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Step selection analysis (SSA) is a common framework for understanding animal movement and resource selection using telemetry data. Such data are, however, inherently autocorrelated in space, a complication that could impact SSA‐based inference if left unaddressed. Accounting for spatial correlation is standard statistical practice when analysing spatial data, and its importance is increasingly recognized in ecological models (e.g. species distribution models). Nonetheless, no framework yet exists to account for such correlation when analysing animal movement using SSA.
Here, we extend the popular method integrated step selection analysis (iSSA) by including a Gaussian field (GF) in the linear predictor to account for spatial correlation. For this, we use the Bayesian framework R‐INLA and the stochastic partial differential equations (SPDE) technique.
We show through a simulation study that our method provides accurate fixed effects estimates, quantifies their uncertainty well and improves the predictions. In addition, we demonstrate the practical utility of our method by applying it to three wolverine (Gulo gulo) tracks.
Our method solves the problems of assuming spatially independent residuals in the SSA framework. In addition, it offers new possibilities for making long‐term predictions of habitat usage.
RangeShifter 2.0
(2021)
Process-based models are becoming increasingly used tools for understanding how species are likely to respond to environmental changes and to potential management options. RangeShifter is one such modelling platform, which has been used to address a range of questions including identifying effective reintroduction strategies, understanding patterns of range expansion and assessing population viability of species across complex landscapes. Here we introduce a new version, RangeShifter 2.0, which incorporates important new functionality. It is now possible to simulate dynamics over user-specified, temporally changing landscapes. Additionally, we integrated a new genetic module, notably introducing an explicit genetic modelling architecture, which allows for simulation of neutral and adaptive genetic processes. Furthermore, emigration, transfer and settlement traits can now all evolve, allowing for sophisticated simulation of the evolution of dispersal. We illustrate the potential application of RangeShifter 2.0's new functionality by two examples. The first illustrates the range expansion of a virtual species across a dynamically changing UK landscape. The second demonstrates how the software can be used to explore the concept of evolving connectivity in response to land-use modification, by examining how movement rules come under selection over landscapes of different structure and composition. RangeShifter 2.0 is built using object-oriented C++ providing computationally efficient simulation of complex individual-based, eco-evolutionary models. The code has been redeveloped to enable use across operating systems, including on high performance computing clusters, and the Windows graphical user interface has been enhanced. RangeShifter 2.0 will facilitate the development of in-silico assessments of how species will respond to environmental changes and to potential management options for conserving or controlling them. By making the code available open source, we hope to inspire further collaborations and extensions by the ecological community.
Movement behavior is an essential element of fundamental ecological processes such as competition and predation. Although intraspecific trait variation (ITV) in movement behaviors is pervasive, its consequences for ecological community dynamics are still not fully understood. Using a newly developed individual-based model, we analyzed how given and constant ITVs in foraging movement affect differences in foraging efficiencies between species competing for common resources under various resource distributions. Further, we analyzed how the effect of ITV on emerging differences in competitive abilities ultimately affects species coexistence. The model is generic but mimics observed patterns of among-individual covariation between personality, movement and space use in ground-dwelling rodents. Interacting species differed in their mean behavioral types along a slow-fast continuum, integrating consistent individual variation in average behavioral expression and responsiveness (i.e. behavioral reaction norms). We found that ITV reduced interspecific differences in competitive abilities by 5-35% and thereby promoted coexistence via an equalizing mechanism. The emergent relationships between behavioral types and foraging efficiency are characteristic for specific environmental contexts of resource distribution and population density. As these relationships are asymmetric, species that were either 'too fast' or 'too slow' benefited differently from ITV. Thus, ITV in movement behavior has consequences for species coexistence but to predict its effect in a given system requires intimate knowledge on how variation in movement traits relates to fitness components along an environmental gradient.
Mathematical analysis of partial differential equations (PDEs) has led to many insights regarding the effect of organism movements on spatial population dynamics. However, their use has mainly been confined to the community of mathematical biologists, with less attention from statistical and empirical ecologists. We conjecture that this is principally due to the inherent difficulties in fitting PDEs to data. To help remedy this situation, in the context of movement ecology, we show how the popular technique of step selection analysis (SSA) can be used to parametrize a class of PDEs, calleddiffusion-taxismodels, from an animal's trajectory. We examine the accuracy of our technique on simulated data, then demonstrate the utility of diffusion-taxis models in two ways. First, for non-interacting animals, we derive the steady-state utilization distribution in a closed analytic form. Second, we give a recipe for deriving spatial pattern formation properties that emerge from interacting animals: specifically, do those interactions cause heterogeneous spatial distributions to emerge and if so, do these distributions oscillate at short times or emerge without oscillations? The second question is applied to data on concurrently tracked bank volesMyodes glareolus. Our results show that SSA can accurately parametrize diffusion-taxis equations from location data, providing the frequency of the data is not too low. We show that the steady-state distribution of our diffusion-taxis model, where it is derived, has an identical functional form to the utilization distribution given by resource selection analysis (RSA), thus formally linking (fine scale) SSA with (broad scale) RSA. For the bank vole data, we show how our SSA-PDE approach can give predictions regarding the spatial aggregation and segregation of different individuals, which are difficult to predict purely by examining results of SSA. Our methods provide a user-friendly way into the world of PDEs, via a well-used statistical technique, which should lead to tighter links between the findings of mathematical ecology and observations from empirical ecology. By providing a non-speculative link between observed movement behaviours and space use patterns on larger spatio-temporal scales, our findings will also aid integration of movement ecology into understanding spatial species distributions.
