The Dilution effect and the Space fill effect: Seeking to offset statistical artifacts when analyzing animal space use from telemetry fixes

Statistical analysis of the spatial dispersion of telemetry locations (fixes) has an important role in ecological studies on animal space use, in particular in the context of home range behaviour. A home range typically emerges as a complex mixture of both short term and long term memory-dependence in movement and side fidelity. An extended statistical mechanical framework – the Multi-scaled Random Walk model (MRW) – seeks to account for the complexity from memory effects on individual space use. In particular, four main classes of movement can be distinguished from analysis of the fractal dimension of the spatial dispersion of fixes; Brownian motion-like (including classic random walk and correlated random walk), Levy walk-like, memory-enhanced Brownian motion-like and MRW-like. The two former classes represent memory-less space use, whilst the latter two classes are memory enhanced. The statistical mechanical approach behind this classification ideally requires large sets of fixes for analysis, and it is also necessary to adjust for two statistical artifacts, the Dilution effect and the Space fill effect. We describe the nature of these artifacts based on output from simulations, and propose statistical model modifications to minimize their influence on parameter estimation. We illustrate the analysis and modification protocols on data from simulations of individual space use and on telemetry fixes from 11 free-ranging domestic sheep, Ovis aries. The material for analysis of the sheep data is very limited (ca. 140 fixes per individual), a common issue for applied ecology. Some fixes were also lost due to occasionally very long-range sallies by the individual (missing signal). The study area was thus too narrowly defined to embed the sheep's true space use during the given sampling period. Still, the proposed methods allows for tweaking consistent parameter estimation from the data, given a close focus on the statistical artifacts.

► Models in the field of animal movement are based on the Markovian assumption. ► Thus, the space use is assumed to be memory-less. ► This creates a paradox, since vertebrates utilize a cognitive map. ► An extended statistical mechanical framework MRW includes memory effects. ► Statistical artifacts are described and tested, based on simulations of MRW.