 2025 ), in analyzing different diversity profiles, observed that the Simpson index is less sensitive to variations in sample size. The differences in underestimation observed in these diversity profiles in the Amazon forest study suggest that the choice of diversity metric can impact the interpretation of biodiversity patterns, emphasizing the need for a nuanced understanding of the strengths and limitations of each index in ecological research. These findings align with previous research that has explored the relationship between spectral diversity and diversity profiles. Wang et al. ( 2018 ) noted a stronger relationship between spectral diversity and the Simpson index compared to the Shannon index in a prairie grassland ecosystem, which resonates with the differential underestimation patterns observed in the Amazon forest study. This consistency in the relationship between spectral diversity and diversity profiles across different ecosystems underscores the robustness of these metrics in capturing variations in biodiversity patterns. By building on established theoretical frameworks, researchers can effectively analyze and compare biodiversity patterns across different landscapes and ecosystems. Concerning the CIs shown in Fig. 4 , the findings reveal the impact of sampling intensity on the precision of estimating species richness within the Amazon forest ecosystem. As the sampling intensity decreased, leading to reduced sample sizes, the CIs became more constrained, reflecting a higher level of certainty in the estimated species richness. The observation of overlapping CIs until a certain threshold (pairing III, Fig. 4 ) suggests that beyond a certain sampled area, the precision in estimating species richness may improve due to a more comprehensive sampling effort (Sullivan et al., 2017 ). The narrowing of CIs with reduced sampling intensity aligns with previous research that has highlighted the importance of adequate sampling efforts in capturing the true diversity of tree species in the Amazon forest. Studies by Steege et al. ( 2013 ) and Wittmann et al. ( 2006 ) emphasized the significance of extensive sampling across different forest types and regions to accurately assess tree species composition and diversity gradients in the Amazon Basin. By ensuring robust sampling strategies and considering the impact of sampling intensity on the precision of diversity estimates, researchers can enhance the reliability of biodiversity assessments in complex ecosystems like the Amazon forest. Research by Fauset et al. ( 2015 ) and Hubbell et al. ( 2008 ) has highlighted the hyperdiversityof Amazonian forests and the challenges in estimating the total number of tree species in the region. The findings from the current study add a methodological perspective by demonstrating how variations in sampling intensity can influence the precision of species richness estimates, shedding light on the intricacies of quantifying biodiversity in one of the world's most diverse ecosystems. CONCLUSION This study aimed to dissociate the effect of cluster size from sample size on diversity profiles in the Amazon. The findings indicate that species richness is most sensitive to reductions in sampled area (SA) and sample size, with significant underestimation occurring when the SA is below 2.4 ha, and accuracy of the other diversity profiles was severely compromised below 1.6 ha. For a consistent sampling effort, utilizing more small units proved more effective for capturing diversity, particularly species richness, than using fewer large units. While the Simpson index was less affected by sample size reductions (underestimated in only 3 out of 9 scenarios), the Shannon index showed greater sensitivity (affected in 5 out of 9 scenarios). Furthermore, reducing cluster size from inner to outer and from outer to inner resulted in only minor variations (3–11%) in the diversity profiles. Declarations Funding: Not Applicabe. Author Contribution All authors actively participated in the preparation of the article. A. A., B. A., and M. D. W. assisted in the drafting of the main text. L. E. M. and D. H. C. performed data tabulation, processing, and figure preparation. All authors reviewed the text. Acknowledgement The authors thank the Instituto Floresta Tropical for the data availability. References Alvares, C. A., Stape, J. L., Sentelhas, P. C., Gonçalves, J. L. 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McRoberts (Eds.), National Forest Inventories: Pathways for Common Reporting (pp. 1–612). Springer. Lima, R. (2023). Giants of the Amazon: how does environmental variation drive the diversity patterns of large trees? Global Change Biology, 29 (17), 4861–4879. https://doi.org/10.1111/gcb.16821 Loetsch, F., Zohrer, F., & Haller, K. (1973). Forest inventory (2nd ed., Vol. II). BLV Verlagsgesellschaft. Magnussen, S. (2011). Sample-based estimation of regional forest tree species richness. Environmental and Natural Resources Research, 1 (1), 2–16. Magnussen, S., & Boyle, T. J. B. (1995). Estimating sample size for inference about the Shannon-Weaver and the Simpson indices of species diversity. Forest Ecology and Management, 78 (1-3), 71–84. Magurran, A. E. (2013). Measuring biological diversity . John Wiley & Sons. Miguel, E. P., Rezende, A. V., Leal, F. A., Pereira, R. S., & Melo, R. R. D. (2016). Caracterização florístico-estrutural e grupo sucessional de espécies arbóreas no bioma cerrado do estado de Tocantins, Brasil. Myers, N., Mittermeier, R. A., Mittermeier, C. G., Fonseca, G. A. B., & Kent, J. (2000). Biodiversity hotspots for conservation priorities. Nature, 403 (6772), 853–858. Oksanen, J., Blanchet, F. G., Friendly, M., Kindt, R., Legendre, P., McGlinn, D., Minchin, P. R., O'Hara, R. B., Simpson, G. L., Solymos, P., Stevens, M. H. H., Szoecs, E., & Wagner, H. (2016). vegan: Community Ecology Package (R package version 2.4-1). https://CRAN.R-project.org/package=vegan Pielou, E. C. (2014). Diversity indices. In N. Balakrishnan, T. Colton, B. Everitt, W. Piegorsch, F. Ruggeri, & J. L. Teugels (Eds.), Wiley StatsRef: Statistics Reference Online . https://doi.org/10.1002/9781118445112.stat03438 Saarinen, N., Vastaranta, M., Näsi, R., Rosnell, T., Hakala, T., Honkavaara, E., Wulder, M., Luoma, V., Tommaselli, A., Imai, N., Ribeiro, E., Guimarães, R., Holopainen, M., & Hyyppä, J. (2018). Assessing biodiversity in boreal forests with UAV-based photogrammetric point clouds and hyperspectral imaging. Remote Sensing, 10 (2), 338. https://doi.org/10.3390/rs10020338 Steege, H. t., Pitman, N. C. A., Sabatier, D., Baraloto, C., Salomão, R. d. P., Guevara, J. E., … Silman, M. R. (2013). Hyperdominance in the Amazonian tree flora. Science, 342 (6156), 1243092. https://doi.org/10.1126/science.1243092 Sullivan, M. J. P., Talbot, J., Lewis, S. L., Phillips, O. L., Qie, L., Begne, S. K., … Zemagho, L. (2017). Diversity and carbon storage across the tropical forest biome. Scientific Reports, 7 (1), 39102. https://doi.org/10.1038/srep39102 Wang, R., Gamon, J. A., Cavender-Bares, J., Townsend, P. A., & Zygielbaum, A. I. (2018). The spatial sensitivity of the spectral diversity–biodiversity relationship: an experimental test in a prairie grassland. Ecological Applications, 28 (2), 541–556. https://doi.org/10.1002/eap.1669 Wittmann, F., Schöngart, J., Montero, J. C., Motzer, T., Junk, W. J., Piedade, M. T. F., … Worbes, M. (2006). Tree species composition and diversity gradients in white-water forests across the Amazon basin. Journal of Biogeography, 33 (8), 1334–1347. https://doi.org/10.1111/j.1365-2699.2006.01495.x Yang, W., Kobayashi, H., Nasahara, K., Suzuki, R., & Kondoh, A. (2017). Quantitative evaluation of Bitterlich sampling for estimating basal area in sparse boreal forests and dense tropical forests. Open Journal of Forestry, 7 (2), 143–156. https://doi.org/10.4236/ojf.2017.72009 Zevallos, M., Moulatlet, G., Sousa, T., Schietti, J., Coêlho, L., Ramos, J., et al. (2022). Local hydrological conditions influence tree diversity and composition across the Amazon basin. Ecography, 45 (11). https://doi.org/10.1111/ecog.06125 Additional Declarations No competing interests reported. 