## Posts

Showing posts from April, 2016

### A Statistical-Mechanical Perspective on Site Fidelity – Part IV

In Part I of this set of posts I described animal space use from the perspective of ergodicity. This is a key concept of standard statistical mechanics, with similar importance to analysis of individual paths and home range data under the extended theoretical framework (the parallel processing conjecture, expressed by the MRW model). Below I elaborate on this theme. I indicate by simulation examples the transition from a fully ergodic state on the home range scale to a narrowing of this scale as the series of fixes become increasingly autocorrelated (higher-frequency sampling). From a biophysical perspective, the following system description may point towards my most important theoretical development since the Scaling cube. This will become clearer as I gradually turn my upcoming posts from description of statistical-mechanical properties towards how to explore these properties in novel methods for ecological inference. First consider the general principle that the transition from

### Population Dispersion under Scale-Free Memory Influence

Over the years the term “density” has provided a convenient variable for ecological inference, since it has a clear definition both at the individual level and the population level. For example, GPS fix density for a given individual and sample size of fixes is proportional with the inverse of the demarcated home range size when this is the area unit. By assuming the standard asymptote model for home range area, fix density N/area is higher when area is smaller. The MRW model, which contradicts the asymptote assumption and is incompatible with the density surface (UD) as a proper proxy for local space use intensity, still presents a proxy variable for intensity of habitat use. In the MRW model the traditional density=N/area is replaced by H=(√N)/c‘ where c‘ is the individual’s characteristic scale of space use, CSSU. Thus, H is proportional with the inverse of CSSU. Contrary to density, which assumes area is intrinsically constant (the asymptote), H adjusts for N-sensitive area dema

### KDE – an Obstacle to Ecological Inference?

In the two foregoing posts I have been quite critical to one of the preferred home range analytical tools among wildlife ecologists, the kernel density estimation (KDE). I have underscored two main points; the well-documented (but mainly ignored) N-paradox and the issue this raises with respect to camouflaging important aspects of the animals’ space use behaviour. In this post I provide an additional illustration of the latter point, and I discuss the serious problem this shortcoming raises for ecological inference based on – for example – GPS fixes (for details and additional examples, see my book). First, a more detailed confirmatory illustration of KDE’s N-paradox. Above I have plotted the 99% isopleths based on a range of sample sizes of fixes, N (open symbols) and compared the result to the alternative area demarcation method incidence (number of non-empty virtual grid cells; filled symbols). The data sets are the series from the two foregoing posts. The “KDE compatible” sp

### Follow-up on the KDE’s Sample Size Paradox

In a previous post I showed how the combination of scale-free movement and spatial memory utilization generates space use that is incompatible with statistical descriptors under the KDE approach. In short, I advocated that the home range – as observed from the scatter of relocation data (fixes) – should be described by methods that are in better coherence with the underlying process in statistical-mechanical terms. The KDE does not comply with scale-free movement, since the emerging fix scatter is a statistical fractal with dimension D≈1, which makes space use incompatible with a density “surface” (utilization distribution, UD). In the present post I elaborate on this issue, and provide further simulation explorations. The illustration to the right shows a home range with a “well-behaved” space use – in close compliance with standard KDE assumptions. The model animal moves scale-specifically (Markov compliant, here represented by correlated random walk), in combination with occasio