Considering landscape heterogeneity improves the inference of inter-individual interactions from movement data

Considering landscape heterogeneity improves the inference of inter-individual interactions from movement data | 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 Considering landscape heterogeneity improves the inference of inter-individual interactions from movement data Thibault Fronville, Niels Blaum, Florian Jeltsch, Stephanie Kramer-Schadt, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-5396058/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 12 Jun, 2025 Read the published version in Movement Ecology → Version 1 posted 9 You are reading this latest preprint version Abstract Background: Animal movement is influenced by both the physical environment and social environment. The effects of both environments are not independent from each other and identifying whether the resulting movement trajectories are shaped by interactions between individuals or whether they are the result of their physical environment, is important for understanding animal movement decisions. Methods: Here, we assessed whether the commonly used methods for inferring interactions between moving individuals could discern the effects of environment and other moving individuals on the movement of the focal individual. We used three statistical methods:Dynamic interaction index, and two methods based on step selection function. We created five scenarios in which the animals' movements were influenced either by their physical environment alone or by inter-individual interactions. The physical environment is constructed such that it leads to a correlation between the movement trajectories of two individuals. Results: We found that neglecting the effects of physical environmental features when analysing interactions between moving animals leads to biased inference, i.e. inter-individual interactions spuriously inferred as affecting the movement of the focal individual. We suggest that landscape data should always be included when analysing animal interactions from movement data. In the absence of landscape data, the inference of inter-individual interactions is improved by applying 'Spatial +', a recently introduced method that reduces the bias of unmeasured spatial factors. Conclusions: This study contributes to improved inference of biotic and abiotic effects on individual movement obtained by telemetry data. Step selection functions are flexible tools that offer the possibility to include multiple factors of interest as well as combine it with spatial +. Statistical methods Movement data Inter-individual interactions Physical environmental Habitat heterogeneity Collinearity Cofounding Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Introduction Animal movement is a fundamental behavioural process that results in a change of spatial locations of an individual and has important implications for its survival and reproduction, with consequences on the population and community level. Different types of movement can be distinguished, such as foraging movement, migratory movement, dispersal, and nomadic movement (Schlaegel et al. 2020; Bastille-Rousseau et al. 2016; Nathan et al. 2008). The decision of how, where and when to move is influenced by both the physical environment of an animal and its social environment (Strandburg-Peshkin et al. 2017; Nathan et al. 2008; Cote and Clobert 2007). The physical environment may consist of habitat features that offer resource and shelter, but also structures like barriers that hinder movement. The social environment consists of con- and heterospecifics and exchange of information with them. The social environment may be beneficial but also disadvantageous. Animals might be attracted to other individuals due to the benefits of sociality like social grooming, reduced predation risk, increased foraging efficiency or access to social information (van Schaik 1983). Or they may avoid other individuals to reduce the risk of pathogen transmission (Marescot et al. 2021), competition (Isbell 1991) and predation (Herbert-Read et al. 2017; Laundre et al. 2010; Fortin et al. 2005). Importantly, the physical environment and social environment are not independent of each other as the physical environment might facilitate or constrain animal interactions. Indeed, a correlation in the movement trajectories of several individuals might emerge from gathering at the same resource. For example, mammal individuals in arid ecosystems regularly come to water holes and are primarily interested in water as resource (Valeix et al. 2010). However, when their movement trajectories would be analysed without explicitly considering water as a resource, it may seem as if individuals interact with each other, while they are foremost interested in the water resource. On the other hand, barriers might prevent them to meet. Populations might get separated due to constraints on their movement introduced by habitat fragmentation (He et al. 2019; Pinter-Wollman et al. 2017; Banks et al. 2007). Thus, the physical environment in which animals move will fundamentally shape the patterns of social interactions. Identifying whether correlated movements paths of two (or more) individuals arise from interactions between them or whether they are the result of their physical environment, is important for understanding the cause of animal movement and behaviour. A rapid development of tracking technologies in recent years allowed the collection of high-resolution data on multiple simultaneously moving individuals. This, in turn, motivated the development of several methods to infer interactions among moving animals (Fronville et al. 2024; Schlaegel et al. 2019; Calabrese et al. 2018; Niu et al. 2016; Spiegel et al. 2016; Long and Nelson 2013), which now open the possibility to explore how animals move relative to one another. For example, dynamic interaction indices (Long et al. 2014) are commonly used to analyse interactions between two individuals, while step selection functions can be used to identify animals’ preference towards landscape features or even other individuals (Schlaegel et al. 2019). Here, we assess the ability of three methods to correctly detect whether animal movement paths emerge from inter-individual interactions or if they are simply the by-product of individuals responding to the same environmental features. We focused on three statistical methods extensively tested inFronville et al. (2024): one commonly used index of dynamic interaction (DI – Dynamic interaction index) that is implemented within the ‘Wildlife DI’ R package (Jed Long et al. 2018) and two novel methods that are based on step-selection functions (SSF): one uses as a covariate the occurrence distribution of the other moving individual (Schlaegel et al. 2019; herewith referred to as SSF-OD) and the other one uses the distance to the other moving individual(s) (Roeleke et al. 2022; herewith referred to as SSF-DIST). All three methods are used to estimate interactions from movement trajectories, i.e. time series of location estimates collected on at least two simultaneously moving individuals. Both SSF-based approaches also can account for other covariates (e.g. environmental data) when assessing inter-individual interactions, allowing us to investigate how these movement trajectories are shaped by resources and obstacles in the environment (Nathan et al. 2022). Furthermore, we tested whether the bias of unmeasured spatial factors on the social interactions can be reduced or even fully eliminated by applying a method called ‘spatial+’ in combination with the SSFs (Dupont et al. 2022). ‘Spatial+’ partials out the effect of space on the considered covariate (e.g. the occurrence distribution of the other moving individual or the distance to it) and thereby reduces the bias in the effect estimates. To test the methods and to investigate the possible risks of neglecting the effects of physical environmental features when analysing interactions between moving animals, we simulated movement data with a spatially-explicit agent-based model (ABM, Grimm et al. 2006; Tang and Bennett 2010) introduced in Fronville et al. (2024). using an agent-based and spatially-explicit modelling approach provided full system knowledge and allowed to generate different landscape scenarios with which the simulated individuals could interact. We simulated four landscape scenarios: in three of them (Fig. 1 A-C) two individuals do not interact with each other but their movement is affected in the same way by their physical environment, leading to resulting correlated movement trajectories; in the fourth scenario (Fig. 1 D) two individuals interact exclusively with each other and are not affected by their physical environment. In this study, the physical environment consists of resources (gradient of habitat quality) that the individuals are attracted to, or barriers (e.g. rivers, human-made structures) that hinder their movement. In scenarios A and B, the individuals are attracted to the same resources and they move along a gradient of habitat quality (scenario A) and within a patchy landscape where resources are clustered (scenario B). In scenario C the individuals move in a homogeneous matrix that is intercepted by barriers, which are randomly scattered in the landscape and can hinder or “guide” individual movement. The landscapes are built in such a way that a correlation in movement trajectories of two individuals arises either because both individuals are attracted to the same habitat quality (in scenarios A and B) or the movement of both individuals is constrained by barriers (in the scenario C) leading to their “enforced” correlation. Since DI does not allow accounting for the effect of environmental predictors when assessing interactions and in case of spatially correlated trajectories results in values close to “1” (Long et al. 2014), we expect that it will falsely detect interactions between both individuals when their movement, in fact is affected by the resource only. When the physical environment is included as a covariate in SSF, we expect the SSF-based approaches to correctly detect that the correlated movement trajectories of the two individuals emerge from the effect of their physical environment. Yet, in case the relevant physical environmental covariate is not considered in the analyses, either because the researchers do not have access to relevant environmental descriptors or because they do not expect environment to strongly affect individual movement, both these methods will, similarly to DI, falsely detect interactions between the individuals. However, we expect that applying spatial + in such cases will partial out the spatial dependence and remove the spurious interaction effects. Methods Simulation of movement trajectories In the Agent-Based Model (ABM) two individuals move according to a biased correlated random walk in discrete time. We model a high persistency in the movement of both individuals that is a high correlation in their facing direction. There are two different mechanisms that generate the biased movement: either through an attraction towards another moving individual or through the attraction to the environmental surroundings. Both these biases in movement direction are considered as interactions (with conspecifics and with the environment, respectively) in our simulation. The individuals are moving within an area of a fixed size with reflecting borders (the area modelled is rather large and encounters with borders are rare). Four different scenarios are then devised in which the individuals interact with their environment (Fig. 1 A-D). The detailed model description follows the Overview, Design, concepts, Details (ODD) protocol (Supporting information) by Grimm et al. (2006) and updated (Grimm et al. 2020). Interaction with environmental surroundings Individuals can interact with their environmental surroundings while moving (Fig. 1 A-C), i.e. are attracted (towards a resource) or avoid (barriers); or do not interact (i.e. purely perform correlated random walk). In these scenarios both individuals are not directly interacting with each other, yet their resulting movement trajectories are correlated due to them responding to the environmental surroundings in the same way. We generated three scenarios of interactions of both individuals with environments (Fig. 1 , A-C). For two scenarios, we used a grid-based environment in which each cell reflects habitat suitability. The values of habitat suitability range from zero to one. In the first scenario A, we model a gradient of habitat suitability with habitat suitability increasing linearly from the west to the east of the simulated area (Fig. 1 , A.a) or increasing linearly from the borders towards the centre (Fig. 1 , A.b). For the second scenario B, the grid cells were assigned with a value generated with the Perlin noise function. The Perlin noise is used to generate not completely random values (Perlin 1985) and is helpful to create procedurally generated landscapes. This produces patches of grid cells with values similar to each other, which gives the appearance of more naturally clustered patchy landscapes compared to full randomness (Fig. 1 , B). For the scenarios A & B, the moving individuals evaluate the cells within their perceptual range and bias their movement towards the cell with the highest value. The Perlin noise function is also used to generate the barriers for the third scenario C, which blocks the path of the individuals (Fig. 1 , C). In this case, the barrier cells receive a value which is avoided by the individuals. The individuals do not express any preference towards a particular grid cell value, but only move according to the correlated random walk and are repulsed by the barriers (turn in the direction opposite of their intended movement direction). For the scenarios A & B the simulations were run with 20 repetitions. For the scenario C the proportion of barriers in the landscape was continually varied from 0 % − 75 % of he totl landscape area with 0.5 % steps, reslting in 150 barrier landscapes. Interaction with other individuals In the scenario D both individuals are attracted towards each other but do not interact with their environmental surroundings (Fig. 1 , D). They both move according to a correlated random walk while they express a positive bias towards each other resulting in them moving as a pair within the environment. The simulation was run for 20 repetitions, each with a new generated landscape structure. Statistical methods for inferring interactions from movement data For a comprehensive description and a summary