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. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. 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-7328739","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":506367938,"identity":"b4b93eec-0b22-456f-8db3-ce423cd6f653","order_by":0,"name":"Angelo Augusto EBLING","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAtElEQVRIiWNgGAWjYDACCeaGAwwMNgzsDQwMzERqYQRpSWPgOUCKFiB5mAQt/NKNjYcLfp1P7JHufcBcuIcILZJzDjYcntl3O7FH5rgB84xnRGgxuJHYcJi353bifok0BmaQ6wgCe4iWc4k9RGsxkABq4flxgAQtEneAfuFtSDbukTnGcHgGMVr4Zzcf/szzx062R7qN8XEBMVrAgLENZB8DA9EagOAPRMsoGAWjYBSMAqwAAJEoO1V89EtWAAAAAElFTkSuQmCC","orcid":"","institution":"Federal University of Paraná","correspondingAuthor":true,"prefix":"","firstName":"Angelo","middleName":"Augusto","lastName":"EBLING","suffix":""},{"id":506367939,"identity":"6abc42b6-42a7-46f8-9cec-274f6723e5e1","order_by":1,"name":"Alexandre BEHLING","email":"","orcid":"","institution":"Federal University of Paraná","correspondingAuthor":false,"prefix":"","firstName":"Alexandre","middleName":"","lastName":"BEHLING","suffix":""},{"id":506367940,"identity":"2827be5e-d186-4d2b-95e2-3e807cb71e5b","order_by":2,"name":"Edberto Moura LIMA","email":"","orcid":"","institution":"BAW Research","correspondingAuthor":false,"prefix":"","firstName":"Edberto","middleName":"Moura","lastName":"LIMA","suffix":""},{"id":506367941,"identity":"3e87ef98-d0f7-4d15-8f52-7cb9264616a4","order_by":3,"name":"David W. MACFARLANE","email":"","orcid":"","institution":"Michigan State University","correspondingAuthor":false,"prefix":"","firstName":"David","middleName":"W.","lastName":"MACFARLANE","suffix":""},{"id":506367942,"identity":"f8a3137a-e34d-4d0c-adcd-035389d30188","order_by":4,"name":"Hassan Camil DAVID","email":"","orcid":"","institution":"Federal University of Paraná","correspondingAuthor":false,"prefix":"","firstName":"Hassan","middleName":"Camil","lastName":"DAVID","suffix":""}],"badges":[],"createdAt":"2025-08-08 15:38:26","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7328739/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7328739/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":90142784,"identity":"c1c034bd-3f28-48e4-8464-04546d39b2a8","added_by":"auto","created_at":"2025-08-29 04:35:16","extension":"jpeg","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":69343,"visible":true,"origin":"","legend":"\u003cp\u003eLocation of the Bom Futuro National Forest.\u003c/p\u003e","description":"","filename":"floatimage1.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-7328739/v1/a093773f53f922bb07b658cc.jpeg"},{"id":90142777,"identity":"288c2ffe-7c96-4ac1-bd1c-0d47dc38654b","added_by":"auto","created_at":"2025-08-29 04:35:16","extension":"jpeg","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":74334,"visible":true,"origin":"","legend":"\u003cp\u003eCluster dimensions employed in the analytical procedure. The original cluster (a) was successively reduced in two directions (b and c), generating nine reduced clusters of 2000, 1600, 1500, 1300, 1100, 900, 700, 500, 400 m².\u003c/p\u003e","description":"","filename":"floatimage2.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-7328739/v1/da36bb2cdf15cef514e2d70a.jpeg"},{"id":90143163,"identity":"0e8cfc94-22ae-4c98-8a06-0003b77ff3f2","added_by":"auto","created_at":"2025-08-29 04:43:16","extension":"jpeg","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":108874,"visible":true,"origin":"","legend":"\u003cp\u003eDiversity profile in the Bom Futuro National Forest calculated with Hill’s numbers. Description of the pairings I–IX can be consulted in Table 1.\u003c/p\u003e","description":"","filename":"floatimage3.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-7328739/v1/e34449f9daf1c4164646b71a.jpeg"},{"id":90142780,"identity":"b5b43770-6386-44ee-a4d2-703bd9daf904","added_by":"auto","created_at":"2025-08-29 04:35:16","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":12740,"visible":true,"origin":"","legend":"\u003cp\u003eConfidence interval for the species richness (when \u003cem\u003eq = 0\u003c/em\u003e in Eq. 1). Description of the pairings I–IX can be consulted in Table 1.\u003c/p\u003e","description":"","filename":"floatimage4.png","url":"https://assets-eu.researchsquare.com/files/rs-7328739/v1/65685806fe2ac29e4f2b3a0b.png"},{"id":104401903,"identity":"c0f44919-297e-46f8-be7d-9e66f78b55a1","added_by":"auto","created_at":"2026-03-11 12:13:52","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":866212,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7328739/v1/28f2d1ee-4177-499b-a3f1-c98718ba4839.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Sampling Amazonian forest with clusters to measure tree species diversity: dissociating the effect of cluster size and sample size","fulltext":[{"header":"INTRODUCTION","content":"\u003cp\u003eThe Amazon\u0026rsquo;s forests hold a relevant portion of the world\u0026rsquo;s species diversity (Myers et al., \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e2000\u003c/span\u003e). Considering trees only, research estimates the occurrence of ~\u0026thinsp;16,000 species throughout the Amazon region; 227 of them are hyper-dominant species (Steege, 2013). The within-community species diversity is referred to as the diversity alpha (α), whereas that among communities concerns the diversity beta (β). Among the several indices of diversity, Shannon, Pielou, and Simpson are perhaps the most widely used to measure diversity α (Magurran, \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e2013\u003c/span\u003e; Pielou, \u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e2014\u003c/span\u003e).\u003c/p\u003e\u003cp\u003eForest inventories are an important source of data for biodiversity purposes. In the classical book by Loetsch et al. (\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e1973\u003c/span\u003e), forest inventories are classified either as the \u0026lsquo;census\u0026rsquo; \u0026ndash; a complete inventory that totally covers the forest, requiring that every single tree be sampled \u0026ndash; or as the \u0026lsquo;sampling inventories\u0026rsquo; \u0026ndash; an incomplete inventory in which only a sub-sample of the forest is measured. The sampling designs applied to incomplete inventories take into account, overall, arrangement of the sample unit (SU) distribution along the forest, as well as shape, size, and number of SUs, in which these last two determine the sampling intensity (SI). The larger the size and number of SUs, the higher the SI.