Ecological theory related to animal distribution and abundance is at present incomplete and to some extent naive. We suggest that this may partly be due to a long tradition in the field of model development for choosing mathematical and statistical tools for convenience rather than applicability. Real population dynamics are influenced by nonlinear interactions, nonequilibrium conditions, and scaling complexity from system openness. Thus, a coherent theory for individual-, population-, and community-level processes should rest on mathematical and statistical methods that explicitly confront these issues in a manner that satisfies principles from statistical mechanics for complex systems. Instead, ecological theory is traditionally based on premises from simpler statistical mechanical theory for memory-free, scale-specific, random-walk, and diffusion processes, while animals from many taxa generally express strategic homing, site fidelity, and conspecific attraction in direct violation of primary model assumptions. Thus, the main challenge is to generalize the theory for memory-free physical, many-body systems to include a more realistic memory-influenced framework that better satisfies ecological realism. We describe, simulate, and discuss three testable aspects of a model for multiscaled habitat use at the individual level: (1) scale-free distribution of movement steps under influence of self-reinforcing site fidelity, (2) fractal spatial dispersion of intra-home range relocations, and (3) nonasymptotic expansion of observed intra-home range patch use with increasing set of relocations. Examples of literature data apparently supporting the conjecture that multiscaled, strategic space use is widespread among many animal taxa are also described. We suggest that the present approach, which provides a protocol to test for influence from scale-free, memory-dependent habitat use at the individual level, may also point toward a guideline for development of a generalized theoretical framework for complex population kinetics and spatiotemporal population dynamics.

No abstract

No abstract

Summary1. Increased inference regarding underlying behavioural mechanisms of animal movement can be achieved by comparing GPS data with statistical mechanical movement models such as random walk and L evy walk with known underlying behaviour and statistical properties. 2. GPS data are typically collected with ! 1 h intervals not exactly tracking every mechanistic step along the movement path, so a statistical mechanical model approach rather than a mechanistic approach is appropriate. However, comparisons require a coherent framework involving both scaling and memory aspects of the underlying process. Thus, simulation models have recently been extended to include memory-guided returns to previously visited patches, that is, site fidelity. 3. We define four main classes of movement, differing in incorporation of memory and scaling (based on respective intervals of the statistical fractal dimension D and presence/absence of site fidelity). Using three statistical protocols to estimate D and site fidelity, we compare these main movement classes with patterns observed in GPS data from 52 females of red deer (Cervus elaphus). 4. The results show best compliance with a scale-free and memory-enhanced kind of space use; that is, a power law distribution of step lengths, a fractal distribution of the spatial scatter of fixes and site fidelity. 5. Our study thus demonstrates how inference regarding memory effects and a hierarchical pattern of space use can be derived from analysis of GPS data.

No abstract

No abstract

Animals moving under the influence of spatio-temporal scaling and long-term memory generate a kind of space-use pattern that has proved difficult to model within a coherent theoretical framework. An extended kind of statistical mechanics is needed, accounting for both the effects of spatial memory and scale-free space use, and put into a context of ecological conditions. Simulations illustrating the distinction between scale-specific and scale-free locomotion are presented. The results show how observational scale (time lag between relocations of an individual) may critically influence the interpretation of the underlying process. In this respect, a novel protocol is proposed as a method to distinguish between some main movement classes. For example, the 'power law in disguise' paradox-from a composite Brownian motion consisting of a superposition of independent movement processes at different scales-may be resolved by shifting the focus from pattern analysis at one particular temporal resolution towards a more process-oriented approach involving several scales of observation. A more explicit consideration of system complexity within a statistical mechanical framework, supplementing the more traditional mechanistic modelling approach, is advocated.

How to differentiate between scale-free space use like Lévy walk and a two-level scale-specific process like composite random walk (mixture of intra-and inter-patch habitat movement) is surrounded by controversy. Composite random walk may under some parameter conditions appear Lévy walk-like from the perspective of the path's distribution of step lengths due to superabundance of very long steps relative to the expectation from a classic (single-level) random walk. However, a more explicit focus on the qualitative differences between studying movement at a high resolution mechanistic (behavioral) level and the more coarse-grained statistical mechanical level may contribute to resolving both this and other issues related to scaling complexity. Specifically, a re-sampling of a composite random walk at larger time lags than the micro-level unit time step for the simulation makes a Lévy-look-alike step length distribution re-shaping towards a Brownian motion-like pattern. Conversely, a true Levy walk maintains its scaling characteristics upon re-sampling. This result illustrates how a confusing pattern at the mechanistic level may be resolved by changing observational scale from the micro level to the coarser statistical mechanical meso-or macro-scale. The instability of the composite random walk pattern under rescaling is a consequence of influence of the central limit theorem. I propose that a coarse-graining test -studying simulated animal paths at a coarsened temporal scale by re-sampling a series -should be routinely performed prior to comparing theoretical results with those patterns generated from GPS data describing animal movement paths. Fixes from terrestrial mammals are often collected at hourly intervals or larger, and such a priori coarse-grained series may thus comply better with the statistical mechanical meso-or macro-level of analysis than the behavioral mechanics observed at finer resolutions typically in the range of seconds and minutes. If fixes of real animals are collected at this high frequency, coarse graining both the simulated and real series is advised in order to bring the analysis into a temporal scale domain where analytical methods from statis tical mechanics can be applied.