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A Statistical-Mechanical Perspective on Site Fidelity – Part IIX

The power law expansion of observed space use in the Multi-scaled random walk model (MRW) shows a non-trivial relationship with sample size N of spatial relocations (fixes). In this post I introduce imaginary numbers to resolve more precisely what I have called the apparent paradox of the time-independent inwards/outwards expansion with increasing N, as it emerges both from the spatial and the temporal aspect of the process. This novel development hopefully contributes to the continued bridge-building between biophysics and space use aspects of behavioural ecology.
The inwards/outwards expansion in the MRW model is popping out of the Home range ghost formula I(N) ≈ c√N (Gautestad and Mysterud 2005), where incidence, I, is the total area of fix-containing virtual grid cells. As verified repeatedly both theoretically and empirically, I(N) is not simply a statistical small-sample size artifact, but an emerging property of the combination of spatio-temporal memory and scale-free habitat ut…

Random Returns Are Not Random

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The statistical-mechanical universality class Multi-scaled random walk (MRW) is a relatively recent addition to the menagerie of various types of random walk (RW). It seeks to capture some key aspects of animal space use, in particular the combined effects of spatio-temporal memory and scale-free movement. In this post I put focus on the statistical property of return events to previously visited positions (memory-dependent site fidelity). How can such events feasibly and realistically be treated as random, knowing that the animal by targeted returns will tend to revisit more profitable patches with a higher probability than other locations? In particular, one specific aspect of the answer, revealed here in detail for the first time, will probably surprise you. Complexity turned into simplicity!What regards the the transition from deterministic behaviour to a RW process in general terms, search my blog for "Markov", or you may for example look into Gautestad (2013). To place…

Roe Deer Comply With the MRW Model

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Animal space use expresses a balance between exploring new localities and returning to the known. However, as stated by Ranc et al. (2020), the link between spatio-temporal resource patterns and animal movement has so far found limited experimental support. In their paper they found that following the loss of the individuals' preferred resource, roe deer Capreolus capreolus actively tracked resource dynamics leading to more exploratory movements, and larger, spatially-shifted home ranges. They also demonstrated the return of individuals to their familiar, preferred resource patches after local resource restoration. On the background of this interesting and dynamic habitat manipulation, I have allowed myself to drill into the raw GPS data as provided by their paper's Supplementary material. How does space use by roe deer fit the Multi-scaled random walk (MRW) property of scale-free, memory-utilizing space use?

Choosing a biophysical universality class of movement that best compl…

A Statistical-Mechanical Perspective on Site Fidelity – Part VII

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Animal space use analysis should be less focused on home range area demarcations and rather explore methods for statistical-mechanical studies of the set of spatial relocations (fixes). The latter approach appears more compatible with a scale-free and memory-influenced habitat utilization, which has recently been repeatedly verified in many species. In this post I develop the theoretical foundation behind the matching scale-free/memory-driven MRW model one step further by clarifying the dual aspect of observation intensity, which I find necessary in complex systems analyses of animal space use. I also show how a change of intensity has to be coherently linked to the concept of system entropy.
This post regards a follow-up on A Statistical-Mechanical Perspective on Site Fidelity – Part I-VI posted during February 1, 2016 to October 7, 2016 (search Archive). 
First, recall that the parsimonious "home range ghost" formula for scale-free and memory influenced space use (the Multi-…