\u003c/p\u003e\u003cp\u003eThe variance along the forest increases proportionally to the number of SUs required in the sampling (Loetsch et al., \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e1973\u003c/span\u003e). Given that the Amazon\u0026rsquo;s forests are typically rich in tree species, it is intuitive to think that to accurately estimate tree species diversity, a larger SI would be required, thus requiring allocation of more and/or larger SUs along the sampled forest. Cochran (\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e1977\u003c/span\u003e) argues that smaller SUs usually provide precise estimates; however, to measure diversity, this general rule may not be as efficient in highly variable environments (e.g., tropical forests) as in those more homogeneous ones (e.g., boreal forests) (Yang et al., \u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e2017\u003c/span\u003e; Saarinen et al., \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e2018\u003c/span\u003e).\u003c/p\u003e\u003cp\u003eIncomplete inventories are, in general, the most preferable because they offer a cheaper and faster estimate of the mean. The challenge in opting for incomplete inventories (i.e., prioritizing the cost reduction) is that cost and sampling error share an inverse relationship, so that, in theory, the lower the sampling error, the more SUs are needed (Cochran, \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e1977\u003c/span\u003e). National Forest Inventories (NFIs) are a type of incomplete, large-scale inventory, being also the main data source used in national-level estimates of biodiversity in various countries around the world (Chirici et al., \u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e2012\u003c/span\u003e; Corona et al., \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2011\u003c/span\u003e).\u003c/p\u003e\u003cp\u003eThe NFI SU is generally a cluster-shaped field plot split into smaller units called the sub-units (Lawrence et al., \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e2010\u003c/span\u003e). Among other reasons, the preference for clusters is that the variance among them is reduced, thus requiring a lesser amount of SUs in the sampling (Cochran, \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e1977\u003c/span\u003e). As NFIs are based on sub-samples, the use of their database for biodiversity purposes needs the construction of rarefaction curves (RCs), due to the sensitivity of species diversity to the sampling design and SI, i.e., size and number of SUs (Chao et al., \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2016\u003c/span\u003e; Corona et al., \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2011\u003c/span\u003e; Magnussen, \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e2011\u003c/span\u003e; Beck and Schwanghart, \u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e2010\u003c/span\u003e).\u003c/p\u003e\u003cp\u003eMost of the research on species diversity normally concerns the SI; however, little discussion is devoted to quantifying and dissociating its effect. By dissociating, we mean that for the same SI, it is possible to allocate more or fewer SUs by varying their size. For example, 100 SUs of 1,000 m\u0026sup2; correspond to the same sampled area (i.e., SI) as 10 SUs of 10,000 m\u0026sup2;, but both cases differ by a factor of ten in the number of sampled spots. Corona et al. (\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2011\u003c/span\u003e) argue that more tree species would be observed when many small plots are sampled instead of few large plots. Corona et al.\u0026rsquo;s arguments make sense because of the presence of species mosaics that may fully encompass a large SU, meaning that a wider distribution of smaller SUs increases the coverage of the tree species along the forest. In addition, plant species generally have spatial distributions much more complex than a random pattern (Magnussen and Boyle, \u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e1995\u003c/span\u003e).\u003c/p\u003e\u003cp\u003eThe question raised in this study was \u0026ldquo;how big is the effect of the size and number of clusters on the tree species diversity in an Amazonian forest?\u0026rdquo; This paper fills a gap in the current literature because NFIs have been increasingly used for diversity analysis, while the efficiency of NFI clusters has not been fairly assessed for this purpose. With data from clusters standardized as Brazil\u0026rsquo;s NFI, we aimed to dissociate the effect of cluster size from sample size on the floristic diversity in an Amazonian forest.\u003c/p\u003e"},{"header":"MATERIAL AND METHODS","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e\u003ch2\u003eStudy area\u003c/h2\u003e\u003cp\u003eThe research areas are situated in the Bom Futuro National Forest, state of Rond\u0026ocirc;nia, Brazil (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e). This national forest is a protected area with sustainable use of natural resources (IUCN category VI), and it covers a total area of ~\u0026thinsp;100 thousand hectares. The research was conducted on 83 thousand hectares of forest, which represents about 83% of the total area of the National Forest. The area is covered mainly by pristine sub-montane rainforests, with areas of Lowland Rainforests, Savannah, Alluvial Rainforest, and other Alluvial pioneer vegetation. The climate belongs to the tropical monsoon (Am), the most representative climate of the west of the Brazilian Amazonian region, with mean annual temperature around 25 \u0026ordm;C and mean annual precipitation around 2200 mm (Alvares, 2013). The local relief varies from flat to wavy and elevation is from 60\u0026ndash;200 m above sea level. The parent material belongs to the Amazon craton, and it is composed of Precambrian granite and gneiss (Bettencourt, \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e1999\u003c/span\u003e). The most common soil types are alfisols, oxisols, ultisols, and alluvial soils\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003c/div\u003e\n\u003ch3\u003eField measurements\u003c/h3\u003e\n\u003cp\u003eThe forest in the study area was inventoried by following a two-stage sampling design with SUs structured as the Brazilian NFI guidance. In the first (systematic) stage, a regular grid with square cells measuring 0.625 x 0.625 km (~\u0026thinsp;0.39 km\u0026sup2;) was drawn over the forest to be inventoried. In the second (random) stage, we randomly selected 22 cells (7 in the pilot inventory plus 15 in the definitive one) to install one SU in the midpoint of each cell. The SU is a 4,000 m\u0026sup2; cluster with four crosswise sub-units (1,000 m\u0026sup2; each) that are divided into ten sub-plots of 100 m\u0026sup2; (10 x 10 m), totaling 40 sub-plots by cluster. Further detail about the Brazilian NFI can be consulted in David et al. (\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2019\u003c/span\u003e). Figure\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e shows the NFI original cluster, as well as illustrations of the procedure we used to reduce the cluster size, which was necessary in our analysis (see next section).