table of the statistical methods employed in this study, please refer to the Supplementary Methods section. Dynamic interaction index (DI) The DI index measures the cohesiveness of simultaneous movement vectors with respect to two independent components of movement: distance (also called displacement) and direction (DI; Long and Nelson 2013). Values for DI range from − 1 and 1 where negative values correspond to repulsive movement paths (opposite direction) and positive values indicate cohesive movement paths (in same direction). Values around 0 indicate neutral movement. SSF-based approaches The SSFs compare observed movement steps of a focal individual to available steps in terms of certain covariates, which allows to quantify a preference for these covariates (usually environmental variables). The step lengths and turning angles for the available steps were drawn from a Gamma and von Mises distribution, respectively, of which the parameter estimates were obtained from the observed steps (Forester et al. 2009). In this study 20 available steps were used. The estimation of selection coefficients was done using a conditional logistic regression, allowing to compare each used step to a different set of available steps. In other words, the available steps depend on the location and movement characteristics of the individual (temporally varying set of available steps). Positive coefficients indicate attraction and negative coefficients indicate repulsion, while zero indicates no detectable preference for the covariates. The SSF-based approach by (Schlaegel et al. 2019) uses as a covariate dynamic occurrence distributions (OD) of other individuals (Fleming et al. 2015) and is referred to as SSF-OD approach in this study. The second SSF-based approach we use is a modification of SSF-OD that, instead of the occurrence distribution, uses distances between individuals (DIST) as covariates in SSFs (Roeleke et al. 2022). We refer to this approach as SSF-DIST. Spatial+ Spatial confounding (collinearity/non-independence between the covariate of interest and unmeasured spatial effect) is often an issue when working with spatial data and can lead to biases in the estimated covariate effects. Spatial+ (Dupont et al. 2022) is used to reduce this bias, by reducing the spatial dependence of the covariate, which is done in two steps. Firstly, the spatial dependence is regressed away by using the covariate of interest as response variable and the spline of coordinates as independent predictor. In the second step, the residuals obtained in the first step are used as covariates (corrected covariate) in the SSF. This approach was only used for the SSFs and not DI, because no environmental covariates can be included as predictors in DI. Evaluating method performance We assessed the performance of the method by focusing on the power of the methods to detect true interaction and by evaluating type 1 error for wrongly detected interactions. We used the p-values of each method to validate its outcome to be significant (< 0.05) or not. The proportion of correctly estimated interactions was then used as a metric indicative of the method performance. We define “correctly estimated interactions” as cases where the effect of another individual on the movement of the focal individual was assessed as being significant when inter-individual interactions were indeed present and the failure to detect the effect of another individual when inter-individual interactions were indeed absent. For the scenarios in which the correlated movement is resulting from the effect of the physical environment (scenarios A, B, C) the estimate of inter-individual interaction should not be significant, while the estimate of environmental effect should be significant. The opposite is the case for the scenario D, in which the correlated movement is resulting from individual interactions. For both SSF-based approaches we fit three different models. In the first model we use occurrence distribution of (SSF-OD) and the distance to (SSF-DIST) the non-focal individual as well as the physical environment as predictors. In the other two models we did not include the physical environment as predictor in the model, which reflects the situation when no environmental data are available for the field researchers to include as a covariate (or, the available environmental data that can be included in the analyses are not relevant for the movement of the individuals). In the second model we only included occurrence distribution of (SSF-OD) and the distance to (SSF-DIST) the non-focal individual as a predictor and in the third model we applied spatial + to the second model. Observed correlated movement arises from interaction with environmental surroundings We expect positive signifant DI indices (type I error). Regarding both SSFs, we expect for model 2 to wrongly detect interactions between individuals (type I error) and thus the coefficient to be positive and significant. If we apply spatial+ (model 3), we expect the coefficients to become non-significant for the SSFs. For model 1 that includes also habitat quality as predictor in the analysis, we expect the two SSF-based approaches to correctly detect an attraction towards the physical enviornment as well as no interactions between the individuals. Observed correlated movement arises from direct interactions of individuals We expect positive significant indices from DI. For the SSFs, we expect that all three models 1, 2 & 3 will correctly detect individual interactions, that is the coefficients will be positive and significant. We also expect the coefficents associated with environmental predictor to be non-significant for model 1. Results 1. Correlated Movement caused by the resource gradient a) Moving next to each other In the scenario A.a where both individuals were moving next two each other along a habitat quality gradient, DI correctly detected no interactions between individuals. For model 2 (DIST/OD as predictor) SSF-OD correctly detected no individual interactions while SSF-DIST detected significant individual interactions. Applying spatial + to the SSF-OD reduced the variance among the interaction estimates. For SSF-DIST, applying spatial + prior to fitting the SSF (model 3) resulted in removing the spurious effect of the individual interaction covariate (Fig. 2 , Fig. 3 ). The full model 1 (DIST/OD and landscape as predictor) for both SSFs correctly revealed significant landscape estimates and non-significant interaction estimates. b) Moving from opposite locations towards the resource in the centre DI correctly detected no interactions of individuals. For model 2 (DIST/OD as predictor) SSF-DIST detected individual interactions. Applying spatial + to SSF-DIST removed the effect of the DIST covariate and thus the inter-individual interaction estimates became non-significant (Fig. 2 , Fig. 4 ). Due to high correlation between both predictors in model 1 (DIST & landscape as predictor), fitting the full model was not possible. Therefore, in this scenario model 1 was only fitted with the landscape covariate as predictor. For both SSFs model 1 estimated landscape effect as significant. For SSF-OD both models 2 and 3 were not shown as SSF-OD is unable to accurately estimate the inter-individual interaction coefficient when their movement paths do not overlap. 2. Correlated movement caused by the patchy landscape DI mostly correctly detected the absence of interactions between the two individuals. For model 2 (DIST/OD as predictor) SSF-DIST, and especially, SSF-OD, erroneously detected significant inter-individual interactions. Applying spatial+ (model 3) to the both SSFs resulted in removing the spurious effect of the individual interaction covariate (Fig. 1 ; Fig. 5 ). The full model 1 (DIST/OD & landscape as predictor) fitted for both SSFs mostly correctly assessed landscape estimates as being significant and interaction estimates as non-significant. 3. Correlated movement caused by avoiding barriers The percentage of barriers in the landscape did not affect the performance of DI (Fig. 6 , A). As the percentage of barriers increased in the landscape, SSF-OD and SSF-DIST falsely detected increasing number of interactions between the individuals, where in fact there were none. This effect was mostly pronounced for SSF-OD (Fig. 6 , B). Applying spatial + effectively improved the performance of SSF-OD, as fewer significant interaction estimates were detected under higher percentage of barriers in landscapes. However, this was not the case for SSF-DIST, as the number of significant interaction estimates (false positives) did not decrease after applying spatial+. In this case significant estimates were detected irrespective of the proportion of the barriers i.e. also at low proportion of barriers. D) Correlated movement caused by individual interactions All three methods correctly detected individual interactions, yielding significant positive estimates (Fig. 2 , Fig. 7 ). Applying spatial + did not change this outcome. Furthermore, both SSF-based approaches correctly detected significant interaction estimates and non- significant landscape estimates in the full model (Fig. 7 ). Discussion Here we assessed how heterogenous environment affects the inference of inter-individual-interactions from movement data. One of the commonly used indices DI performed well, but it does not consider the physical environment at all. On the contrary, SSFs allow disentangling the effects of direct inter-individual interactions (i.e. social factors) from environmental effects (i.e. physical factors) on the movement of individuals. Including the physical environment as a predictor in SSFs increased the performance by decreasing the rate of false positives. A similar effect was achieved by applying Spatial + to SSFs that only included the movement of other individuals as covariate. In our scenarios A.a and A.b in which the simulated animals do not interact with each other directly but move persistently along a linear habitat gradient, we have shown that neglecting the physical environment results in falsely detecting interactions between the two individuals by SSF-DIST. Including the landscape as a covariate in the step selection function reduced the rates of falsely detected inter-individual-interactions. However, including both the social and physical environment as predictors in the model is not always possible, since they can become highly collinear. For instance, we simulated such a collinearity in our scenario A.b in which two individuals move from opposite locations towards the same resource in the middle, such that the value of the habitat quality increases while the distance to the other individual decreases. In such cases, revealing the true effect will be difficult and the focus should be on gaining understanding of how animals interact with their environment prior to analysing inter-individual interactions. Especially when interested in commuting, dispersal or migration movements, persistent movement along linear habitat gradients/features can occur regularly (Owen-Smith et al. 2020; Bedrosian et al. 2018; Fryxell and Avgar 2012; Hahn et al. 2008). For instance, in animals such as caribou the movement is strongly attributed to seasonal environmental conditions, resulting in following the vegetative growth during spring (Avgar et al. 2013; Fryxell and Avgar 2012). Other examples of such movement patterns are found in savannas where different herbivores are attracted to the same food/water resources forming big aggregations of different species moving together (Fryxell and Sinclair 1988). In such cases the landscape is the reason for the correlation in movement trajectories of individuals. While it is acknowledged that animal space use is affected by both inter-individual-interactions as well as the physical environment, it is often not addressed by leaving the physical descriptors out of the analyses, especially when inter-individual interactions are the point of interest. Yet, neglecting the physical environment could result in a so-called spatial cofounding, meaning the covariate of interest (here: coefficient of inter-individual interaction) is spatially dependant, thus resulting in unreliable estimates (Arce Guillen et al. 2023; Urdangarin et al. 2023; Gilbert et al. 2021). In such cases when no environmental data is available, applying spatial + in addition to the step selection function allows to reduce spatial cofounding in animal movement and leads to an improved inference of inter-individual-interactions, according to our findings. Furthermore, a extension of SSFs, called iSSFs, can be used instead (Avgar et al. 2016; Fieberg et al. 2021) in which in addition to estimating the effects of physical and social environment on movement preferences of the individuals, also the effects of those environments on step length and turning angles can be estimated, allowing to infer the movement characteristics of the animals. In the scenario B, in which the physical environment consists of a patchy landscape, we found similar responses as in the two first scenarios A.a and A.b. When the environmental landscape was neglected, all three methods falsely detected a high rate of interactions between the individuals. Including the physical environment as a covariate reduced the rate of false positives for the SSFs. Also, in case no environment data were included in the analysis, applying spatial + with the SSFs reduced the spurious inflation of inter-individual interactions induced by the environment. The movements modelled in such a patchy landscape reflect movements during foraging behaviour of animals, which are expressed by many animals on a daily basis, with many species being attracted to the same resource (Owen-Smith et al. 2020; Abrahms et al. 2021). Zebrafish use a combination of the physical and social environment to increase their foraging efficiency (Harpaz and Schneidman 2020). An aggregation of zebrafishes at a food resource could therefore primarily result from the attraction towards the same resource. This reinforces the difficulty to distinguish whether the physical or the biotic environment affected the movement, since the physical environment can act as attractor or facilitator. Moreover, animals change how they interact with their physical and biotic environment over time. Such switches in behaviours could be detected by applying HMM-SSF(Pohle et al. 2024; Klappstein et al. 2024) which is a new approach that contributes to better inference of inter-individual interactions, as it allows detecting changes in behavioural states due to the environment. This allows then to split the movement trajectory into