Complex animal distribution and abundance from memory-dependent kinetics

Abstract

A realistic implementation of population kinetics, i.e., the transformation of individual movements to population mixing, intraspecific cohesion, site fidelity effects and other statistical mechanical aspects of population dynamics, is crucial for spatio-temporal modeling in ecology. Spatial memory effects on movements and homing are currently not realistically implemented in population dynamical modeling, which is based on an assumption of memory-free random walk and diffusion processes beyond fine-scaled behavior. We suggest a generic model where the animal relates to its familiar space strategically, by utilizing historic information for spatial memory mapping of its environment beyond its instant field of perception. Simulations illustrate how this mechanism may self-organize a scale-free, or fractal, habitat utilization even in a homogeneous environment, over a potentially large range of spatial scales. By tuning parameters for fractal dimension of step length distributions and return probability to previous locations, a continuum from a scale-free, memory-influenced displacement process to a classic, scale-specific and memory-free random walk-like process is achieved. Individual series of locations are superimposed with a varying degree of inter-connectedness to explore memory-influenced space use patterns in the context of population kinetics, i.e., by considering an ensemble of model individuals utilizing the same environment at the same time. A memory-dependent transition towards inter-individual dependency of space use is described as “intraspecific cohesion”.