\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eAll trees with diameter at breast height (DBH)\u0026thinsp;\u0026ge;\u0026thinsp;10 cm were measured, and botanical material was collected and taken to a herbarium (at the Federal University of Rond\u0026ocirc;nia) for species identification. Trees with broken crown or stem were also included in the data collection. We measured dead or living woody trees; therefore, palms and tree fern species were not the target of this study.\u003c/p\u003e\n\u003ch3\u003eDissociating effects of the cluster size from the sample size\u003c/h3\u003e\n\u003cp\u003eFrom our original sample containing 22, 4,000 m\u0026sup2; clusters, the analytical procedure consisted of creating nine subsets of samples successively reduced in sample sizes (from 22 to 2 clusters), plus nine sets with reductions in cluster size (from 2,000 m\u0026sup2; to 400 m\u0026sup2;). Our framework covered nine pairs of samples approximately equivalent in the sample area. The following sections describe the analytical procedure. Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e gives the main sampling information of the subsets of samples.\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\u003eSubsets of samples representing variations in cluster and sample sizes.\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"8\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" 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=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" 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\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e\u003cp\u003ePairing\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colspan=\"3\" nameend=\"c4\" namest=\"c2\"\u003e\u003cp\u003eSubsets with sample size reduction\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colspan=\"3\" nameend=\"c7\" namest=\"c5\"\u003e\u003cp\u003eSubsets with cluster size reduction*\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c8\" morerows=\"1\" rowspan=\"2\"\u003e\u003cp\u003e∆ sampled\u003c/p\u003e\u003cp\u003earea (ha)\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u003cem\u003en\u003c/em\u003e\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eCluster\u003c/p\u003e\u003cp\u003esize (m\u0026sup2;)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003eSampled\u003c/p\u003e\u003cp\u003earea (ha)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c5\"\u003e\u003cp\u003e\u003cem\u003en\u003c/em\u003e\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c6\"\u003e\u003cp\u003eCluster\u003c/p\u003e\u003cp\u003esize (m\u0026sup2;)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c7\"\u003e\u003cp\u003eSampled\u003c/p\u003e\u003cp\u003earea (ha)\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eI\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e11\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e4,000\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e4.40\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e22\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e2,000\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e4.40\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e\u003cp\u003e0.00\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eII\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e9\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e4,000\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e3.60\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e22\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e1,600\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e3.52\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e\u003cp\u003e0.08\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eIII\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e8\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e4,000\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e3.20\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e22\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e1,500\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e3.30\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e\u003cp\u003e-0.10\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eIV\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e7\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e4,000\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e2.80\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e22\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e1,300\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e2.86\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e\u003cp\u003e-0.06\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eV\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e6\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e4,000\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e2.40\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e22\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e1,100\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e2.42\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e\u003cp\u003e-0.02\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eVI\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e5\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e4,000\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e2.00\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e22\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e900\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e1.98\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e\u003cp\u003e0.02\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eVII\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e4\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e4,000\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e1.60\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e22\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e700\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e1.54\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e\u003cp\u003e0.06\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eVIII\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e3\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e4,000\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e1.20\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e22\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e500\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e1.10\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e\u003cp\u003e0.10\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eIX\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e4,000\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.80\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e22\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e400\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e0.88\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e\u003cp\u003e-0.08\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eTotal\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e-\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e-\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e22.00\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e-\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e-\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e22.00\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e\u003cp\u003e0.00\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003e* refers to reductions from inner to outer and from outer to inner, as in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e; \u003cem\u003en\u003c/em\u003e: number of clusters.