meaningful chunks depending on their behavioural states. In the scenario C we revealed the emerging bias of correlated movements due to increasing habitat fragmentation. For both SSFs, with increasing proportion of obstacles (non-favourable elements) in the landscape, an increase in falsely detected social interactions was observed. Applying spatial + was again successful in removing this spatial cofounding when applied to SSF-OD, reducing the rates of falsely detected social interactions. This finding is of high importance when analysing individual movement in fragmented landscapes. As the landscape fragmentation increases, hostile matrix acting as a barrier becomes larger and thus the space use of animals becomes restricted to smaller areas (Eycott et al. 2012). This then results in a higher overlap in movement paths of individuals, causing higher correlation in their movement trajectories that is not necessarily due to the direct interactions between individuals. Furthermore linear features in the landscape used by many animals(Dickie et al. 2020) can cause such correlations in animal movement. For example, corridors in highly fragmented landscapes act as “drift fences”, intercepting and redirecting the movement of different animals (Haddad et al. 2003), thus potentially increasing the risk of detecting interactions between individuals that might only be due to them using the same space. Wildlife crossings such as green bridges over highways, used by wolves, dears and boars (Plaschke et al. 2021), might also increase the potential of spuriously detecting inter-individual interactions. Another example of animals using linear structures as guidance for navigation are golden eagles who use the Rocky Mountain range to migrate to the north (Bedrosian et al. 2018). Thus, including such landscape structure as a covariate in the analyses is of high importance to account for this bias. However, one must be careful when interpreting the estimates of an SSF. In case an animal uses an environmental structure as guidance and not as a resource, for example boars moving along forest patches(Thurfjell et al. 2009) but never entering that landscape structure, the SSFs will detect an avoidance of that structure (Thurfjell et al. 2014). In scenario D we have shown that including physical environmental data as predictors in the model does not worsen the inference of inter-individual interactions. We advise that field ecologists should be more cautious about false positives, as it seems that false negatives are less likely to be of an issue than false positives in a heterogenous landscape, at least in the investigated scenarios. The addressed three methods (Long and Nelson 2013, Schlaegel et al. 2019, Roeleke et al. 2022), as well as the recently published methods considering the behavioural states of the animals (Pohle et al. 2024; Klappstein et al. 2024), show promising results in dealing with confounding factors when assessing inter-individual interactions of moving individuals. We show that especially when the physical environment strongly affects the animal movement, including physical environmental data or applying spatial+(Dupont et al. 2022) is essential to improve inference of inter-individual interactions and avoid detection of spurious effects. The inclusion of relevant physical environment descriptors as predictors in the model hinges on the prior knowledge of the resource use by the study species and detailed understanding of its spatial ecology. We suggest that, when interested in inter-individual interactions, collecting movement data should, whenever possible, be accompanied by the collection of environmental data relevant to the study species. Declarations Acknowledgements This work was supported by Deutsche Forschungsgemeinschaft in the framework of the BioMove Research Training Group. We thank the colleagues from the Department of Ecological Dynamics (IZW) for constructive feedback on our manuscript. Funding This work was funded by the “Deutsche Forschungsgemeinschaft (DFG)“ in the framework of the BioMove Research Training Group. Author contribution Thibault Fronville, Viktoriia Radchuk, Stephanie Kramer-Schadt, Florian Jeltsch and Niels Blaum conceived the ideas and designed methodology. Thibault Fronville simulated the data and analysed the data. Thibault Fronville and Viktoriia Radchuk led the writing of the manuscript. All authors contributed critically to the drafts and gave final approval for publication. Conflict of interest The authors have no conflicts of interest to declare. Ethics and consent Ethics and Consent to Participate declarations: not applicable References Abrahms, Briana; Aikens, Ellen O.; Armstrong, Jonathan B.; Deacy, William W.; Kauffman, Matthew J.; Merkle, Jerod A. (2021): Emerging Perspectives on Resource Tracking and Animal Movement Ecology. In Trends in ecology & evolution 36 (4), pp. 308–320. DOI: 10.1016/j.tree.2020.10.018. Arce Guillen, Rafael; Lindgren, Finn; Muff, Stefanie; Glass, Thomas W.; Breed, Greg A.; Schlägel, Ulrike E. (2023): Accounting for unobserved spatial variation in step selection analyses of animal movement via spatial random effects. In Methods Ecol Evol 14 (10), pp. 2639–2653. DOI: 10.1111/2041-210X.14208. Avgar, Tal; Mosser, Anna; Brown, Glen S.; Fryxell, John M. (2013): Environmental and individual drivers of animal movement patterns across a wide geographical gradient. In Journal of Animal Ecology 82 (1), pp. 96–106. DOI: 10.1111/j.1365-2656.2012.02035.x. Avgar, Tal; Potts, Jonathan R.; Lewis, Mark A.; Boyce, Mark S. (2016): Integrated step selection analysis: bridging the gap between resource selection and animal movement. In Methods Ecol Evol 7 (5), pp. 619–630. DOI: 10.1111/2041-210X.12528. Banks, Sam C.; Piggott, Maxine P.; Stow, Adam J.; Taylor, Andrea C. (2007): Sex and sociality in a disconnected world: a review of the impacts of habitat fragmentation on animal social interactions. In Can. J. Zool. 85 (10), pp. 1065–1079. DOI: 10.1139/Z07-094. Barrio, Isabel C.; Hik, David S. (2013): Good neighbours? Determinants of aggregation and segregation among alpine herbivores. In Écoscience 20 (3), pp. 276–282. DOI: 10.2980/20-3-3595. Bastille-Rousseau, Guillaume; Potts, Jonathan R.; Yackulic, Charles B.; Frair, Jacqueline L.; Ellington, E. Hance; Blake, Stephen (2016): Flexible characterization of animal movement pattern using net squared displacement and a latent state model. In Movement ecology 4, p. 15. DOI: 10.1186/s40462-016-0080-y. Bedrosian, Bryan E.; Domenech, Robert; Shreading, Adam; Hayes, Matthew M.; Booms, Travis L.; Barger, Christopher R. (2018): Migration corridors of adult Golden Eagles originating in northwestern North America. In PLoS ONE 13 (11), e0205204. DOI: 10.1371/journal.pone.0205204. Calabrese, Justin M.; Fleming, Christen H.; Fagan, William F.; Rimmler, Martin; Kaczensky, Petra; Bewick, Sharon et al. (2018): Disentangling social interactions and environmental drivers in multi-individual wildlife tracking data. In Philosophical transactions of the Royal Society of London. Series B, Biological sciences 373 (1746). DOI: 10.1098/rstb.2017.0007. Cote, J.; Clobert, J. (2007): Social information and emigration: lessons from immigrants. In Ecology letters 10 (5), pp. 411–417. DOI: 10.1111/j.1461-0248.2007.01032.x. Dickie, Melanie; McNay, Scott R.; Sutherland, Glenn D.; Cody, Michael; Avgar, Tal (2020): Corridors or risk? Movement along, and use of, linear features varies predictably among large mammal predator and prey species. In Journal of Animal Ecology 89 (2), pp. 623–634. DOI: 10.1111/1365-2656.13130. Dupont, Emiko; Wood, Simon N.; Augustin, Nicole H. (2022): Spatial+: A novel approach to spatial confounding. In Biometrics 78 (4), pp. 1279–1290. DOI: 10.1111/biom.13656. Eycott, Amy E.; Stewart, Gavin B.; Buyung-Ali, Lisette M.; Bowler, Diana E.; Watts, Kevin; Pullin, Andrew S. (2012): A meta-analysis on the impact of different matrix structures on species movement rates. In Landscape Ecol 27 (9), pp. 1263–1278. DOI: 10.1007/s10980-012-9781-9. Fieberg, John; Signer, Johannes; Smith, Brian; Avgar, Tal (2021): A 'How to' guide for interpreting parameters in habitat-selection analyses. In Journal of Animal Ecology 90 (5), pp. 1027–1043. DOI: 10.1111/1365-2656.13441. Fleming, C. H.; Fagan, W. F.; Mueller, T.; Olson, K. A.; Leimgruber, P.; Calabrese, J. M. (2015): Rigorous home range estimation with movement data: a new autocorrelated kernel density estimator. In Ecology 96 (5), pp. 1182–1188. DOI: 10.1890/14-2010.1. Forester, James D.; Im, Hae Kyung; Rathouz, Paul J. (2009): Accounting for animal movement in estimation of resource selection functions: sampling and data analysis. In Ecology 90 (12), pp. 3554–3565. DOI: 10.1890/08-0874.1. Fortin, Daniel; Beyer, Hawthorne L.; Boyce, Mark S.; Smith, Douglas W.; Duchesne, Thierry; Mao, Julie S. (2005): WOLVES INFLUENCE ELK MOVEMENTS: BEHAVIOR SHAPES A TROPHIC CASCADE IN YELLOWSTONE NATIONAL PARK. In Ecology 86 (5), pp. 1320–1330. DOI: 10.1890/04-0953. Fortin, Daniel; Buono, Pietro-Luciano; Fortin, André; Courbin, Nicolas; Tye Gingras, Christian; Moorcroft, Paul R. et al. (2013): Movement responses of caribou to human-induced habitat edges lead to their aggregation near anthropogenic features. In The American naturalist 181 (6), pp. 827–836. DOI: 10.1086/670243. Fronville, Thibault; Blaum, Niels; Kramer‐Schadt, Stephanie; Schlägel, Ulrike; Radchuk, Viktoriia (2024): Performance of five statistical methods to infer interactions among moving individuals in a predator–prey system. In Methods Ecol Evol 15 (6), pp. 1097–1112. DOI: 10.1111/2041-210X.14323. Fryxell, J. M.; Sinclair, A. R. (1988): Causes and consequences of migration by large herbivores. In Trends in ecology & evolution 3 (9), pp. 237–241. DOI: 10.1016/0169-5347(88)90166-8. Fryxell, John M.; Avgar, Tal (2012): Animal migration: Catching the wave. In Nature 490 (7419), pp. 182–183. DOI: 10.1038/490182a. Gilbert, Brian; Datta, Abhirup; Casey, Joan A.; Ogburn, Elizabeth L. (2021): A causal inference framework for spatial confounding. Grimm, Volker; Berger, Uta; Bastiansen, Finn; Eliassen, Sigrunn; Ginot, Vincent; Giske, Jarl et al. (2006): A standard protocol for describing individual-based and agent-based models. In Ecological Modelling 198 (1-2), pp. 115–126. DOI: 10.1016/j.ecolmodel.2006.04.023. Grimm, Volker; Railsback, Steven F.; Vincenot, Christian E.; Berger, Uta; Gallagher, Cara; DeAngelis, Donald L. et al. (2020): The ODD Protocol for Describing Agent-Based and Other Simulation Models: A Second Update to Improve Clarity, Replication, and Structural Realism. In JASSS 23 (2), Article 7. DOI: 10.18564/jasss.4259. Haddad, Nick M.; Bowne, David R.; Cunningham, Alan; Danielson, Brent J.; Levey, Douglas J.; Sargent, Sarah; Spira, Tim (2003): Corridor Use by Diverse Taxa. In Ecology 84 (3), pp. 609–615. DOI: 10.1890/0012-9658(2003)084[0609:CUBDT]2.0.CO;2. Hahn, Thomas P.; Cornelius, Jamie M.; Sewall, Kendra B.; Kelsey, T. Rodd; Hau, Michaela; Perfito, Nicole (2008): Environmental regulation of annual schedules in opportunistically-breeding songbirds: adaptive specializations or variations on a theme of white-crowned sparrow? In General and comparative endocrinology 157 (3), pp. 217–226. DOI: 10.1016/j.ygcen.2008.05.007. Harpaz, Roy; Schneidman, Elad (2020): Social interactions drive efficient foraging and income equality in groups of fish. In eLife 9. DOI: 10.7554/eLife.56196. Haydon, Daniel T.; Morales, Juan M.; Yott, Adelle; Jenkins, Deborah A.; Rosatte, Rick; Fryxell, John M. (2008): Socially informed random walks: incorporating group dynamics into models of population spread and growth. In Proceedings. Biological sciences 275 (1638), pp. 1101–1109. DOI: 10.1098/rspb.2007.1688. He, Peng; Maldonado-Chaparro, Adriana A.; Farine, Damien R. (2019): The role of habitat configuration in shaping social structure: a gap in studies of animal social complexity. In Behav Ecol Sociobiol 73 (1). DOI: 10.1007/s00265-018-2602-7. Herbert-Read, James E.; Rosén, Emil; Szorkovszky, Alex; Ioannou, Christos C.; Rogell, Björn; Perna, Andrea et al. (2017): How predation shapes the social interaction rules of shoaling fish. In Proceedings. Biological sciences 284 (1861). DOI: 10.1098/rspb.2017.1126. Isbell, Lynne A. (1991): Contest and scramble competition: patterns of female aggression and ranging behavior among primates. In Behavioral Ecology 2 (2), pp. 143–155. DOI: 10.1093/beheco/2.2.143. Klappstein, Natasha J.; Michelot, Théo; Fieberg, John; Pedersen, Eric J.; Mills Flemming, Joanna (2024): Step selection functions with non‐linear and random effects. In Methods Ecol Evol 15 (8), pp. 1332–1346. DOI: 10.1111/2041-210X.14367. Laundre, John W.; Hernandez, Lucina; Ripple, William J. (2010): The Landscape of Fear: Ecological Implications of Being Afraid~!2009-09-09~!2009-11-16~!2010-02-02~! In TOECOLJ 3 (3), pp. 1–7. DOI: 10.2174/1874213001003030001. Long, Jed A.; Nelson, Trisalyn A. (2013): Measuring Dynamic Interaction in Movement Data. In Transactions in GIS 17 (1), pp. 62–77. DOI: 10.1111/j.1467-9671.2012.01353.x. Long, Jed A.; Nelson, Trisalyn A.; Webb, Stephen L.; Gee, Kenneth L. (2014): A critical examination of indices of dynamic interaction for wildlife telemetry studies. In The Journal of animal ecology 83 (5), pp. 1216–1233. DOI: 10.1111/1365-2656.12198. Luca Bastianelli, Matteo; Hoermann, Christian von; Kirchner, Katrin; Signer, Johannes; Dupke, Claudia; Henrich, Maik et al. (2024): Risk response towards roads is consistent across multiple species in a temperate forest ecosystem. In Oikos 2024 (7), Article e10433. DOI: 10.1111/oik.10433. Marescot, Lucile; Franz, Mathias; Benhaiem, Sarah; Hofer, Heribert; Scherer, Cédric; East, Marion L.; Kramer-Schadt, Stephanie (2021): 'Keeping the kids at home' can limit the persistence of contagious pathogens in social animals. In The Journal of animal ecology 90 (11), pp. 2523–2535. DOI: 10.1111/1365-2656.13555. Miller, Jennifer R. B.; Ament, Judith M.; Schmitz, Oswald J. (2014): Fear on the move: predator hunting mode predicts variation in prey mortality and plasticity in prey spatial response. In Journal of Animal Ecology 83 (1), pp. 214–222. DOI: 10.1111/1365-2656.12111. Nathan, Ran; Getz, Wayne M.; Revilla, Eloy; Holyoak, Marcel; Kadmon, Ronen; Saltz, David; Smouse, Peter E. (2008): A movement ecology paradigm for unifying organismal movement research. In Proceedings of the National Academy of Sciences of the United States of America 105 (49), pp. 19052–19059. DOI: 10.1073/pnas.0800375105. Nathan, Ran; Monk, Christopher T.; Arlinghaus, Robert; Adam, Timo; Alós, Josep; Assaf, Michael et al. (2022): Big-data approaches lead to an increased understanding of the ecology of animal movement. In Science (New York, N.Y.) 375 (6582), eabg1780. DOI: 10.1126/science.abg1780. Niu, Mu; Blackwell, Paul G.; Skarin, Anna (2016): Modeling interdependent animal movement in continuous time. In Biometrics 72 (2), pp. 315–324. DOI: 10.1111/biom.12454. Owen‐Smith, Norman; Hopcraft, Grant; Morrison, Thomas; Chamaillé‐Jammes, Simon; Hetem, Robyn; Bennitt, Emily; van Langevelde, Frank (2020): Movement ecology of large herbivores in African savannas: current knowledge and gaps. In Mammal Review 50 (3), pp. 252–266. DOI: 10.1111/mam.12193. Perlin, Ken (1985): An image synthesizer. In SIGGRAPH Comput. Graph. 