Statistical Independence in Space Use Data?

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 patches at a within-season temporal scale. In fact, the home range itself is an emergent property from non-random crossing of its movement path. Photo: AOG.

The Schoener’s ratio (t2/r2) (Shoener 1981) or other methods can easily be applied to test for serial independency in space use data. The ‘time to independence’ (TTI) is estimated by subsampling sets of observations and thus increasing the time intervals between spatial fixes, and calculating t2/r2. The null hypothesis of independence is rejected; i.e., auto-correlation is supported, if the observed t2/r2 is outside the defined critical values around the expected value of 2. However, does a ratio with t2/r2 ∼ 2 satisfy a series of independent events? It does not!

The Schoener’s ratio and other methods in wildlife ecology rest on an assumption that data represents a pattern that is generated from a Markov-compliant process (this property has been repeatedly explained and criticized both in my book, my papers, and in this blog; search Archive: “The Beautiful Anatomy of a Home Range” and in “A Statistical-Mechanical Perspective on Site Fidelity – Part I“). An animal that tends to revisit previous patches by directed returns, i.e., utilizing a memory map, will violate the basic statistical assumption of TTI-methods. In short, such revisits lead to self-reinforcing use of some patches on expense of other patches with a priori similar qualities. Strangely, this confounding effect does not seem to frighten ecologists from applying TTI as a criterion for statistical independence. My wild guess is that…

  • One third of ecologists disregard the memory effect on fix dispersion data because they are not aware of the issue in relation to the TTI assumption. 
  • One third disregard memory effect because they believe it doesn’t matter much for their subsequent data analysis 
  • One third disregard memory because everybody else seems to do so. 
The latter category reflects sloppy science. Hopefully you are not there. If you are in the first category, you are currently seeking personal updating. Welcome.

The second category regards sound scientific skepticism. However, my impression is that many ecologists after scrutinizing papers on this issue may agree on the memory effect on space use data, but they are still reluctant to step away from common methods – even when it comes to concept-testing the alternative methods that are now emerging. Moving out of one’s personal comfort zone is a mental struggle with uncertain reward. Thus, status quo prevails.


Schoener, T.W. 1981 An empirically based estimate of home range. Theoretical Population Biology, 20, 281325.