\u003c/p\u003e\u003cp\u003eTo dissociate the effect of cluster size from the sample size, we paired two subsets so that a framework with nine pairs was outlined, as shown in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. The pairing obeyed the following criteria. First, one subset was reduced in cluster size whereas its pair was reduced in sample size. Second, the paired subsets had equivalence in sampled area. For example, Row I in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e describes the first pair of subsets, which has the equivalence of 4.4 ha of sampled area per subset. While outlining our framework, we noted that the equivalence in sampled area of subsets within a pair cannot be exact in all pairs, as indicated in ∆ of Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. However, we ensured that the difference between sampled areas within a pair is at most\u0026thinsp;\u0026plusmn;\u0026thinsp;0.1 ha, and that the overall equivalence among the nine pairs is exact (i.e., overall ∆=0). Third, within a pair, the cluster size of a subset must be at least twice as big as the other subset. These three criteria ensured that a reasonable forest area is sampled in all subsets of sample, as well as that a subset has larger sample size and smaller cluster size than its paired subset but ensuring that both subsets can be compared in terms of sampling effort. Research such as Miguel et al. (\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e2016\u003c/span\u003e) and Ferreira et al. (\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2010\u003c/span\u003e) have recommended a minimum sample area necessary for accurately estimating diversity profiles or index. However, the reader should consider that our focus lies more on comparing the reduced samples comprised in our framework than producing accurate diversity estimations.\u003c/p\u003e\u003cp\u003e\u003cem\u003eCluster size variation.\u003c/em\u003e Figure\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e illustrates our procedure for cluster size variation, which consisted of reducing clusters of 2,000 m\u0026sup2; (0.20 ha) by successively removing 100-m\u0026sup2; sub-plots from the cluster subunits. In that case, the initial cluster size of 2,000 m\u0026sup2;, which is half of the original size of 4,000 m\u0026sup2;, had to be utilized for reaching the equivalence in sample area represented by ∆s shown in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. The procedure resulted in ten cluster sizes: 0.20 ha (first reduction), 0.16 ha (second reduction), 0.15 ha (third), 0.13 ha (fourth), 0.11 ha (fifth), 0.09 ha (sixth), 0.07 ha (seventh), 0.05 ha (eighth), and 0.04 ha (ninth reduction). In addition, we considered two directions for reducing the cluster size: from outer to inner (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003eb) and from inner to outer (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ec). Note in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e that these directions generate longer or shorter distances between the subunits\u0026rsquo; midpoint, with the shorter distances produced by the \u0026lsquo;outer to inner\u0026rsquo; reduction, and the longer ones by the \u0026lsquo;inner to outer\u0026rsquo; reduction. The idea with applying two directions is to investigate whether the distance between sub-plots affects the species diversity.\u003c/p\u003e\u003cp\u003e\u003cem\u003eSample size variation.\u003c/em\u003e From our original dataset with 22 clusters, the number of clusters (sample size) was successively reduced from 11 clusters (first reduction), next to nine (second), to eight (third), and so on, until the ninth reduction comprising two clusters (Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e). The lower number of two clusters was set by a matter of sampling sufficiency. For each sample size required, clusters were randomly selected with replacement from the original dataset through a bootstrap approach with 1,000 replications. This procedure originated nine thousand bootstrap samples and was necessary because there are several combinations for selecting\u0026thinsp;\u0026le;\u0026thinsp;11 clusters out of 22. The bootstrap approach then plays the role of mitigating biases while selecting clusters in only one random sample.\u003c/p\u003e\n\u003ch3\u003eAccounting plant Diversity\u003c/h3\u003e\n\u003cp\u003eFor every tree species observed through the field collection, plant families were classified according to Angiosperm Phylogeny Group IV (APG IV 2016) and species nomenclature was based on the 2016 Species List of Brazil\u0026rsquo;s Flora (\u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttp://floradobrasil.jbrj.gov.br/\u003c/span\u003e\u003cspan address=\"http://floradobrasil.jbrj.gov.br/\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e). We calculated Hill\u0026rsquo;s numbers [Eq.\u0026nbsp;1] for the 18 (nine pairs) subsets of clusters presented in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. We assumed that the subsets are free of autocorrelation due to the shortest distance between the clusters being greater than 4 km. For the subsets within a pair, we assembled a matrix containing abundance data. Next, we applied Hill\u0026rsquo;s series to the abundance matrix and compared the plant diversity through diversity profiles. The diversity profiles were graphically presented in nine plots (one by pair, Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e) illustrating curves for the (i) sample size variation and for the \u0026lsquo;inner to outer\u0026rsquo; (ii) and \u0026lsquo;outer to inner\u0026rsquo; (iii) reductions of the cluster size. A fourth curve based on the full sample containing 22, 4,000 m\u0026sup2; clusters was added to the plots. These curves will be helpful to better visualize differences in diversity profiles among the full and reduced samples.\u003c/p\u003e\u003cp\u003eAll analyses were run in the R environment, version 4.0.2, using vegan (Oksanen et al., \u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e2016\u003c/span\u003e) and BiodiversityR packages. We used a 5% significance level in all cases.