19 (3), pp. 287–296. DOI: 10.1145/325165.325247. Pinter-Wollman, Noa; Fiore, Stephen M.; Theraulaz, Guy (2017): The impact of architecture on collective behaviour. In Nature ecology & evolution 1 (5), p. 111. DOI: 10.1038/s41559-017-0111. Plaschke, Mike; Bhardwaj, Manisha; König, Hannes J.; Wenz, Elena; Dobiáš, Kornelia; Ford, Adam T. (2021): Green bridges in a re‐colonizing landscape: Wolves (Canis lupus ) in Brandenburg, Germany. In Conservat Sci and Prac 3 (3), Article e364. DOI: 10.1111/csp2.364. Pohle, Jennifer; Signer, Johannes; Eccard, Jana A.; Dammhahn, Melanie; Schlägel, Ulrike E. (2024): How to account for behavioral states in step-selection analysis: a model comparison. In PeerJ 12, e16509. DOI: 10.7717/peerj.16509. Roeleke, Manuel; Schlaegel, Ulrike E.; Gallagher, Cara; Pufelski, Jan; Blohm, Torsten; Nathan, Ran et al. (2022): Insectivorous bats form mobile sensory networks to optimize prey localization: The case of the common noctule bat. In Proceedings of the National Academy of Sciences of the United States of America 119 (33), e2203663119. DOI: 10.1073/pnas.2203663119. Schlaegel, Ulrike E.; Grimm, Volker; Blaum, Niels; Colangeli, Pierluigi; Dammhahn, Melanie; Eccard, Jana A. et al. (2020): Movement-mediated community assembly and coexistence. In Biological reviews of the Cambridge Philosophical Society 95 (4), pp. 1073–1096. DOI: 10.1111/brv.12600. Schlaegel, Ulrike E.; Signer, Johannes; Herde, Antje; Eden, Sophie; Jeltsch, Florian; Eccard, Jana A.; Dammhahn, Melanie (2019): Estimating interactions between individuals from concurrent animal movements. In Methods Ecol Evol 10 (8), pp. 1234–1245. DOI: 10.1111/2041-210X.13235. Spiegel, Orr; Leu, Stephan T.; Sih, Andrew; Bull, C. Michael (2016): Socially interacting or indifferent neighbours? Randomization of movement paths to tease apart social preference and spatial constraints. In Methods Ecol Evol 7 (8), pp. 971–979. DOI: 10.1111/2041-210X.12553. Strandburg-Peshkin, Ariana; Farine, Damien R.; Crofoot, Margaret C.; Couzin, Iain D. (2017): Habitat and social factors shape individual decisions and emergent group structure during baboon collective movement. In eLife 6. DOI: 10.7554/eLife.19505. Tang, Wenwu; Bennett, David A. (2010): Agent-based Modeling of Animal Movement: A Review. In Geography Compass 4 (7), pp. 682–700. DOI: 10.1111/j.1749-8198.2010.00337.x. Thurfjell, Henrik; Ball, John P.; Åhlén, Per-Arne; Kornacher, Peter; Dettki, Holger; Sjöberg, Kjell (2009): Habitat use and spatial patterns of wild boar Sus scrofa (L.): agricultural fields and edges. In Eur J Wildl Res 55 (5), pp. 517–523. DOI: 10.1007/s10344-009-0268-1. Thurfjell, Henrik; Ciuti, Simone; Boyce, Mark S. (2014): Applications of step-selection functions in ecology and conservation. In Movement ecology 2 (1), p. 4. DOI: 10.1186/2051-3933-2-4. Urdangarin, Arantxa; Goicoa, Tomás; Ugarte, María Dolores (2023): Evaluating recent methods to overcome spatial confounding. In Rev Mat Complut 36 (2), pp. 333–360. DOI: 10.1007/s13163-022-00449-8. Valeix, Marion; Loveridge, Andrew J.; Davidson, Zeke; Madzikanda, Hillary; Fritz, Hervé; Macdonald, David W. (2010): How key habitat features influence large terrestrial carnivore movements: waterholes and African lions in a semi-arid savanna of north-western Zimbabwe. In Landscape Ecol 25 (3), pp. 337–351. DOI: 10.1007/s10980-009-9425-x. van Schaik, C. P. (1983): Why Are Diurnal Primates Living in Groups? In Behav 87 (1-2), pp. 120–144. DOI: 10.1163/156853983X00147. Wilson; Richards (2000): Consuming and grouping: recource‐mediated animal aggregation. In Ecology letters 3 (3), pp. 175–180. DOI: 10.1046/j.1461-0248.2000.00135.x. Additional Declarations No competing interests reported. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-5396058","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":381513478,"identity":"60ae7ca6-ff18-4e4c-9462-91f184463c25","order_by":0,"name":"Thibault Fronville","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA8UlEQVRIie3OMWvCQBTA8XccmOVR1xcU/QqRQOsQ6le5IMRFoVPWRgLJVwj4ZSIHdhF30aEQyGxxldZLGgeHC3brcP/h7nHw4x2AyfQPs6LqdMZ9sJbVmKsnpoaOnmBeE0LAdUP4QwQUIQENqe420pObAt8Iu3YRnxGOg5eYJ58QenryFMxcVB+zV37kIpRuX7LUgV2gJRPEZztTxDn40XTxLf2Ms4RYIvVbbmSyX0dyDvK9IT+thE7VFmLLWBFBvyRvIZ2gJrT1Y36BclRvEbtpC+EbEhdv0E0/iq8MjkOy0pJO4auWaBJ/BSaTyWS66wpV50Yf+eWyrwAAAABJRU5ErkJggg==","orcid":"","institution":"Leibniz Institute for Zoo and Wildlife Research","correspondingAuthor":true,"prefix":"","firstName":"Thibault","middleName":"","lastName":"Fronville","suffix":""},{"id":381513479,"identity":"3956e868-acb4-4908-9c52-3f7dad12331f","order_by":1,"name":"Niels Blaum","email":"","orcid":"","institution":"University of Potsdam","correspondingAuthor":false,"prefix":"","firstName":"Niels","middleName":"","lastName":"Blaum","suffix":""},{"id":381513481,"identity":"301b93e1-4bb3-42ef-897e-dab1368de600","order_by":2,"name":"Florian Jeltsch","email":"","orcid":"","institution":"University of Potsdam","correspondingAuthor":false,"prefix":"","firstName":"Florian","middleName":"","lastName":"Jeltsch","suffix":""},{"id":381513484,"identity":"d3d20788-88d0-45b5-aa0b-1a3ea5614631","order_by":3,"name":"Stephanie Kramer-Schadt","email":"","orcid":"","institution":"Leibniz Institute for Zoo and Wildlife Research","correspondingAuthor":false,"prefix":"","firstName":"Stephanie","middleName":"","lastName":"Kramer-Schadt","suffix":""},{"id":381513485,"identity":"0e665fee-9714-41f1-929a-3a3176c7100b","order_by":4,"name":"Viktoriia Radchuk","email":"","orcid":"","institution":"Leibniz Institute for Zoo and Wildlife Research","correspondingAuthor":false,"prefix":"","firstName":"Viktoriia","middleName":"","lastName":"Radchuk","suffix":""}],"badges":[],"createdAt":"2024-11-05 14:08:26","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-5396058/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-5396058/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1186/s40462-025-00567-0","type":"published","date":"2025-06-12T15:57:59+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":69800859,"identity":"56a45ee8-8945-4eab-9bd7-c590b55b8288","added_by":"auto","created_at":"2024-11-25 11:03:01","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":309347,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cem\u003eSchematic representation of the four scenarios: Panels A-C show correlated movements of two individuals caused by habitat quality and barriers (no social interaction). A.a: moving next to each other along a linear resource gradient, A.b: moving from opposite initial locations towards the resource in the centre. B: moving in a realistic landscape where resources are clustered in space. C: Movement in a homogeneous matrix with barriers randomly scattered in the landscape blocking the movement o findividuals. In Panel D the two individuals are attracted to each other and move as a group in the landscape, irrespective of habitat quality or other features. The violet and blue arrows depict the movement path of two individuals, the direction shown by the arrow. In panel A, B and D each grid cell reflects habitat quality that ranges from zero (orange) to one (green). Panel C shows the matrix in grey and the barriers, which are avoided by the individuals, in black.\u003c/em\u003e\u003c/p\u003e","description":"","filename":"floatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-5396058/v1/25e1af0d9086000a82f1be14.png"},{"id":69800858,"identity":"8dc3970d-a9e1-4fad-89e2-59c89bb23e6d","added_by":"auto","created_at":"2024-11-25 11:03:01","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":61465,"visible":true,"origin":"","legend":"\u003cp\u003eFor each scenario, the proportion of cases in which DI, SSF-OD and SSF-DIST methods correctly detected whether the interactions are present are shown. For both SSFs three models were fitted; (1) a full model with OD/DIST and landscape used as covariates, (2) OD/DIST used as covariate, (3) Spatial+ was applied prior to fitting the model 2. Columns with “Interaction” indicate the interaction between two individuals, while columns with “Landscape” indicate the attraction of the individual towards the landscape features. Cells with “-” indicate cases in which models could not be fitted (See text).\u003c/p\u003e","description":"","filename":"floatimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-5396058/v1/3ca3c3d620e1604d45ec73cb.png"},{"id":69801884,"identity":"9dfef4f3-57e4-4e1f-b32f-35b5ee5da9a6","added_by":"auto","created_at":"2024-11-25 11:11:01","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":62461,"visible":true,"origin":"","legend":"\u003cp\u003ePerformance of three statistical methods when applied to movement data generated under scenario A.a, correlated movement of two individuals moving next to each other caused by following a linear resource gradient. No inter-individual interaction but interactions with the physical landscape were present. Estimates were obtained by applying three methods to the simulated movement data: DI (panel A), SSF-OD \u0026amp; SSF-DIST (panel B). For both SSFs three models were fitted; (1) a full model with OD/DIST and landscape used as covariates, (2) a model with OD/DIST used as covariate, (3) Spatial+ was applied prior to fitting the model 2. The estimates of the interactions between two individuals are shown in orange, while the estimates of the interaction between the focal individual and the landscape are shown in blue. The values that are significantly different from 0 (at p \u0026lt; 0.05) are shown with filled points and those that are not significantly different from 0 are shown with crosses.\u003c/p\u003e","description":"","filename":"floatimage3.png","url":"https://assets-eu.researchsquare.com/files/rs-5396058/v1/cfc76955ba6166ce155167c1.png"},{"id":69800564,"identity":"eba80533-47ce-43c3-a6f4-332988297ae1","added_by":"auto","created_at":"2024-11-25 10:55:01","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":58225,"visible":true,"origin":"","legend":"\u003cp\u003ePerformance of three statistical methods when applied to movement data generated under scenario A.b, correlated movement of two individuals moving from opposite locations towards the resource in the centre. No inter-individual interactions but interactions with the landscape were present. Estimates were obtained by applying three methods to the simulated movement data: DI (panel A), SSF-OD \u0026amp; SSF-DIST (panel B). For both SSF-DIST \u0026amp; SSF-OD, model 1 was fitted with landscape as the only predictor due to high collinearity between DIST/OD and landscape covariates. For SSF-OD model 2 and 3 were not fitted due to the lack of overlapping movement paths. Annotations as in Figure 3.\u003c/p\u003e","description":"","filename":"floatimage4.png","url":"https://assets-eu.researchsquare.com/files/rs-5396058/v1/cc79364983d3ad1d50cbd80e.png"},{"id":69800566,"identity":"a36ab415-a0e6-47ce-a1df-2a217b2fd328","added_by":"auto","created_at":"2024-11-25 10:55:01","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":67080,"visible":true,"origin":"","legend":"\u003cp\u003ePerformance of three statistical methods when applied to movement data generated under scenario B: correlated movement of two individuals moving in a patchy landscape, i.e. no social interaction between individuals but attraction of individuals to the physical landscape. Estimates were obtained by applying three methods to the simulated movement data: DI (panel A), SSF-OD \u0026amp; SSF-DIST (panel B). Annotations as in Figure 3.\u003c/p\u003e","description":"","filename":"floatimage5.png","url":"https://assets-eu.researchsquare.com/files/rs-5396058/v1/d9da3250c8501d7150316b25.png"},{"id":69800560,"identity":"733bbdbd-aeea-4bae-923d-1293dfa85102","added_by":"auto","created_at":"2024-11-25 10:55:01","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":125363,"visible":true,"origin":"","legend":"\u003cp\u003ePerformance of three statistical methods when applied to movement data generated under scenario C: correlated movement of two individuals due to their avoidance of barriers. Estimates were obtained by applying three methods (A: SSF-DIST, B: SSF-OD, C: DI) to the movement data. \u0026nbsp;The effect of the percentage of barriers in the landscape on the interaction estimate is shown in black colouring. For both SSFs two models were fitted; (1) OD/DIST were used as covariate, (2) spatial+ was applied prior to fitting the model 1 (orange colouring). The values that are significantly different from 0 (at p \u0026lt; 0.05) are shown with filled points and those that are not significantly different from 0 are shown with crosses.\u003c/p\u003e","description":"","filename":"floatimage6.png","url":"https://assets-eu.researchsquare.com/files/rs-5396058/v1/06bb0022fd24365c8286f29a.png"},{"id":69800568,"identity":"9f65ed63-da7e-41b2-85d9-0026964cbb82","added_by":"auto","created_at":"2024-11-25 10:55:01","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":57546,"visible":true,"origin":"","legend":"\u003cp\u003ePerformance of three statistical methods when applied to movement data generated under scenario D: correlated movement of two individuals due to their attraction to each other and not due to landscape effects. Estimates were obtained by applying three methods to the simulated movement data: DI (panel A), SSF-OD \u0026amp; SSF-DIST (panel B). Annotations as in Figure 3.