Animal Space Use

Taylor’s power law regards the statistical relationship between population variance and population abundance, V = aM b . I refer to Parts I–II for background information. Whether V(M) is studied at a given spatial resolution or from varying abundance M in a sample by changing grid resolution the still unresolved problem is that animal populations (covering a wide range of taxa) upon re-scaling tend to show b≈2. Typical range is 1.5<≈b<≈2.2 rather than b≈1. In other words, due to the power law structure population dispersion seems to be scale-invariant; also called self-similar and thus compliant with a statistical fractal (aggregations within aggregations within…). In this post, I illustrate how V(M) in the Zoomer model becomes compliant with real-life V(M) patterns when the model is parameter-tuned towards its default condition – scale-free population dynamics! Many model proposals exist for V(M) when sampling at a given spatial resolution, but despite thousands of papers ov...

In a previous post I introduced the empirically observed Taylor’s power law, by referring to some of its history and one of its paradoxical properties: population abundance typically seems to satisfy a very aggregated pattern, V = aM b with b≈2, which seems to be self-similar (satisfying a statistical fractal) over a wide range of spatial resolutions. I also hinted towards chapters of my book, where I describe and discuss this and other strange statistical aspects relative to expectation from traditional population-dynamical models. In this post I study how my Zoomer model for scale-free population dynamics behave with respect to compliance with Taylor’s power law if I parameter-tune it towards more standard assumptions. Consider the generic statistical pattern that would be expected from a “well mixed” population (satisfying, for example the default assumption for a standard differential or difference equation model). In this case, which by the way also makes the model population...

A provocative headline is a double-edged sword. Why do I indicate that one of the most rapidly developing fields of animal ecology should still be regarded as a soft science? When it comes to individual space use rest assured that I’m thrilled by the substantial leaps forward in some parts of the theory of animal whereabouts. On the other hand, I also have critical comments. In my view there is still too strong disconnection between some general properties of movement-related animal behaviour and theoretical representations of this behaviour in models. Patch and resource sharing – butterfly Aglais io and bumblebee. Photo: AOG. Both in my book and in previous blog posts I have repeatedly pointed out the unfortunate fact that contemporary models in the field often referred to as “movement ecology” have matured into two quite distinct premise foundations. On one hand we see a broadened recognition of scale-free movement as a quite general property and on the other hand also a bro...

Already from the early days of statistical analysis of home range data one particular property has received particular attention, the degree of serial autocorrelation of the individual’s positions during a period of sampling. In short, if a data series is autocorrelated (due to high frequency sampling of fixes), one is advised to use methods involving path analysis. If data is non-autocorrelated, one should use methods involving a study of locally varying fix density (like classic use-availability analysis). In the latter case, verification of non-significant serial autocorrelation is assumed to imply that each fix can be treated as an independent representation of visits to this particular part of the home range. However, this assumption is in fact deeply erroneous, and it continues to hamper progress in statistical analysis of animal space use. The willow warbler Phylloscopus trochilus toggles between two continents during a year, and between various preferred intra-home range p...

Data collection of individual movement like a series of GPS fixes provides a potential for a physical – a statistical-mechanical – interpretation of animal space use. Such material represents indirect studies of behaviour in contrast to direct observation and interpretation. The GPS pattern of dots on the map provides a coarse-grained image of how the individual in overall terms relocated itself during the period of sampling. It is fascinating that this “out of focus” image may in fact not only be scrutinized with respect to verifying many similar behavioural traits as traditionally studied by ethological methods, but also allows for interpretation of specific relationships that are difficult or outright impossible to test from the classic methods in behavioural ecology. In this post I’m focusing on one of these space use properties, scale-free habitat utilization. First, what is “scale-free movement”? Statistically, this property apparently should be easy to verify (or falsify) by...

The parallel processing concept (PP) is a core postulate of the Multiscaled random walk model. PP provides the backbone of an attempt to understand in a statistical-mechanically consistent manner why animal movement generally tend to show scale-free distribution of displacement lengths at a given frequency of GPS position sampling (Lévy walk-like movement). Contrary to standard Lévy walk theory, PP-based movement seems to offer a plausible explanation for why superlong displacements – the “long tail” part of the Lévy walk-like step length distribution – may appear even in environments with frequent direction-perturbing events. From standard theory such events should tend to “shorten the tail” by prematurely terminate long steps, and simultaneously inflate the frequency of shorter displacements. Thus, the standard Lévy model is – in my view – lacking some essential aspects of many animals’ cognitive computation of environmental conditions and the individual’s internal state.  In m...

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...