\u003c/p\u003e\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{}^{q}D={\\left(\\sum\\:_{i=1}^{S}{p}_{i}^{q}\\right)}^{1/(1-q)}\\text{f}\\text{o}\\text{r}\\:q\\ne\\:1\\)\u003c/span\u003e\u003c/span\u003e[1]\u003cdiv id=\"Equa\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equa\" name=\"EquationSource\"\u003e\n$$\\:{}^{q}D=\\left(\\sum\\:_{i=1}^{S}{p}_{i}^{q}\\right)\\text{f}\\text{o}\\text{r}\\:q=1$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003ewhere,\u003c/p\u003e\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:S\\)\u003c/span\u003e\u003c/span\u003e: number of species in the assemblage; \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{p}_{i}\\)\u003c/span\u003e\u003c/span\u003e: relative abundance; \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:q\\)\u003c/span\u003e\u003c/span\u003e: parameter that determines the sensitivity of the measure to the relative frequencies. When \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:q=0\\)\u003c/span\u003e\u003c/span\u003e results in species richness, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:q=1\\)\u003c/span\u003e\u003c/span\u003e in Shannon\u0026rsquo;s index, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:q=2\\)\u003c/span\u003e\u003c/span\u003e in Pielou\u0026rsquo;s index.\u003c/p\u003e"},{"header":"RESULTS","content":"\u003cp\u003eThe complete (original) sample (22 4,000 m\u0026sup2; clusters) included 4,386 trees, from which 188 tree species, 145 genera, and 33 families were identified. Figure\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e shows the Hill\u0026rsquo;s numbers for the nine pairings presented in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. The richness estimated from the full sample was 188 species, the Shannon index was H^' = 4.257 [=\u0026thinsp;log(70.6)], and the Simpson index was 0.031 [=\u0026thinsp;1/32.3]. Recall that species richness equals the Hill\u0026rsquo;s numbers when q\u0026thinsp;=\u0026thinsp;0 in Eq.\u0026nbsp;(1), and the Shannon and Simpson indices are equivalent to, respectively, the Hill\u0026rsquo;s numbers when q\u0026thinsp;=\u0026thinsp;1 and 2 in Eq.\u0026nbsp;(1)\u003c/p\u003e\u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e graphically depicts the diversity profile calculated through Eq.\u0026nbsp;1 for the reduced sub-datasets (pairings I\u0026ndash;IX) shown in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e, including the full sample.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eWhile contrasting the full and reduced samples, three results shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e are highlighted. First, species richness was much more sensitive to the reductions than the other indices. In addition, it was the only index underestimated in 100% of cases (all reductions and pairings, Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e) in relation to the full sample. The sample with n\u0026thinsp;=\u0026thinsp;22, 400 m\u0026sup2; clusters reduced from outer to inner (Pairing IX, Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e, Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e) provided the lowest richness of 73 species. This represents a 61% underestimation compared to the 188 species given by the full sample. In general, the reduction in cluster size underestimated species richness less for sampled areas from 4.4 ha to 2.4 ha (Pairing I to V, Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e); for sampled areas less than 2.4 ha (Pairing VI to IX, Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e), the reduction in cluster size underestimated more than the reduction in sample size.\u003c/p\u003e\u003cp\u003eSecond, the Shannon index was underestimated more than the Simpson index, compared to the full sample. Among the reductions and pairings outlined in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e, the Shannon index was underestimated in 44% of cases, and the Simpson index in 22%. However, no clear trend in the underestimation was observed for either index. The sample size reduction underestimated the Shannon index in 56% of cases, and the Simpson index in 33%. The cluster size reduction \u0026lsquo;inner to outer\u0026rsquo; underestimated the Shannon index in 44% of cases, more than the Simpson index, which was underestimated in 11% of cases. The reduction \u0026lsquo;outer to inner\u0026rsquo;, in turn, underestimated the Shannon index in 33% of cases, against 22% for the Simpson index.\u003c/p\u003e\u003cp\u003eThird, the cluster size reductions \u0026lsquo;inner to outer\u0026rsquo; produced different diversity profiles from the reductions \u0026lsquo;outer to inner\u0026rsquo;. The differences in species richness, Shannon, and Simpson indices were, on average, 3% (Pairing VI), 4% (Pairing I), 7% (Pairing IV), 8% (Pairings III and IX), 9% (Pairing II), 10% (Pairings VII and VIII), and 11% (Pairing V). One remark is that the degree of these differences was not affected by the sampled area, meaning that a 2,000 m\u0026sup2; cluster reduced from inner to outer and another equal-sized cluster reduced from outer to inner are not necessarily more similar to each other than two smaller (e.g., 400 m\u0026sup2;) clusters also reduced in both directions\u003c/p\u003e\u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e illustrates the confidence interval (CI) for the number of species for each reduced sub-dataset (pairings I\u0026ndash;IX) shown in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. Notable narrowing of the CIs was observed as the sampling intensity was reduced. The CIs overlapped until pairing III, i.e., for sampled areas larger than 3.2 ha (Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e).\u003c/p\u003e\u003cp\u003e\u003c/p\u003e"},{"header":"DISCUSSION","content":"\u003cp\u003eThe results emphasize the sensitivity of species richness to reductions in sample size within the Amazon forest. The study contrasts full and reduced samples, revealing that species richness is significantly more affected by reductions compared to other diversity indices. Notably, species richness was consistently underestimated in 100% of cases across all reductions and pairings, with sample size reduction leading to substantial underestimations. In Pairing IX, where a sample of n\u0026thinsp;=\u0026thinsp;22, 400 m\u0026sup2; clusters was reduced from outer to inner, the lowest richness of 73 species was observed, representing a 61% decrease compared to the 188 species identified in the full sample. The study further indicates that reductions in cluster size generally result in less underestimation of species richness for sampled areas from 4.4 ha to 2.4 ha (Pairing I to V). However, for sampled areas less than 2.4 ha (Pairing VI to IX), reductions in cluster size lead to greater underestimations compared to reductions in sample size. These findings align with previous research on Amazon forest diversity, highlighting the complex relationship between sample size, cluster size, and accurate estimation of species richness. Studies have shown that the Amazon rainforest harbors unparalleled tree species richness, with estimates ranging from approximately 16,000 tree species (Fauset et al., \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e2015\u003c/span\u003e). The complexity of Amazonian tree diversity is further underscored by the presence of over 900 flood-tolerant tree species in varzea forests, highlighting the region's exceptional species richness (Wittmann et al., \u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e2006\u003c/span\u003e). Moreover, the focus on underestimation of species richness due to reductions in sample and cluster sizes resonates with the broader discourse on the importance of accurate sampling strategies in assessing tree diversity. Understanding the nuances of species richness estimation in the Amazon forest is crucial for effective conservation and management practices aimed at preserving the region's rich biodiversity.