\u003c/p\u003e","description":"","filename":"floatimage7.png","url":"https://assets-eu.researchsquare.com/files/rs-5396058/v1/0e1c43830199b5022dc2f2ee.png"},{"id":84726985,"identity":"feff0858-d6ba-4529-bf07-80ca70756ecf","added_by":"auto","created_at":"2025-06-16 16:09:09","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1496609,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-5396058/v1/0a4f1768-893d-4609-be1d-8b4f891a27f2.pdf"},{"id":69800567,"identity":"3e5f056d-f916-48c9-89e1-c6318453fd2e","added_by":"auto","created_at":"2024-11-25 10:55:01","extension":"docx","order_by":2,"title":"","display":"","copyAsset":false,"role":"supplement","size":27723,"visible":true,"origin":"","legend":"","description":"","filename":"SupplementaryInfo112024.docx","url":"https://assets-eu.researchsquare.com/files/rs-5396058/v1/cafeec6a25062e4625c4103a.docx"}],"financialInterests":"No competing interests reported.","formattedTitle":"Considering landscape heterogeneity improves the inference of inter-individual interactions from movement data","fulltext":[{"header":"Introduction","content":"\u003cp\u003eAnimal movement is a fundamental behavioural process that results in a change of spatial locations of an individual and has important implications for its survival and reproduction, with consequences on the population and community level. Different types of movement can be distinguished, such as foraging movement, migratory movement, dispersal, and nomadic movement (Schlaegel et al. 2020; Bastille-Rousseau et al. 2016; Nathan et al. 2008). The decision of how, where and when to move is influenced by both the physical environment of an animal and its social environment (Strandburg-Peshkin et al. 2017; Nathan et al. 2008; Cote and Clobert 2007). The physical environment may consist of habitat features that offer resource and shelter, but also structures like barriers that hinder movement. The social environment consists of con- and heterospecifics and exchange of information with them. The social environment may be beneficial but also disadvantageous. Animals might be attracted to other individuals due to the benefits of sociality like social grooming, reduced predation risk, increased foraging efficiency or access to social information (van Schaik 1983). Or they may avoid other individuals to reduce the risk of pathogen transmission (Marescot et al. 2021), competition (Isbell 1991) and predation (Herbert-Read et al. 2017; Laundre et al. 2010; Fortin et al. 2005). Importantly, the physical environment and social environment are not independent of each other as the physical environment might facilitate or constrain animal interactions. Indeed, a correlation in the movement trajectories of several individuals might emerge from gathering at the same resource. For example, mammal individuals in arid ecosystems regularly come to water holes and are primarily interested in water as resource (Valeix et al. 2010). However, when their movement trajectories would be analysed without explicitly considering water as a resource, it may seem as if individuals interact with each other, while they are foremost interested in the water resource. On the other hand, barriers might prevent them to meet. Populations might get separated due to constraints on their movement introduced by habitat fragmentation (He et al. 2019; Pinter-Wollman et al. 2017; Banks et al. 2007). Thus, the physical environment in which animals move will fundamentally shape the patterns of social interactions. Identifying whether correlated movements paths of two (or more) individuals arise from interactions between them or whether they are the result of their physical environment, is important for understanding the cause of animal movement and behaviour.\u003c/p\u003e \u003cp\u003eA rapid development of tracking technologies in recent years allowed the collection of high-resolution data on multiple simultaneously moving individuals. This, in turn, motivated the development of several methods to infer interactions among moving animals (Fronville et al. 2024; Schlaegel et al. 2019; Calabrese et al. 2018; Niu et al. 2016; Spiegel et al. 2016; Long and Nelson 2013), which now open the possibility to explore how animals move relative to one another. For example, dynamic interaction indices (Long et al. 2014) are commonly used to analyse interactions between two individuals, while step selection functions can be used to identify animals’ preference towards landscape features or even other individuals (Schlaegel et al. 2019).\u003c/p\u003e \u003cp\u003eHere, we assess the ability of three methods to correctly detect whether animal movement paths emerge from inter-individual interactions or if they are simply the by-product of individuals responding to the same environmental features. We focused on three statistical methods extensively tested inFronville et al. (2024): one commonly used index of dynamic interaction (DI – Dynamic interaction index) that is implemented within the ‘Wildlife DI’ R package (Jed Long et al. 2018) and two novel methods that are based on step-selection functions (SSF): one uses as a covariate the occurrence distribution of the other moving individual (Schlaegel et al. 2019; herewith referred to as SSF-OD) and the other one uses the distance to the other moving individual(s) (Roeleke et al. 2022; herewith referred to as SSF-DIST). All three methods are used to estimate interactions from movement trajectories, i.e. time series of location estimates collected on at least two simultaneously moving individuals. Both SSF-based approaches also can account for other covariates (e.g. environmental data) when assessing inter-individual interactions, allowing us to investigate how these movement trajectories are shaped by resources and obstacles in the environment (Nathan et al. 2022). Furthermore, we tested whether the bias of unmeasured spatial factors on the social interactions can be reduced or even fully eliminated by applying a method called ‘spatial+’ in combination with the SSFs (Dupont et al. 2022). ‘Spatial+’ partials out the effect of space on the considered covariate (e.g. the occurrence distribution of the other moving individual or the distance to it) and thereby reduces the bias in the effect estimates.\u003c/p\u003e \u003cp\u003eTo test the methods and to investigate the possible risks of neglecting the effects of physical environmental features when analysing interactions between moving animals, we simulated movement data with a spatially-explicit agent-based model (ABM, Grimm et al. 2006; Tang and Bennett 2010) introduced in Fronville et al. (2024). using an agent-based and spatially-explicit modelling approach provided full system knowledge and allowed to generate different landscape scenarios with which the simulated individuals could interact. We simulated four landscape scenarios: in three of them (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003eA-C) two individuals do not interact with each other but their movement is affected in the same way by their physical environment, leading to resulting correlated movement trajectories; in the fourth scenario (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003eD) two individuals interact exclusively with each other and are not affected by their physical environment. In this study, the physical environment consists of resources (gradient of habitat quality) that the individuals are attracted to, or barriers (e.g. rivers, human-made structures) that hinder their movement. In scenarios A and B, the individuals are attracted to the same resources and they move along a gradient of habitat quality (scenario A) and within a patchy landscape where resources are clustered (scenario B). In scenario C the individuals move in a homogeneous matrix that is intercepted by barriers, which are randomly scattered in the landscape and can hinder or “guide” individual movement. The landscapes are built in such a way that a correlation in movement trajectories of two individuals arises either because both individuals are attracted to the same habitat quality (in scenarios A and B) or the movement of both individuals is constrained by barriers (in the scenario C) leading to their “enforced” correlation.\u003c/p\u003e \u003cp\u003eSince DI does not allow accounting for the effect of environmental predictors when assessing interactions and in case of spatially correlated trajectories results in values close to “1” (Long et al. 2014), we expect that it will falsely detect interactions between both individuals when their movement, in fact is affected by the resource only. When the physical environment is included as a covariate in SSF, we expect the SSF-based approaches to correctly detect that the correlated movement trajectories of the two individuals emerge from the effect of their physical environment. Yet, in case the relevant physical environmental covariate is not considered in the analyses, either because the researchers do not have access to relevant environmental descriptors or because they do not expect environment to strongly affect individual movement, both these methods will, similarly to DI, falsely detect interactions between the individuals. However, we expect that applying spatial + in such cases will partial out the spatial dependence and remove the spurious interaction effects.\u003c/p\u003e "},{"header":"Methods","content":"\u003ch3\u003eSimulation of movement trajectories\u003c/h3\u003e\u003cp\u003eIn the Agent-Based Model (ABM) two individuals move according to a biased correlated random walk in discrete time. We model a high persistency in the movement of both individuals that is a high correlation in their facing direction. There are two different mechanisms that generate the biased movement: either through an attraction towards another moving individual or through the attraction to the environmental surroundings. Both these biases in movement direction are considered as interactions (with conspecifics and with the environment, respectively) in our simulation. The individuals are moving within an area of a fixed size with reflecting borders (the area modelled is rather large and encounters with borders are rare). Four different scenarios are then devised in which the individuals interact with their environment (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003eA-D). The detailed model description follows the Overview, Design, concepts, Details (ODD) protocol (Supporting information) by Grimm et al. (2006) and updated (Grimm et al. 2020).\u003c/p\u003e\u003ch2\u003eInteraction with environmental surroundings\u003c/h2\u003e\u003cp\u003eIndividuals can interact with their environmental surroundings while moving (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003eA-C), i.e. are attracted (towards a resource) or avoid (barriers); or do not interact (i.e. purely perform correlated random walk). In these scenarios both individuals are not directly interacting with each other, yet their resulting movement trajectories are correlated due to them responding to the environmental surroundings in the same way.\u003c/p\u003e\u003cp\u003eWe generated three scenarios of interactions of both individuals with environments (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e, A-C). For two scenarios, we used a grid-based environment in which each cell reflects habitat suitability. The values of habitat suitability range from zero to one. In the first scenario A, we model a gradient of habitat suitability with habitat suitability increasing linearly from the west to the east of the simulated area (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e, A.a) or increasing linearly from the borders towards the centre (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e, A.b). For the second scenario B, the grid cells were assigned with a value generated with the Perlin noise function. The Perlin noise is used to generate not completely random values (Perlin 1985) and is helpful to create procedurally generated landscapes. This produces patches of grid cells with values similar to each other, which gives the appearance of more naturally clustered patchy landscapes compared to full randomness (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e, B). For the scenarios A \u0026amp; B, the moving individuals evaluate the cells within their perceptual range and bias their movement towards the cell with the highest value. The Perlin noise function is also used to generate the barriers for the third scenario C, which blocks the path of the individuals (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e, C). In this case, the barrier cells receive a value which is avoided by the individuals. The individuals do not express any preference towards a particular grid cell value, but only move according to the correlated random walk and are repulsed by the barriers (turn in the direction opposite of their intended movement direction). For the scenarios A \u0026amp; B the simulations were run with 20 repetitions. For the scenario C the proportion of barriers in the landscape was continually varied from 0 % − 75 % of he totl landscape area with 0.5 % steps, reslting in 150 barrier landscapes.\u003c/p\u003e\u003ch3\u003eInteraction with other individuals\u003c/h3\u003e\u003cp\u003eIn the scenario D both individuals are attracted towards each other but do not interact with their environmental surroundings (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e, D). They both move according to a correlated random walk while they express a positive bias towards each other resulting in them moving as a pair within the environment. The simulation was run for 20 repetitions, each with a new generated landscape structure.\u003c/p\u003e\u003ch3\u003eStatistical methods for inferring interactions from movement data\u003c/h3\u003e\u003cp\u003eFor a comprehensive description and a summary table of the statistical methods employed in this study, please refer to the Supplementary Methods section.\u003c/p\u003e\u003ch3\u003eDynamic interaction index (DI)\u003c/h3\u003e\u003cp\u003eThe DI index measures the cohesiveness of simultaneous movement vectors with respect to two independent components of movement: distance (also called displacement) and direction (DI; Long and Nelson 2013). Values for DI range from − 1 and 1 where negative values correspond to repulsive movement paths (opposite direction) and positive values indicate cohesive movement paths (in same direction). Values around 0 indicate neutral movement.\u003c/p\u003e\u003ch3\u003eSSF-based approaches\u003c/h3\u003e\u003cp\u003eThe SSFs compare observed movement steps of a focal individual to available steps in terms of certain covariates, which allows to quantify a preference for these covariates (usually environmental variables). The step lengths and turning angles for the available steps were drawn from a Gamma and von Mises distribution, respectively, of which the parameter estimates were obtained from the observed steps (Forester et al. 2009). In this study 20 available steps were used. The estimation of selection coefficients was done using a conditional logistic regression, allowing to compare each used step to a different set of available steps. In other words, the available steps depend on the location and movement characteristics of the individual (temporally varying set of available steps). Positive coefficients indicate attraction and negative coefficients indicate repulsion, while zero indicates no detectable preference for the covariates. The SSF-based approach by (Schlaegel et al. 2019) uses as a covariate dynamic occurrence distributions (OD) of other individuals (Fleming et al. 2015) and is referred to as SSF-OD approach in this study. The second SSF-based approach we use is a modification of SSF-OD that, instead of the occurrence distribution, uses distances between individuals (DIST) as covariates in SSFs (Roeleke et al. 2022). We refer to this approach as SSF-DIST.