Parametrising diffusion-taxis equations from animal movement trajectories using step selection analysis

Abstract

O_LIMathematical 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. C_LIO_LITo 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 parametrise a class of PDEs, called diffusion-taxis models, from an animals trajectory. We examine the accuracy of our technique on simulated data, then demonstrate the utility of diffusion-taxis models in two ways. First, we derive the steady-state utilisation distribution in a closed analytic form. Second, we give a simple recipe for deriving spatial pattern formation properties that emerge from inferred movement-and-interaction processes: specifically, do those processes lead to heterogeneous spatial distributions and if so, do these distributions oscillate in perpetuity or eventually stabilise? The second question is demonstrated by application to data on concurrently-tracked bank voles (Myodes glareolus). C_LIO_LIOur results show that SSA can accurately parametrise 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 exists, has an identical functional form to the utilisation 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. C_LIO_LIOur methods give a user-friendly way in to 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. C_LI