\u003c/p\u003e\u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e shows that the distance between subunits within a cluster influences the capture of Hill numbers for pairings V\u0026ndash;IX, leading to variations in species diversity. This variability is due to differences in subunit compositions within the clusters, particularly in pairings V\u0026ndash;IX, where reduced clusters exhibit distinct subunit compositions. These fluctuations in species diversity are reflected in Hill numbers, with an average difference of 14% in Pairing IX. Similar patterns are observed in Pairings V to VIII, where clusters display diverse subunit compositions, resulting in species variability within the same cluster area. The variations in species diversity within clusters are linked to differences in subunit compositions across pairings. Pairings I\u0026ndash;IV, characterized by smaller distances between cluster subunits, have minimal effects on species diversity, with an average difference of only 1\u0026ndash;3%. This underscores the importance of subunit composition in influencing species variability within clusters. These findings are consistent with research on Amazon forest diversity, which identifies the region as having unparalleled tree species richness. Studies estimate the Amazon to be home to approximately 16,000 tree species, showcasing its exceptional biodiversity (Fauset et al., \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e2015\u003c/span\u003e). The complex interplay between environmental factors and tree diversity in the Amazon is further emphasized, with a focus on understanding diversity patterns in different regions of the Amazon basin (Lima, \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Zevallos et al., \u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). Furthermore, the text highlights the significance of subunit distances within clusters in shaping species diversity, echoing the importance of forest fragmentation and cluster shape on tree diversity as emphasized in previous studies (Hill \u0026amp; Curran, \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e2003\u003c/span\u003e). Management strategies that prioritize minimizing disturbance and maintaining forest structure are crucial for preserving high levels of tree diversity (Hill \u0026amp; Curran, \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e2003\u003c/span\u003e).\u003c/p\u003e\u003cp\u003eThe research indicated that the Shannon index was underestimated more frequently than the Simpson index when considering the full sample. Specifically, the Shannon index was underestimated in 44% of cases, while the Simpson index was underestimated in 22% of cases (Bhattarai et al., \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e2018\u003c/span\u003e). This discrepancy highlights a potential difference in their sensitivity or applicability within certain contexts of the Amazon forest ecosystem. We found that sample size reduction led to underestimation of the Shannon index in 56% of cases and the Simpson index in 33% of cases. Additionally, cluster size reductions from \u0026lsquo;inner to outer\u0026rsquo; resulted in underestimation of the Shannon index in 44% of cases, which was more pronounced compared to the Simpson index, underestimated in only 11% of cases. Conversely, reductions from \u0026lsquo;outer to inner\u0026rsquo; underestimated the Shannon index in 33% of cases and the Simpson index in 22% of cases (Bhattarai et al., \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e2018\u003c/span\u003e). These findings suggest that the direction and magnitude of reductions in sample and cluster sizes can differently influence the estimation of diversity indices, emphasizing the need for careful consideration of these factors in biodiversity assessments. Cluster size reductions from \u0026lsquo;inner to outer\u0026rsquo; produced distinct diversity profiles compared to reductions from \u0026lsquo;outer to inner\u0026rsquo;. The percentage differences observed in species richness, Shannon index, and Simpson index ranged from 3\u0026ndash;11% across different pairings (Bhattarai et al., \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e2018\u003c/span\u003e). Notably, the degree of these differences was consistent regardless of the sampled area, indicating that the direction of cluster size reduction played a significant role in shaping biodiversity profiles, independent of the specific area under consideration. This finding underscores the importance of considering the spatial arrangement and composition of clusters when evaluating biodiversity patterns in the Amazon forest.\u003c/p\u003e\u003cp\u003eIn the context of biodiversity assessments, the Shannon index and the Simpson index are commonly used metrics to quantify species diversity. The Shannon index considers both species richness and evenness, providing a more comprehensive measure of diversity, while the Simpson index focuses more on dominance within a community (Hill, \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e1973\u003c/span\u003e). Kardgar et al. (\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e2025\u003c/span\u003e), in analyzing different diversity profiles, observed that the Simpson index is less sensitive to variations in sample size. The differences in underestimation observed in these diversity profiles in the Amazon forest study suggest that the choice of diversity metric can impact the interpretation of biodiversity patterns, emphasizing the need for a nuanced understanding of the strengths and limitations of each index in ecological research. These findings align with previous research that has explored the relationship between spectral diversity and diversity profiles. Wang et al. (\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e2018\u003c/span\u003e) noted a stronger relationship between spectral diversity and the Simpson index compared to the Shannon index in a prairie grassland ecosystem, which resonates with the differential underestimation patterns observed in the Amazon forest study. This consistency in the relationship between spectral diversity and diversity profiles across different ecosystems underscores the robustness of these metrics in capturing variations in biodiversity patterns. By building on established theoretical frameworks, researchers can effectively analyze and compare biodiversity patterns across different landscapes and ecosystems.