\u003c/p\u003e\u003ch2\u003eSpatial+\u003c/h2\u003e\u003cp\u003eSpatial confounding (collinearity/non-independence between the covariate of interest and unmeasured spatial effect) is often an issue when working with spatial data and can lead to biases in the estimated covariate effects. Spatial+ (Dupont et al. 2022) is used to reduce this bias, by reducing the spatial dependence of the covariate, which is done in two steps. Firstly, the spatial dependence is regressed away by using the covariate of interest as response variable and the spline of coordinates as independent predictor. In the second step, the residuals obtained in the first step are used as covariates (corrected covariate) in the SSF. This approach was only used for the SSFs and not DI, because no environmental covariates can be included as predictors in DI.\u003c/p\u003e\u003ch3\u003eEvaluating method performance\u003c/h3\u003e\u003cp\u003eWe assessed the performance of the method by focusing on the power of the methods to detect true interaction and by evaluating type 1 error for wrongly detected interactions. We used the \u003cem\u003ep-values\u003c/em\u003e of each method to validate its outcome to be significant (\u0026lt; 0.05) or not. The proportion of correctly estimated interactions was then used as a metric indicative of the method performance. We define “correctly estimated interactions” as cases where the effect of another individual on the movement of the focal individual was assessed as being significant when inter-individual interactions were indeed present and the failure to detect the effect of another individual when inter-individual interactions were indeed absent. For the scenarios in which the correlated movement is resulting from the effect of the physical environment (scenarios A, B, C) the estimate of inter-individual interaction should not be significant, while the estimate of environmental effect should be significant. The opposite is the case for the scenario D, in which the correlated movement is resulting from individual interactions.\u003c/p\u003e\u003cp\u003eFor both SSF-based approaches we fit three different models. In the first model we use occurrence distribution of (SSF-OD) and the distance to (SSF-DIST) the non-focal individual as well as the physical environment as predictors. In the other two models we did not include the physical environment as predictor in the model, which reflects the situation when no environmental data are available for the field researchers to include as a covariate (or, the available environmental data that can be included in the analyses are not relevant for the movement of the individuals). In the second model we only included occurrence distribution of (SSF-OD) and the distance to (SSF-DIST) the non-focal individual as a predictor and in the third model we applied spatial + to the second model.\u003c/p\u003e\u003ch3\u003eObserved correlated movement arises from interaction with environmental surroundings\u003c/h3\u003e\u003cp\u003eWe expect positive signifant DI indices (type I error). Regarding both SSFs, we expect for model 2 to wrongly detect interactions between individuals (type I error) and thus the coefficient to be positive and significant. If we apply spatial+ (model 3), we expect the coefficients to become non-significant for the SSFs. For model 1 that includes also habitat quality as predictor in the analysis, we expect the two SSF-based approaches to correctly detect an attraction towards the physical enviornment as well as no interactions between the individuals.\u003c/p\u003e\u003ch2\u003eObserved correlated movement arises from direct interactions of individuals\u003c/h2\u003e\u003cp\u003eWe expect positive significant indices from DI. For the SSFs, we expect that all three models 1, 2 \u0026amp; 3 will correctly detect individual interactions, that is the coefficients will be positive and significant. We also expect the coefficents associated with environmental predictor to be non-significant for model 1.\u003c/p\u003e"},{"header":"Results","content":"\u003cp\u003e\u003cstrong\u003e1. Correlated Movement caused by the resource gradient\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003ea)\u003c/strong\u003e Moving next to each other\u003c/p\u003e\n\u003cp\u003eIn the scenario A.a where both individuals were moving next two each other along a habitat quality gradient, DI correctly detected no interactions between individuals. For model 2 (DIST/OD as predictor) SSF-OD correctly detected no individual interactions while SSF-DIST detected significant individual interactions. Applying spatial\u0026thinsp;+\u0026thinsp;to the SSF-OD reduced the variance among the interaction estimates. For SSF-DIST, applying spatial\u0026thinsp;+\u0026thinsp;prior to fitting the SSF (model 3) resulted in removing the spurious effect of the individual interaction covariate (Fig. \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e, Fig. \u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003e). The full model 1 (DIST/OD and landscape as predictor) for both SSFs correctly revealed significant landscape estimates and non-significant interaction estimates.\u003c/p\u003e\n\u003cp\u003eb) Moving from opposite locations towards the resource in the centre\u003c/p\u003e\n\u003cp\u003eDI correctly detected no interactions of individuals. For model 2 (DIST/OD as predictor) SSF-DIST detected individual interactions. Applying spatial\u0026thinsp;+\u0026thinsp;to SSF-DIST removed the effect of the DIST covariate and thus the inter-individual interaction estimates became non-significant (Fig. \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e, Fig. \u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003e). Due to high correlation between both predictors in model 1 (DIST \u0026amp; landscape as predictor), fitting the full model was not possible. Therefore, in this scenario model 1 was only fitted with the landscape covariate as predictor. For both SSFs model 1 estimated landscape effect as significant. For SSF-OD both models 2 and 3 were not shown as SSF-OD is unable to accurately estimate the inter-individual interaction coefficient when their movement paths do not overlap.\u003c/p\u003e\n\u003cdiv id=\"Sec13\" class=\"Section2\"\u003e\n \u003ch2\u003e2. Correlated movement caused by the patchy landscape\u003c/h2\u003e\n \u003cp\u003eDI mostly correctly detected the absence of interactions between the two individuals. For model 2 (DIST/OD as predictor) SSF-DIST, and especially, SSF-OD, erroneously detected significant inter-individual interactions. Applying spatial+ (model 3) to the both SSFs resulted in removing the spurious effect of the individual interaction covariate (Fig. \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e; Fig. \u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003e). The full model 1 (DIST/OD \u0026amp; landscape as predictor) fitted for both SSFs mostly correctly assessed landscape estimates as being significant and interaction estimates as non-significant.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec14\" class=\"Section2\"\u003e\n \u003ch2\u003e3. Correlated movement caused by avoiding barriers\u003c/h2\u003e\n \u003cp\u003eThe percentage of barriers in the landscape did not affect the performance of DI (Fig. \u003cspan class=\"InternalRef\"\u003e6\u003c/span\u003e, A). As the percentage of barriers increased in the landscape, SSF-OD and SSF-DIST falsely detected increasing number of interactions between the individuals, where in fact there were none. This effect was mostly pronounced for SSF-OD (Fig. \u003cspan class=\"InternalRef\"\u003e6\u003c/span\u003e, B). Applying spatial\u0026thinsp;+\u0026thinsp;effectively improved the performance of SSF-OD, as fewer significant interaction estimates were detected under higher percentage of barriers in landscapes. However, this was not the case for SSF-DIST, as the number of significant interaction estimates (false positives) did not decrease after applying spatial+. In this case significant estimates were detected irrespective of the proportion of the barriers i.e. also at low proportion of barriers.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec15\" class=\"Section2\"\u003e\n \u003ch3\u003eD) Correlated movement caused by individual interactions\u003c/h3\u003e\n \u003cp\u003eAll three methods correctly detected individual interactions, yielding significant positive estimates (Fig. \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e, Fig. \u003cspan class=\"InternalRef\"\u003e7\u003c/span\u003e). Applying spatial\u0026thinsp;+\u0026thinsp;did not change this outcome. Furthermore, both SSF-based approaches correctly detected significant interaction estimates and non- significant landscape estimates in the full model (Fig. \u003cspan class=\"InternalRef\"\u003e7\u003c/span\u003e).\u003c/p\u003e\n\u003c/div\u003e"},{"header":"Discussion","content":"\u003cp\u003eHere we assessed how heterogenous environment affects the inference of inter-individual-interactions from movement data. One of the commonly used indices DI performed well, but it does not consider the physical environment at all. On the contrary, SSFs allow disentangling the effects of direct inter-individual interactions (i.e. social factors) from environmental effects (i.e. physical factors) on the movement of individuals. Including the physical environment as a predictor in SSFs increased the performance by decreasing the rate of false positives. A similar effect was achieved by applying Spatial\u0026thinsp;+\u0026thinsp;to SSFs that only included the movement of other individuals as covariate.\u003c/p\u003e \u003cp\u003eIn our scenarios A.a and A.b in which the simulated animals do not interact with each other directly but move persistently along a linear habitat gradient, we have shown that neglecting the physical environment results in falsely detecting interactions between the two individuals by SSF-DIST. Including the landscape as a covariate in the step selection function reduced the rates of falsely detected inter-individual-interactions. However, including both the social and physical environment as predictors in the model is not always possible, since they can become highly collinear. For instance, we simulated such a collinearity in our scenario A.b in which two individuals move from opposite locations towards the same resource in the middle, such that the value of the habitat quality increases while the distance to the other individual decreases. In such cases, revealing the true effect will be difficult and the focus should be on gaining understanding of how animals interact with their environment prior to analysing inter-individual interactions. Especially when interested in commuting, dispersal or migration movements, persistent movement along linear habitat gradients/features can occur regularly (Owen-Smith et al. 2020; Bedrosian et al. 2018; Fryxell and Avgar 2012; Hahn et al. 2008). For instance, in animals such as caribou the movement is strongly attributed to seasonal environmental conditions, resulting in following the vegetative growth during spring (Avgar et al. 2013; Fryxell and Avgar 2012). Other examples of such movement patterns are found in savannas where different herbivores are attracted to the same food/water resources forming big aggregations of different species moving together (Fryxell and Sinclair 1988). In such cases the landscape is the reason for the correlation in movement trajectories of individuals. While it is acknowledged that animal space use is affected by both inter-individual-interactions as well as the physical environment, it is often not addressed by leaving the physical descriptors out of the analyses, especially when inter-individual interactions are the point of interest. Yet, neglecting the physical environment could result in a so-called spatial cofounding, meaning the covariate of interest (here: coefficient of inter-individual interaction) is spatially dependant, thus resulting in unreliable estimates (Arce Guillen et al. 2023; Urdangarin et al. 2023; Gilbert et al. 2021). In such cases when no environmental data is available, applying spatial\u0026thinsp;+\u0026thinsp;in addition to the step selection function allows to reduce spatial cofounding in animal movement and leads to an improved inference of inter-individual-interactions, according to our findings. Furthermore, a extension of SSFs, called iSSFs, can be used instead (Avgar et al. 2016; Fieberg et al. 2021) in which in addition to estimating the effects of physical and social environment on movement preferences of the individuals, also the effects of those environments on step length and turning angles can be estimated, allowing to infer the movement characteristics of the animals.\u003c/p\u003e \u003cp\u003eIn the scenario B, in which the physical environment consists of a patchy landscape, we found similar responses as in the two first scenarios A.a and A.b. When the environmental landscape was neglected, all three methods falsely detected a high rate of interactions between the individuals. Including the physical environment as a covariate reduced the rate of false positives for the SSFs. Also, in case no environment data were included in the analysis, applying spatial\u0026thinsp;+\u0026thinsp;with the SSFs reduced the spurious inflation of inter-individual interactions induced by the environment. The movements modelled in such a patchy landscape reflect movements during foraging behaviour of animals, which are expressed by many animals on a daily basis, with many species being attracted to the same resource (Owen-Smith et al. 2020; Abrahms et al. 2021). Zebrafish use a combination of the physical and social environment to increase their foraging efficiency (Harpaz and Schneidman 2020). An aggregation of zebrafishes at a food resource could therefore primarily result from the attraction towards the same resource. This reinforces the difficulty to distinguish whether the physical or the biotic environment affected the movement, since the physical environment can act as attractor or facilitator. Moreover, animals change how they interact with their physical and biotic environment over time. Such switches in behaviours could be detected by applying HMM-SSF(Pohle et al. 2024; Klappstein et al. 2024) which is a new approach that contributes to better inference of inter-individual interactions, as it allows detecting changes in behavioural states due to the environment. This allows then to split the movement trajectory into meaningful chunks depending on their behavioural states.