Accurately quantifying species' area requirements is a prerequisite for effective area-based conservation. This typically involves collecting tracking data on species of interest and then conducting home-range analyses. Problematically, autocorrelation in tracking data can result in space needs being severely underestimated. Based on the previous work, we hypothesized the magnitude of underestimation varies with body mass, a relationship that could have serious conservation implications. To evaluate this hypothesis for terrestrial mammals, we estimated home-range areas with global positioning system (GPS) locations from 757 individuals across 61 globally distributed mammalian species with body masses ranging from 0.4 to 4000 kg. We then applied block cross-validation to quantify bias in empirical home-range estimates. Area requirements of mammals <10 kg were underestimated by a mean approximately15%, and species weighing approximately100 kg were underestimated by approximately50% on average. Thus, we found area estimation was subject to autocorrelation-induced bias that was worse for large species. Combined with the fact that extinction risk increases as body mass increases, the allometric scaling of bias we observed suggests the most threatened species are also likely to be those with the least accurate home-range estimates. As a correction, we tested whether data thinning or autocorrelation-informed home-range estimation minimized the scaling effect of autocorrelation on area estimates. Data thinning required an approximately93% data loss to achieve statistical independence with 95% confidence and was, therefore, not a viable solution. In contrast, autocorrelation-informed home-range estimation resulted in consistently accurate estimates irrespective of mass. When relating body mass to home range size, we detected that correcting for autocorrelation resulted in a scaling exponent significantly >1, meaning the scaling of the relationship changed substantially at the upper end of the mass spectrum.
Home range estimation is routine practice in ecological research. While advances in animal tracking technology have increased our capacity to collect data to support home range analysis, these same advances have also resulted in increasingly autocorrelated data. Consequently, the question of which home range estimator to use on modern, highly autocorrelated tracking data remains open. This question is particularly relevant given that most estimators assume independently sampled data. Here, we provide a comprehensive evaluation of the effects of autocorrelation on home range estimation. We base our study on an extensive data set of GPS locations from 369 individuals representing 27 species distributed across five continents. We first assemble a broad array of home range estimators, including Kernel Density Estimation (KDE) with four bandwidth optimizers (Gaussian reference function, autocorrelated‐Gaussian reference function [AKDE], Silverman's rule of thumb, and least squares cross‐validation), Minimum Convex Polygon, and Local Convex Hull methods. Notably, all of these estimators except AKDE assume independent and identically distributed (IID) data. We then employ half‐sample cross‐validation to objectively quantify estimator performance, and the recently introduced effective sample size for home range area estimation ( N̂ area
) to quantify the information content of each data set. We found that AKDE 95% area estimates were larger than conventional IID‐based estimates by a mean factor of 2. The median number of cross‐validated locations included in the hold‐out sets by AKDE 95% (or 50%) estimates was 95.3% (or 50.1%), confirming the larger AKDE ranges were appropriately selective at the specified quantile. Conversely, conventional estimates exhibited negative bias that increased with decreasing N̂ area. To contextualize our empirical results, we performed a detailed simulation study to tease apart how sampling frequency, sampling duration, and the focal animal's movement conspire to affect range estimates. Paralleling our empirical results, the simulation study demonstrated that AKDE was generally more accurate than conventional methods, particularly for small N̂ area. While 72% of the 369 empirical data sets had >1,000 total observations, only 4% had an N̂ area >1,000, where 30% had an N̂ area <30. In this frequently encountered scenario of small N̂ area, AKDE was the only estimator capable of producing an accurate home range estimate on autocorrelated data.
Identifying behavioral mechanisms that underlie observed movement patterns is difficult when animals employ sophisticated cognitive‐based strategies. Such strategies may arise when timing of return visits is important, for instance to allow for resource renewal or territorial patrolling. We fitted spatially explicit random‐walk models to GPS movement data of six wolves (Canis lupus; Linnaeus, 1758) from Alberta, Canada to investigate the importance of the following: (1) territorial surveillance likely related to renewal of scent marks along territorial edges, to reduce intraspecific risk among packs, and (2) delay in return to recently hunted areas, which may be related to anti‐predator responses of prey under varying prey densities. The movement models incorporated the spatiotemporal variable “time since last visit,” which acts as a wolf's memory index of its travel history and is integrated into the movement decision along with its position in relation to territory boundaries and information on local prey densities. We used a model selection framework to test hypotheses about the combined importance of these variables in wolf movement strategies. Time‐dependent movement for territory surveillance was supported by all wolf movement tracks. Wolves generally avoided territory edges, but this avoidance was reduced as time since last visit increased. Time‐dependent prey management was weak except in one wolf. This wolf selected locations with longer time since last visit and lower prey density, which led to a longer delay in revisiting high prey density sites. Our study shows that we can use spatially explicit random walks to identify behavioral strategies that merge environmental information and explicit spatiotemporal information on past movements (i.e., “when” and “where”) to make movement decisions. The approach allows us to better understand cognition‐based movement in relation to dynamic environments and resources.