Equivalence between Step Selection Functions and Biased Correlated Random Walks for Statistical Inference on Animal Movement

Abstract

Animal movement has a fundamental impact on population and community structure and dynamics. Biased correlated random walks (BCRW) and step selection functions (SSF) are commonly used to study movements. Because no studies have contrasted the parameters and the statistical properties of their estimators for models constructed under these two Lagrangian approaches, it remains unclear whether or not they allow for similar inference. First, we used the Weak Law of Large Numbers to demonstrate that the log-likelihood function for estimating the parameters of BCRW models can be approximated by the log-likelihood of SSFs. Second, we illustrated the link between the two approaches by fitting BCRW with maximum likelihood and with SSF to simulated movement data in virtual environments and to the trajectory of bison (Bison bison L.) trails in natural landscapes. Using simulated and empirical data, we found that the parameters of a BCRW estimated directly from maximum likelihood and by fitting an SSF were remarkably similar. Movement analysis is increasingly used as a tool for understanding the influence of landscape properties on animal distribution. In the rapidly developing field of movement ecology, management and conservation biologists must decide which method they should implement to accurately assess the determinants of animal movement. We showed that BCRW and SSF can provide similar insights into the environmental features influencing animal movements. Both techniques have advantages. BCRW has already been extended to allow for multi-state modeling. Unlike BCRW, however, SSF can be estimated using most statistical packages, it can simultaneously evaluate habitat selection and movement biases, and can easily integrate a large number of movement taxes at multiple scales. SSF thus offers a simple, yet effective, statistical technique to identify movement taxis.

Secrets of Success in a Landscape of Fear: Urban Wild Boar Adjust Risk Perception and Tolerate Disturbance

“…This resource selection function (Boyce et al, 2002) could alternatively have been assessed with step selection function which compare original steps with random steps (Thurfjell et al, 2014) instead of CRWs. Since both methods were shown to provide similar results (Duchesne et al, 2015), we assume that our results are a good reflection of wild boar's resource selection. Thereby we were for example able to show that urban wild boar do not select agricultural areas although they are available for them.…”

Incorporating movement in species distribution models

“…The benefit of using SSF within a BCRW over other implementations is that it includes the results of conditional logistic regression. As movement is simulated using a statistical model generated from observed movements, more realistic movement behaviors are simulated compared to a model specified solely on subjective assumptions, and results better illustrate the influences of the environment on actual movements (Duchesne et al 2015). Similarly, SSF can be deconstructed to capture the variations in movement patterns across days and seasons (e.g.…”

“…A recent criticism of SSF has been the lack of methodology with which to incorporate a measure of memory (Fagan et al 2013;Duchesne et al 2015). To ignore the effects of memory when analyzing movement decisions made by animals can lead to biased estimates of resource selection coefficients (Oliveira-Santos et al 2016).…”

“…Recently Duchesne et al (2015) showed that BCRW and step-selection function (SSF) provided similar insights into the environmental factors influencing bison movement in Canada. SSF is a powerful spatial modelling approach that uses telemetry data to analyze movement patterns and resource use based on the underlying environment (Thurfjell et al 2014).…”

A general hidden state random walk model for animal movement

“…Another example is the biased correlated random walk model (BCWR, see for example [4]). It has h y t , d t |S t , F c t−1 = f (y t |y t−1 , x 1t ), see also [16] for additional discussion of the consensus model when p = 1.…”