\u003c/p\u003e \u003cp\u003eIn the scenario C we revealed the emerging bias of correlated movements due to increasing habitat fragmentation. For both SSFs, with increasing proportion of obstacles (non-favourable elements) in the landscape, an increase in falsely detected social interactions was observed. Applying spatial\u0026thinsp;+\u0026thinsp;was again successful in removing this spatial cofounding when applied to SSF-OD, reducing the rates of falsely detected social interactions. This finding is of high importance when analysing individual movement in fragmented landscapes. As the landscape fragmentation increases, hostile matrix acting as a barrier becomes larger and thus the space use of animals becomes restricted to smaller areas (Eycott et al. 2012). This then results in a higher overlap in movement paths of individuals, causing higher correlation in their movement trajectories that is not necessarily due to the direct interactions between individuals. Furthermore linear features in the landscape used by many animals(Dickie et al. 2020) can cause such correlations in animal movement. For example, corridors in highly fragmented landscapes act as \u0026ldquo;drift fences\u0026rdquo;, intercepting and redirecting the movement of different animals (Haddad et al. 2003), thus potentially increasing the risk of detecting interactions between individuals that might only be due to them using the same space. Wildlife crossings such as green bridges over highways, used by wolves, dears and boars (Plaschke et al. 2021), might also increase the potential of spuriously detecting inter-individual interactions. Another example of animals using linear structures as guidance for navigation are golden eagles who use the Rocky Mountain range to migrate to the north (Bedrosian et al. 2018). Thus, including such landscape structure as a covariate in the analyses is of high importance to account for this bias. However, one must be careful when interpreting the estimates of an SSF. In case an animal uses an environmental structure as guidance and not as a resource, for example boars moving along forest patches(Thurfjell et al. 2009) but never entering that landscape structure, the SSFs will detect an avoidance of that structure (Thurfjell et al. 2014).\u003c/p\u003e \u003cp\u003eIn scenario D we have shown that including physical environmental data as predictors in the model does not worsen the inference of inter-individual interactions. We advise that field ecologists should be more cautious about false positives, as it seems that false negatives are less likely to be of an issue than false positives in a heterogenous landscape, at least in the investigated scenarios.\u003c/p\u003e \u003cp\u003eThe addressed three methods (Long and Nelson 2013, Schlaegel et al. 2019, Roeleke et al. 2022), as well as the recently published methods considering the behavioural states of the animals (Pohle et al. 2024; Klappstein et al. 2024), show promising results in dealing with confounding factors when assessing inter-individual interactions of moving individuals. We show that especially when the physical environment strongly affects the animal movement, including physical environmental data or applying spatial+(Dupont et al. 2022) is essential to improve inference of inter-individual interactions and avoid detection of spurious effects. The inclusion of relevant physical environment descriptors as predictors in the model hinges on the prior knowledge of the resource use by the study species and detailed understanding of its spatial ecology. We suggest that, when interested in inter-individual interactions, collecting movement data should, whenever possible, be accompanied by the collection of environmental data relevant to the study species.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eAcknowledgements\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThis work was supported by Deutsche Forschungsgemeinschaft in the framework of the BioMove Research Training Group. We thank the colleagues from the Department of Ecological Dynamics (IZW) for constructive feedback on our manuscript.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFunding\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThis work was funded by the “Deutsche Forschungsgemeinschaft\u0026nbsp;(DFG)“ in the framework of the BioMove Research Training Group.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAuthor contribution\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThibault Fronville, Viktoriia Radchuk, Stephanie Kramer-Schadt, Florian Jeltsch and Niels Blaum conceived the ideas and designed methodology. Thibault Fronville simulated the data and analysed the data. Thibault Fronville and Viktoriia Radchuk led the writing of the manuscript. All authors contributed critically to the drafts and gave final approval for publication.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConflict of interest\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors have no conflicts of interest to declare.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eEthics and consent\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eEthics and Consent to Participate declarations: not applicable\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eAbrahms, Briana; Aikens, Ellen O.; Armstrong, Jonathan B.; Deacy, William W.; Kauffman, Matthew J.; Merkle, Jerod A. (2021): Emerging Perspectives on Resource Tracking and Animal Movement Ecology. In \u003cem\u003eTrends in ecology \u0026amp; evolution \u003c/em\u003e36 (4), pp. 308\u0026ndash;320. DOI: 10.1016/j.tree.2020.10.018.\u003c/li\u003e\n\u003cli\u003eArce Guillen, Rafael; Lindgren, Finn; Muff, Stefanie; Glass, Thomas W.; Breed, Greg A.; Schl\u0026auml;gel, Ulrike E. (2023): Accounting for unobserved spatial variation in step selection analyses of animal movement via spatial random effects. In \u003cem\u003eMethods Ecol Evol \u003c/em\u003e14 (10), pp. 2639\u0026ndash;2653. DOI: 10.1111/2041-210X.14208.\u003c/li\u003e\n\u003cli\u003eAvgar, Tal; Mosser, Anna; Brown, Glen S.; Fryxell, John M. (2013): Environmental and individual drivers of animal movement patterns across a wide geographical gradient. In \u003cem\u003eJournal of Animal Ecology \u003c/em\u003e82 (1), pp. 96\u0026ndash;106. DOI: 10.1111/j.1365-2656.2012.02035.x.\u003c/li\u003e\n\u003cli\u003eAvgar, Tal; Potts, Jonathan R.; Lewis, Mark A.; Boyce, Mark S. (2016): Integrated step selection analysis: bridging the gap between resource selection and animal movement. In \u003cem\u003eMethods Ecol Evol \u003c/em\u003e7 (5), pp. 619\u0026ndash;630. DOI: 10.1111/2041-210X.12528.\u003c/li\u003e\n\u003cli\u003eBanks, Sam C.; Piggott, Maxine P.; Stow, Adam J.; Taylor, Andrea C. (2007): Sex and sociality in a disconnected world: a review of the impacts of habitat fragmentation on animal social interactions. In \u003cem\u003eCan. J. Zool. \u003c/em\u003e85 (10), pp. 1065\u0026ndash;1079. DOI: 10.1139/Z07-094.\u003c/li\u003e\n\u003cli\u003eBarrio, Isabel C.; Hik, David S. (2013): Good neighbours? Determinants of aggregation and segregation among alpine herbivores. In \u003cem\u003e\u0026Eacute;coscience \u003c/em\u003e20 (3), pp. 276\u0026ndash;282. DOI: 10.2980/20-3-3595.\u003c/li\u003e\n\u003cli\u003eBastille-Rousseau, Guillaume; Potts, Jonathan R.; Yackulic, Charles B.; Frair, Jacqueline L.; Ellington, E. Hance; Blake, Stephen (2016): Flexible characterization of animal movement pattern using net squared displacement and a latent state model. In \u003cem\u003eMovement ecology \u003c/em\u003e4, p. 15. DOI: 10.1186/s40462-016-0080-y.\u003c/li\u003e\n\u003cli\u003eBedrosian, Bryan E.; Domenech, Robert; Shreading, Adam; Hayes, Matthew M.; Booms, Travis L.; Barger, Christopher R. (2018): Migration corridors of adult Golden Eagles originating in northwestern North America. In \u003cem\u003ePLoS ONE \u003c/em\u003e13 (11), e0205204. DOI: 10.1371/journal.pone.0205204.\u003c/li\u003e\n\u003cli\u003eCalabrese, Justin M.; Fleming, Christen H.; Fagan, William F.; Rimmler, Martin; Kaczensky, Petra; Bewick, Sharon et al. (2018): Disentangling social interactions and environmental drivers in multi-individual wildlife tracking data. In \u003cem\u003ePhilosophical transactions of the Royal Society of London. Series B, Biological sciences \u003c/em\u003e373 (1746). DOI: 10.1098/rstb.2017.0007.\u003c/li\u003e\n\u003cli\u003eCote, J.; Clobert, J. (2007): Social information and emigration: lessons from immigrants. In \u003cem\u003eEcology letters \u003c/em\u003e10 (5), pp. 411\u0026ndash;417. DOI: 10.1111/j.1461-0248.2007.01032.x.\u003c/li\u003e\n\u003cli\u003eDickie, Melanie; McNay, Scott R.; Sutherland, Glenn D.; Cody, Michael; Avgar, Tal (2020): Corridors or risk? Movement along, and use of, linear features varies predictably among large mammal predator and prey species. In \u003cem\u003eJournal of Animal Ecology \u003c/em\u003e89 (2), pp. 623\u0026ndash;634. DOI: 10.1111/1365-2656.13130.\u003c/li\u003e\n\u003cli\u003eDupont, Emiko; Wood, Simon N.; Augustin, Nicole H. (2022): Spatial+: A novel approach to spatial confounding. In \u003cem\u003eBiometrics \u003c/em\u003e78 (4), pp. 1279\u0026ndash;1290. DOI: 10.1111/biom.13656.\u003c/li\u003e\n\u003cli\u003eEycott, Amy E.; Stewart, Gavin B.; Buyung-Ali, Lisette M.; Bowler, Diana E.; Watts, Kevin; Pullin, Andrew S. (2012): A meta-analysis on the impact of different matrix structures on species movement rates. In \u003cem\u003eLandscape Ecol \u003c/em\u003e27 (9), pp. 1263\u0026ndash;1278. DOI: 10.1007/s10980-012-9781-9.\u003c/li\u003e\n\u003cli\u003eFieberg, John; Signer, Johannes; Smith, Brian; Avgar, Tal (2021): A \u0026apos;How to\u0026apos; guide for interpreting parameters in habitat-selection analyses. In \u003cem\u003eJournal of Animal Ecology \u003c/em\u003e90 (5), pp. 1027\u0026ndash;1043. DOI: 10.1111/1365-2656.13441.\u003c/li\u003e\n\u003cli\u003eFleming, C. H.; Fagan, W. F.; Mueller, T.; Olson, K. A.; Leimgruber, P.; Calabrese, J. M. (2015): Rigorous home range estimation with movement data: a new autocorrelated kernel density estimator. In \u003cem\u003eEcology \u003c/em\u003e96 (5), pp. 1182\u0026ndash;1188. DOI: 10.1890/14-2010.1.\u003c/li\u003e\n\u003cli\u003eForester, James D.; Im, Hae Kyung; Rathouz, Paul J. (2009): Accounting for animal movement in estimation of resource selection functions: sampling and data analysis. In \u003cem\u003eEcology \u003c/em\u003e90 (12), pp. 3554\u0026ndash;3565. DOI: 10.1890/08-0874.1.\u003c/li\u003e\n\u003cli\u003eFortin, Daniel; Beyer, Hawthorne L.; Boyce, Mark S.; Smith, Douglas W.; Duchesne, Thierry; Mao, Julie S. (2005): WOLVES INFLUENCE ELK MOVEMENTS: BEHAVIOR SHAPES A TROPHIC CASCADE IN YELLOWSTONE NATIONAL PARK. In \u003cem\u003eEcology \u003c/em\u003e86 (5), pp. 1320\u0026ndash;1330. DOI: 10.1890/04-0953.\u003c/li\u003e\n\u003cli\u003eFortin, Daniel; Buono, Pietro-Luciano; Fortin, Andr\u0026eacute;; Courbin, Nicolas; Tye Gingras, Christian; Moorcroft, Paul R. et al. (2013): Movement responses of caribou to human-induced habitat edges lead to their aggregation near anthropogenic features. In \u003cem\u003eThe American naturalist \u003c/em\u003e181 (6), pp. 827\u0026ndash;836. DOI: 10.1086/670243.\u003c/li\u003e\n\u003cli\u003eFronville, Thibault; Blaum, Niels; Kramer‐Schadt, Stephanie; Schl\u0026auml;gel, Ulrike; Radchuk, Viktoriia (2024): Performance of five statistical methods to infer interactions among moving individuals in a predator\u0026ndash;prey system. In \u003cem\u003eMethods Ecol Evol \u003c/em\u003e15 (6), pp. 1097\u0026ndash;1112. DOI: 10.1111/2041-210X.14323.\u003c/li\u003e\n\u003cli\u003eFryxell, J. M.; Sinclair, A. R. (1988): Causes and consequences of migration by large herbivores. In \u003cem\u003eTrends in ecology \u0026amp; evolution \u003c/em\u003e3 (9), pp. 237\u0026ndash;241. DOI: 10.1016/0169-5347(88)90166-8.\u003c/li\u003e\n\u003cli\u003eFryxell, John M.; Avgar, Tal (2012): Animal migration: Catching the wave. In \u003cem\u003eNature \u003c/em\u003e490 (7419), pp. 182\u0026ndash;183. DOI: 10.1038/490182a.\u003c/li\u003e\n\u003cli\u003eGilbert, Brian; Datta, Abhirup; Casey, Joan A.; Ogburn, Elizabeth L. (2021): A causal inference framework for spatial confounding.\u003c/li\u003e\n\u003cli\u003eGrimm, Volker; Berger, Uta; Bastiansen, Finn; Eliassen, Sigrunn; Ginot, Vincent; Giske, Jarl et al. (2006): A standard protocol for describing individual-based and agent-based models. In \u003cem\u003eEcological Modelling \u003c/em\u003e198 (1-2), pp. 115\u0026ndash;126. DOI: 10.1016/j.ecolmodel.2006.04.023.\u003c/li\u003e\n\u003cli\u003eGrimm, Volker; Railsback, Steven F.; Vincenot, Christian E.; Berger, Uta; Gallagher, Cara; DeAngelis, Donald L. et al. (2020): The ODD Protocol for Describing Agent-Based and Other Simulation Models: A Second Update to Improve Clarity, Replication, and Structural Realism. In \u003cem\u003eJASSS \u003c/em\u003e23 (2), Article 7. DOI: 10.18564/jasss.4259.\u003c/li\u003e\n\u003cli\u003eHaddad, Nick M.; Bowne, David R.; Cunningham, Alan; Danielson, Brent J.; Levey, Douglas J.; Sargent, Sarah; Spira, Tim (2003): Corridor Use by Diverse Taxa. In \u003cem\u003eEcology \u003c/em\u003e84 (3), pp. 609\u0026ndash;615. DOI: 10.1890/0012-9658(2003)084[0609:CUBDT]2.0.CO;2.\u003c/li\u003e\n\u003cli\u003eHahn, Thomas P.; Cornelius, Jamie M.; Sewall, Kendra B.; Kelsey, T. Rodd; Hau, Michaela; Perfito, Nicole (2008): Environmental regulation of annual schedules in opportunistically-breeding songbirds: adaptive specializations or variations on a theme of white-crowned sparrow? In \u003cem\u003eGeneral and comparative endocrinology \u003c/em\u003e157 (3), pp. 217\u0026ndash;226. DOI: 10.1016/j.ygcen.2008.05.007.\u003c/li\u003e\n\u003cli\u003eHarpaz, Roy; Schneidman, Elad (2020): Social interactions drive efficient foraging and income equality in groups of fish. In \u003cem\u003eeLife \u003c/em\u003e9. DOI: 10.7554/eLife.56196.\u003c/li\u003e\n\u003cli\u003eHaydon, Daniel T.; Morales, Juan M.; Yott, Adelle; Jenkins, Deborah A.; Rosatte, Rick; Fryxell, John M. (2008): Socially informed random walks: incorporating group dynamics into models of population spread and growth. In \u003cem\u003eProceedings. Biological sciences \u003c/em\u003e275 (1638), pp. 1101\u0026ndash;1109. DOI: 10.1098/rspb.2007.1688.