Showing posts from October, 2016

The Mysterious Taylor’s Power Law – Part I

Interesting statistical properties of population dispersion emerge from the simulations of the Zoomer model (search Archive), which represents the population level variant of my Multi-scaled random walk model (MRW). The Zoomer model seems to offer a potential to cast new light on a particular scaling pattern, Taylor’s power law (Taylor 1961, 1986), which has been a nagging stone in the shoe for population ecology for more than 50 years. Taylor’s power law is one of the most widely tested empirical patterns in ecology and is the subject of an estimated thousand papers (Eisler et al. 2008)! Despite this effort, a consensus to explain it has still not been obtained (Kendal and Jørgensen 2011). The scale-free pattern has been observed far beyond animal populations: Taylor’s law is remarkable in that it is evident over the scale of a single chromosome (Kendal 2003, 2004) to the lungs of mice (Kendal and frost 1987), a farmer’s field (Kendal 2002), and upward to the breadth of the Britis

A Statistical-Mechanical Perspective on Site Fidelity – Part VI

In Part III of this group of posts I described how to estimate an animal’s characteristic scale of space use, CSSU, by zooming over a range of pixel resolutions until “focus” is achieved according to the Home range ghost function I(N)=c√N. This pixel size regards the balancing point where observed inward contraction of entropy equals outward expansion of entropy, as sample size of fixes N is changed. If the power exponent satisfies 0.5 [i.e., square root expansion of I(N)], the MRW theory states that the animal – in statistical terms – had put equal weight into habitat utilization over the actual scale range of space use. In Part V I explained two new statistical-mechanical concepts, micro-and macrostates of a system, but in the context of the classical framework. In this follow-up post I’m approaching the behaviour of these key properties under the condition of complex space use, both at the “balancing scale” CSSU and by zooming over its surrounding range of scales. In other words, wh