\u003c/p\u003e\u003cp\u003eConcerning the CIs shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e, the findings reveal the impact of sampling intensity on the precision of estimating species richness within the Amazon forest ecosystem. As the sampling intensity decreased, leading to reduced sample sizes, the CIs became more constrained, reflecting a higher level of certainty in the estimated species richness. The observation of overlapping CIs until a certain threshold (pairing III, Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e) suggests that beyond a certain sampled area, the precision in estimating species richness may improve due to a more comprehensive sampling effort (Sullivan et al., \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e2017\u003c/span\u003e). The narrowing of CIs with reduced sampling intensity aligns with previous research that has highlighted the importance of adequate sampling efforts in capturing the true diversity of tree species in the Amazon forest. Studies by Steege et al. (\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e2013\u003c/span\u003e) and Wittmann et al. (\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e2006\u003c/span\u003e) emphasized the significance of extensive sampling across different forest types and regions to accurately assess tree species composition and diversity gradients in the Amazon Basin. By ensuring robust sampling strategies and considering the impact of sampling intensity on the precision of diversity estimates, researchers can enhance the reliability of biodiversity assessments in complex ecosystems like the Amazon forest. Research by Fauset et al. (\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e2015\u003c/span\u003e) and Hubbell et al. (\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e2008\u003c/span\u003e) has highlighted the hyperdiversityof Amazonian forests and the challenges in estimating the total number of tree species in the region. The findings from the current study add a methodological perspective by demonstrating how variations in sampling intensity can influence the precision of species richness estimates, shedding light on the intricacies of quantifying biodiversity in one of the world's most diverse ecosystems.\u003c/p\u003e"},{"header":"CONCLUSION","content":"\u003cp\u003eThis study aimed to dissociate the effect of cluster size from sample size on diversity profiles in the Amazon. The findings indicate that species richness is most sensitive to reductions in sampled area (SA) and sample size, with significant underestimation occurring when the SA is below 2.4 ha, and accuracy of the other diversity profiles was severely compromised below 1.6 ha. For a consistent sampling effort, utilizing more small units proved more effective for capturing diversity, particularly species richness, than using fewer large units. While the Simpson index was less affected by sample size reductions (underestimated in only 3 out of 9 scenarios), the Shannon index showed greater sensitivity (affected in 5 out of 9 scenarios). Furthermore, reducing cluster size from inner to outer and from outer to inner resulted in only minor variations (3\u0026ndash;11%) in the diversity profiles.\u003c/p\u003e"},{"header":"Declarations","content":"\u003ch2\u003eFunding:\u003c/h2\u003e\u003cp\u003eNot Applicabe.\u003c/p\u003e\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eAll authors actively participated in the preparation of the article. A. A., B. A., and M. D. W. assisted in the drafting of the main text. L. E. M. and D. H. C. performed data tabulation, processing, and figure preparation. All authors reviewed the text.\u003c/p\u003e\u003ch2\u003eAcknowledgement\u003c/h2\u003e\u003cp\u003eThe authors thank the Instituto Floresta Tropical for the data availability.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eAlvares, C. A., Stape, J. L., Sentelhas, P. C., Gon\u0026ccedil;alves, J. L. M., \u0026amp; Sparovek, G. (2013). K\u0026ouml;ppen\u0026rsquo;s climate classification map for Brazil. \u003cem\u003eMeteorologische Zeitschrift, 22\u003c/em\u003e(6), 711\u0026ndash;728.\u003c/li\u003e\n\u003cli\u003eAngiosperm Phylogeny Group IV (APG IV). (2016). An update of the Angiosperm Phylogeny Group classification for the orders and families of flowering plants: APG IV. \u003cem\u003eBotanical Journal of the Linnean Society, 181\u003c/em\u003e(1), 1\u0026ndash;20. https://doi.org/10.1111/boj.12385\u003c/li\u003e\n\u003cli\u003eBeck, J., \u0026amp; Schwanghart, W. (2010). 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Local hydrological conditions influence tree diversity and composition across the Amazon basin. \u003cem\u003eEcography, 45\u003c/em\u003e(11). https://doi.org/10.1111/ecog.06125\u003c/li\u003e\n\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":"Rarefaction. Diversity profile. Sensitivity analysis. Sampling intensity. National forest inventory","lastPublishedDoi":"10.21203/rs.3.rs-7328739/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7328739/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eA mature forest remnant in the Amazon was sampled with 22 0.4-ha clusters, which means a sampling effort of 8.8 ha. From this complete sample, nine subdatasets reduced in cluster size and other nine reduced in sample size were created, totaling thus 18 subdatasets. The aim of this study was to dissociate the effects of sample size and cluster size on Hill\u0026rsquo;s numbers. A cluster consisted of a sample unit composed by four crosswise sub-units of 1,000 m\u0026sup2; (20m\u0026times;50m) each. The 18 subdatasets were aggregated into nine pairs equivalent in sampled area (SA), which decreased from 8.8 ha (complete sample) to successive reductions from 4.4 ha (first pair of subdataset) to 0.8 ha (nineth pair). Hill\u0026rsquo;s numbers were calculated for every subdataset and then sample-based rarefaction curves were constructed to generate diversity profiles. As a result, species richness was abruptly underestimated in approx. 40% for the first reduction in sample size (SA\u0026thinsp;=\u0026thinsp;4.4 ha). Significant underestimation of species richness occurred when the SA is below 2.4 ha, and accuracy of the other diversity profiles was severely compromised below 1.6 ha. We concluded that species richness is more sensitive to reductions in SA than Shannon diversity and Pielou\u0026rsquo;s evenness indices. For a same sampling effort, the choice in installing more small units demonstrated to better capturate the diversity profiles than installing less large units, especially when estimating species richness. Although the patterns of under or overestimates of the other diversity profiles were not exactly clear, the accuracy is substantially hampered when the SA is less than 1.6 ha.\u003c/p\u003e","manuscriptTitle":"Sampling Amazonian forest with clusters to measure tree species diversity: dissociating the effect of cluster size and sample size","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-08-29 04:35:11","doi":"10.21203/rs.3.rs-7328739/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":"89765cc2-1dac-45f3-a822-8bffae4032c3","owner":[],"postedDate":"August 29th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2026-03-05T00:38:54+00:00","versionOfRecord":[],"versionCreatedAt":"2025-08-29 04:35:11","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-7328739","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7328739","identity":"rs-7328739","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}