\u003c/li\u003e\n\u003cli\u003eHe, Peng; Maldonado-Chaparro, Adriana A.; Farine, Damien R. (2019): The role of habitat configuration in shaping social structure: a gap in studies of animal social complexity. In \u003cem\u003eBehav Ecol Sociobiol \u003c/em\u003e73 (1). DOI: 10.1007/s00265-018-2602-7.\u003c/li\u003e\n\u003cli\u003eHerbert-Read, James E.; Ros\u0026eacute;n, Emil; Szorkovszky, Alex; Ioannou, Christos C.; Rogell, Bj\u0026ouml;rn; Perna, Andrea et al. (2017): How predation shapes the social interaction rules of shoaling fish. In \u003cem\u003eProceedings. Biological sciences \u003c/em\u003e284 (1861). DOI: 10.1098/rspb.2017.1126.\u003c/li\u003e\n\u003cli\u003eIsbell, Lynne A. (1991): Contest and scramble competition: patterns of female aggression and ranging behavior among primates. In \u003cem\u003eBehavioral Ecology \u003c/em\u003e2 (2), pp. 143\u0026ndash;155. DOI: 10.1093/beheco/2.2.143.\u003c/li\u003e\n\u003cli\u003eKlappstein, Natasha J.; Michelot, Th\u0026eacute;o; Fieberg, John; Pedersen, Eric J.; Mills Flemming, Joanna (2024): Step selection functions with non‐linear and random effects. In \u003cem\u003eMethods Ecol Evol \u003c/em\u003e15 (8), pp. 1332\u0026ndash;1346. DOI: 10.1111/2041-210X.14367.\u003c/li\u003e\n\u003cli\u003eLaundre, John W.; Hernandez, Lucina; Ripple, William J. (2010): The Landscape of Fear: Ecological Implications of Being Afraid~!2009-09-09~!2009-11-16~!2010-02-02~! In \u003cem\u003eTOECOLJ \u003c/em\u003e3 (3), pp. 1\u0026ndash;7. DOI: 10.2174/1874213001003030001.\u003c/li\u003e\n\u003cli\u003eLong, Jed A.; Nelson, Trisalyn A. (2013): Measuring Dynamic Interaction in Movement Data. In \u003cem\u003eTransactions in GIS \u003c/em\u003e17 (1), pp. 62\u0026ndash;77. DOI: 10.1111/j.1467-9671.2012.01353.x.\u003c/li\u003e\n\u003cli\u003eLong, Jed A.; Nelson, Trisalyn A.; Webb, Stephen L.; Gee, Kenneth L. (2014): A critical examination of indices of dynamic interaction for wildlife telemetry studies. In \u003cem\u003eThe Journal of animal ecology \u003c/em\u003e83 (5), pp. 1216\u0026ndash;1233. DOI: 10.1111/1365-2656.12198.\u003c/li\u003e\n\u003cli\u003eLuca Bastianelli, Matteo; Hoermann, Christian von; Kirchner, Katrin; Signer, Johannes; Dupke, Claudia; Henrich, Maik et al. (2024): Risk response towards roads is consistent across multiple species in a temperate forest ecosystem. In \u003cem\u003eOikos \u003c/em\u003e2024 (7), Article e10433. DOI: 10.1111/oik.10433.\u003c/li\u003e\n\u003cli\u003eMarescot, Lucile; Franz, Mathias; Benhaiem, Sarah; Hofer, Heribert; Scherer, C\u0026eacute;dric; East, Marion L.; Kramer-Schadt, Stephanie (2021): \u0026apos;Keeping the kids at home\u0026apos; can limit the persistence of contagious pathogens in social animals. In \u003cem\u003eThe Journal of animal ecology \u003c/em\u003e90 (11), pp. 2523\u0026ndash;2535. DOI: 10.1111/1365-2656.13555.\u003c/li\u003e\n\u003cli\u003eMiller, Jennifer R. B.; Ament, Judith M.; Schmitz, Oswald J. (2014): Fear on the move: predator hunting mode predicts variation in prey mortality and plasticity in prey spatial response. In \u003cem\u003eJournal of Animal Ecology \u003c/em\u003e83 (1), pp. 214\u0026ndash;222. DOI: 10.1111/1365-2656.12111.\u003c/li\u003e\n\u003cli\u003eNathan, Ran; Getz, Wayne M.; Revilla, Eloy; Holyoak, Marcel; Kadmon, Ronen; Saltz, David; Smouse, Peter E. (2008): A movement ecology paradigm for unifying organismal movement research. In \u003cem\u003eProceedings of the National Academy of Sciences of the United States of America \u003c/em\u003e105 (49), pp. 19052\u0026ndash;19059. DOI: 10.1073/pnas.0800375105.\u003c/li\u003e\n\u003cli\u003eNathan, Ran; Monk, Christopher T.; Arlinghaus, Robert; Adam, Timo; Al\u0026oacute;s, Josep; Assaf, Michael et al. (2022): Big-data approaches lead to an increased understanding of the ecology of animal movement. In \u003cem\u003eScience (New York, N.Y.) \u003c/em\u003e375 (6582), eabg1780. DOI: 10.1126/science.abg1780.\u003c/li\u003e\n\u003cli\u003eNiu, Mu; Blackwell, Paul G.; Skarin, Anna (2016): Modeling interdependent animal movement in continuous time. In \u003cem\u003eBiometrics \u003c/em\u003e72 (2), pp. 315\u0026ndash;324. DOI: 10.1111/biom.12454.\u003c/li\u003e\n\u003cli\u003eOwen‐Smith, Norman; Hopcraft, Grant; Morrison, Thomas; Chamaill\u0026eacute;‐Jammes, Simon; Hetem, Robyn; Bennitt, Emily; van Langevelde, Frank (2020): Movement ecology of large herbivores in African savannas: current knowledge and gaps. In \u003cem\u003eMammal Review \u003c/em\u003e50 (3), pp. 252\u0026ndash;266. DOI: 10.1111/mam.12193.\u003c/li\u003e\n\u003cli\u003ePerlin, Ken (1985): An image synthesizer. In \u003cem\u003eSIGGRAPH Comput. Graph. \u003c/em\u003e19 (3), pp. 287\u0026ndash;296. DOI: 10.1145/325165.325247.\u003c/li\u003e\n\u003cli\u003ePinter-Wollman, Noa; Fiore, Stephen M.; Theraulaz, Guy (2017): The impact of architecture on collective behaviour. In \u003cem\u003eNature ecology \u0026amp; evolution \u003c/em\u003e1 (5), p. 111. DOI: 10.1038/s41559-017-0111.\u003c/li\u003e\n\u003cli\u003ePlaschke, Mike; Bhardwaj, Manisha; K\u0026ouml;nig, Hannes J.; Wenz, Elena; Dobi\u0026aacute;\u0026scaron;, Kornelia; Ford, Adam T. (2021): Green bridges in a re‐colonizing landscape: Wolves (Canis lupus ) in Brandenburg, Germany. In \u003cem\u003eConservat Sci and Prac \u003c/em\u003e3 (3), Article e364. DOI: 10.1111/csp2.364.\u003c/li\u003e\n\u003cli\u003ePohle, Jennifer; Signer, Johannes; Eccard, Jana A.; Dammhahn, Melanie; Schl\u0026auml;gel, Ulrike E. (2024): How to account for behavioral states in step-selection analysis: a model comparison. In \u003cem\u003ePeerJ \u003c/em\u003e12, e16509. DOI: 10.7717/peerj.16509.\u003c/li\u003e\n\u003cli\u003eRoeleke, Manuel; Schlaegel, Ulrike E.; Gallagher, Cara; Pufelski, Jan; Blohm, Torsten; Nathan, Ran et al. (2022): Insectivorous bats form mobile sensory networks to optimize prey localization: The case of the common noctule bat. In \u003cem\u003eProceedings of the National Academy of Sciences of the United States of America \u003c/em\u003e119 (33), e2203663119. DOI: 10.1073/pnas.2203663119.\u003c/li\u003e\n\u003cli\u003eSchlaegel, Ulrike E.; Grimm, Volker; Blaum, Niels; Colangeli, Pierluigi; Dammhahn, Melanie; Eccard, Jana A. et al. (2020): Movement-mediated community assembly and coexistence. In \u003cem\u003eBiological reviews of the Cambridge Philosophical Society \u003c/em\u003e95 (4), pp. 1073\u0026ndash;1096. DOI: 10.1111/brv.12600.\u003c/li\u003e\n\u003cli\u003eSchlaegel, Ulrike E.; Signer, Johannes; Herde, Antje; Eden, Sophie; Jeltsch, Florian; Eccard, Jana A.; Dammhahn, Melanie (2019): Estimating interactions between individuals from concurrent animal movements. In \u003cem\u003eMethods Ecol Evol \u003c/em\u003e10 (8), pp. 1234\u0026ndash;1245. DOI: 10.1111/2041-210X.13235.\u003c/li\u003e\n\u003cli\u003eSpiegel, Orr; Leu, Stephan T.; Sih, Andrew; Bull, C. Michael (2016): Socially interacting or indifferent neighbours? Randomization of movement paths to tease apart social preference and spatial constraints. In \u003cem\u003eMethods Ecol Evol \u003c/em\u003e7 (8), pp. 971\u0026ndash;979. DOI: 10.1111/2041-210X.12553.\u003c/li\u003e\n\u003cli\u003eStrandburg-Peshkin, Ariana; Farine, Damien R.; Crofoot, Margaret C.; Couzin, Iain D. (2017): Habitat and social factors shape individual decisions and emergent group structure during baboon collective movement. In \u003cem\u003eeLife \u003c/em\u003e6. DOI: 10.7554/eLife.19505.\u003c/li\u003e\n\u003cli\u003eTang, Wenwu; Bennett, David A. (2010): Agent-based Modeling of Animal Movement: A Review. In \u003cem\u003eGeography Compass \u003c/em\u003e4 (7), pp. 682\u0026ndash;700. DOI: 10.1111/j.1749-8198.2010.00337.x.\u003c/li\u003e\n\u003cli\u003eThurfjell, Henrik; Ball, John P.; \u0026Aring;hl\u0026eacute;n, Per-Arne; Kornacher, Peter; Dettki, Holger; Sj\u0026ouml;berg, Kjell (2009): Habitat use and spatial patterns of wild boar Sus scrofa (L.): agricultural fields and edges. In \u003cem\u003eEur J Wildl Res \u003c/em\u003e55 (5), pp. 517\u0026ndash;523. DOI: 10.1007/s10344-009-0268-1.\u003c/li\u003e\n\u003cli\u003eThurfjell, Henrik; Ciuti, Simone; Boyce, Mark S. (2014): Applications of step-selection functions in ecology and conservation. In \u003cem\u003eMovement ecology \u003c/em\u003e2 (1), p. 4. DOI: 10.1186/2051-3933-2-4.\u003c/li\u003e\n\u003cli\u003eUrdangarin, Arantxa; Goicoa, Tom\u0026aacute;s; Ugarte, Mar\u0026iacute;a Dolores (2023): Evaluating recent methods to overcome spatial confounding. In \u003cem\u003eRev Mat Complut \u003c/em\u003e36 (2), pp. 333\u0026ndash;360. DOI: 10.1007/s13163-022-00449-8.\u003c/li\u003e\n\u003cli\u003eValeix, Marion; Loveridge, Andrew J.; Davidson, Zeke; Madzikanda, Hillary; Fritz, Herv\u0026eacute;; Macdonald, David W. (2010): How key habitat features influence large terrestrial carnivore movements: waterholes and African lions in a semi-arid savanna of north-western Zimbabwe. In \u003cem\u003eLandscape Ecol \u003c/em\u003e25 (3), pp. 337\u0026ndash;351. DOI: 10.1007/s10980-009-9425-x.\u003c/li\u003e\n\u003cli\u003evan Schaik, C. P. (1983): Why Are Diurnal Primates Living in Groups? In \u003cem\u003eBehav \u003c/em\u003e87 (1-2), pp. 120\u0026ndash;144. DOI: 10.1163/156853983X00147.\u003c/li\u003e\n\u003cli\u003eWilson; Richards (2000): Consuming and grouping: recource‐mediated animal aggregation. In \u003cem\u003eEcology letters \u003c/em\u003e3 (3), pp. 175\u0026ndash;180. DOI: 10.1046/j.1461-0248.2000.00135.x.\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"movement-ecology","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"move","sideBox":"Learn more about [Movement Ecology](http://movementecologyjournal.biomedcentral.com/)","snPcode":"40462","submissionUrl":"https://submission.nature.com/new-submission/40462/3","title":"Movement Ecology","twitterHandle":"@BioMedCentral","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"BMC/SO AJ","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"Statistical methods, Movement data, Inter-individual interactions, Physical environmental, Habitat heterogeneity, Collinearity, Cofounding","lastPublishedDoi":"10.21203/rs.3.rs-5396058/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-5396058/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003e\u003cstrong\u003eBackground: \u003c/strong\u003eAnimal movement is influenced by both the physical environment and social environment. The effects of both environments are not independent from each other and identifying whether the resulting movement trajectories are shaped by interactions between individuals or whether they are the result of their physical environment, is important for understanding animal movement decisions.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eMethods: \u003c/strong\u003eHere, we assessed whether the commonly used methods for inferring interactions between moving individuals could discern the effects of environment and other moving individuals on the movement of the focal individual. We used three statistical methods:Dynamic interaction index, and two methods based on step selection function. We created five scenarios in which the animals' movements were influenced either by their physical environment alone or by inter-individual interactions. The physical environment is constructed such that it leads to a correlation between the movement trajectories of two individuals.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eResults:\u003c/strong\u003e We found that neglecting the effects of physical environmental features when analysing interactions between moving animals leads to biased inference, i.e. inter-individual interactions spuriously inferred as affecting the movement of the focal individual. We suggest that landscape data should always be included when analysing animal interactions from movement data. In the absence of landscape data, the inference of inter-individual interactions is improved by applying 'Spatial +', a recently introduced method that reduces the bias of unmeasured spatial factors.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConclusions: \u003c/strong\u003eThis study contributes to improved inference of biotic and abiotic effects on individual movement obtained by telemetry data. Step selection functions are flexible tools that offer the possibility to include multiple factors of interest as well as combine it with spatial +.\u003c/p\u003e","manuscriptTitle":"Considering landscape heterogeneity improves the inference of inter-individual interactions from movement data","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-11-25 10:54:56","doi":"10.21203/rs.3.rs-5396058/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2025-01-09T18:48:14+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-01-08T17:11:45+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"81275610067539081808659752670829351326","date":"2024-12-30T15:02:55+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2024-12-09T22:28:54+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"28838884235341417679755285802901568027","date":"2024-12-02T14:41:44+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2024-11-15T15:53:44+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2024-11-07T00:36:49+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2024-11-07T00:34:34+00:00","index":"","fulltext":""},{"type":"submitted","content":"Movement Ecology","date":"2024-11-05T14:06:46+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"movement-ecology","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"move","sideBox":"Learn more about [Movement Ecology](http://movementecologyjournal.biomedcentral.com/)","snPcode":"40462","submissionUrl":"https://submission.nature.com/new-submission/40462/3","title":"Movement Ecology","twitterHandle":"@BioMedCentral","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"BMC/SO AJ","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"f1483171-d7b4-48c9-b92c-92d0fe0e77bb","owner":[],"postedDate":"November 25th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[],"tags":[],"updatedAt":"2025-06-16T16:07:54+00:00","versionOfRecord":{"articleIdentity":"rs-5396058","link":"https://doi.org/10.1186/s40462-025-00567-0","journal":{"identity":"movement-ecology","isVorOnly":false,"title":"Movement Ecology"},"publishedOn":"2025-06-12 15:57:59","publishedOnDateReadable":"June 12th, 2025"},"versionCreatedAt":"2024-11-25 10:54:56","video":"","vorDoi":"10.1186/s40462-025-00567-0","vorDoiUrl":"https://doi.org/10.1186/s40462-025-00567-0","workflowStages":[]},"version":"v1","identity":"rs-5396058","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-5396058","identity":"rs-5396058","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}