The capacity, tendency, and manner for which an organism moves, under particular internal and external conditions, is central to its fitness. Constituting a fundamental element of life, movement traits shape a plethora of large-scale phenomena from land-use patterns to ecosystem maintenance. Recently, this area of investigation has been heralded as a frontier of biological research, acquiring, in the mean time, the shiny subject label of “movement ecology”. The overarching aim of this burgeoning field is to identify the fundamental behavioral and ecological mechanisms underlying movement pathways, taking into account a diverse array of internal and external drivers such cognitive capacity, environmental cues, and motion and navigational properties tied to physiological constraints. However, due to technical complications and an incomplete understanding of movement mechanisms, much of the current literature deal with asymptotic, long-term space use pattern while largely ignoring the more ecologically relevant transient dynamics that are spatio-temporally modulated. Here, we rebuild a new analytically tractable home range model that combines various established mechanisms. Through the use of finite volume method, we also produce from it the elusive transient solutions of which the complexity shines new light on our understanding of animal movement.
Results/Conclusions
Despite the relatively simplistic mathematical form adopted, a self-feedback dynamical spatial structure emerges from the system whereby the home range boundary pulsates periodically when observed within particular time scale. This result predicts specific modulations of the spatial time series as a function of time scale resolution the observations are made under, thereby lending support to recent field studies of ungulate movement. Further Monte Carlo simulation reveals the presence of a stochastic limit cycle between the animal displacement and its cognitive acuity. The discovery of this phase plane provides the groundwork for a new graphical measure for home range stability. Autocorrelated sampling of the simulated space-use distribution reinforces the intuition that the animal returns to its den site via the probabilistically least recently-explored path in a way that is contigent upon seasonal, ecological variables that affect both the den site value and the preferred residence time of neighboring sites. The emergent locally-Brownian, locally-ballistic movement pattern converges on the classic Lévy walk distribution over time, suggesting strong behavioral-ecological drivers behind the latter’s repeated appearances in empirical data. Prospectively, this model serves as a potential theoretical scaffold that enables and facilitates easy integations of foraging theory, biomechanics, and other subdisciplines.