### Why W. H. Burt is Now Hampering Progress in Modern Home Range Analysis

**The term “Home range” (HR) generally follows Burt’s (1943) definition, the area traversed by the individual in its normal activities of food gathering, mating, and caring for young. Occasional sallies outside of the area, perhaps exploratory in nature, should not be considered as home range. However, with respect to fine-grained perception of a HR, Burt’s definition seems to have guided – in fact cemented – the HR concept into a too narrow and partly misleading perception of individual space use. Hence, in my view the Burt definition is hampering progress in this important field of animal ecology.**

From the perspective of a regional map, an individual’s home range is a zero-dimensional dot. When zooming in towards medium scale, it makes sense to demarcate a home range as a two-dimensional area (or a three-dimensional volume in the context of aquatic or marine systems). The challenge to define HR borders at this scale is reflected in Burt’s second part of his HR definition, leaving some “occasional sallies” outside the polygon, ellipse, isopleth-based demarcation, or whatever kind of area that is differentiating “inside” from “outside”. For more than 60-70 years Ecology has lived well with this medium-resolution definition of a HR. However, recently the Burt definition has become an obstacle as its application has been extended towards finer scales as a consequence of better data.

Modern methods of path collection have greatly improved the length of data series both with respect to extent and temporal resolution. Further, sophisticated statistical analyses for HR demarcations (e.g., KDE and Brownian Bridge) have replaced polygons and other initial protocols for area demarcation. However, the improved quality and quantity of space use data has not made life easier for statistical analyses. Rather, the “inside” versus “outside” issue has surfaced as a core challenge for studies of animal space use and its ecological aspects. Introducing a more sophisticated HR concept by differentiating between the HR and its intra-HR “core areas” has created new challenges. As a result, the Burt definition’s shortcomings are now surfacing and causing seeds of confusion and controversy. In this post I claim that these issues go beyond the normal maturing of ecological methods, where more sophisticated approaches are evolving as a natural progression from (

*i.e.*, refinement of) the older approaches. Hence, the present headline, “Why W. H. Burt is Now Hampering Progress in Modern Home Range Analysis“.

The HR is a challenging concept

*per se*, as illustrated by this mixed-species flock of gulls at the western coast of Norway (observe the relatively rare glaucous gull

*Larus hyperboreus*, number 4 from the right). Inter- and intra-species HR overlap, temporal HR stability and other quantifications require statistically precise variables that are spun from a realistic statistical-mechanical framework. Photo: AOG.

Several assumptions are included in the Burt definition, explicitly or implicitly:

**HR as an area**. Our non-standard approach to analyze the spatial scatter of GPS fixes across a range of spatial resolutions has shown that the respective individuals’ home range better satisfy the concept of a statistical fractal; i.e., a non-Euclidean fractional dimension typically in the range 0.9 < D < 1.2, than an Euclidean area (D=2, surrounded by some Euclidean dots with D=0 called occasional sallies). Thus, treating a HR as a two-dimensional object may be non-realistic and thus misleading for ecological research involving finer spatial scale than the medium “Burt scale” referred to above.**HR as a stationary area**. Recent theoretical work on the HR concept is still implicitly or explicitly assuming that any realistic HR model (for example, as reflected in the output from a simulation) should satisfy a stationary HR area. In statistical-mechanical terms, HR as an area requires a scale-specific kind of habitat utilization ( a Brownian motion-like model that is extended with HR-mimicking mechanics satisfies this criterion). In other words, after accounting for the trivial effects from serial autocorrelation (high-frequency path sampling), drifting HR, and small-sample statistical artifacts, a HR model that still shows a non-stationary range as a function of sample size of fixes should be considered pathological. Non-stationary area implies that the model does not represent HR behaviour. By clinging to this view, one has to disregard a growing set of empirical analyses spanning many species confirming sample-size-dependent HR area (“the home range ghost”). Such non-stationary space use – remaining after the trivial sample effects have been accounted for – becomes a statistical paradox from the perspective of the Burt paradigm, but a trivial property from the perspective of scale-free space use under influence of spatial memory. The latter leads to a set of GPS fixes satisfying a statistical fractal object rather than an integer-dimensional object.**Occasional sallies versus intra-HR displacements**. Turning from the Eulerian to the Lagrangian perspective of space use, the Burt definition forces upon us a distinction between “normal” HR activities and occasional long-distance moves spanning larger ranges than the HR. When successive inter-fix distances are presented in a histogram (frequency of “step lengths” as a function of length), the typical pattern shows the majority of such step lengths located in the small-step bins, some steps in medium-range bins and some (occasional) steps of very large extent. Thus, in the spirit of the Burt definition several attempts have been proposed to differentiate true HR movement from occasional sallies. However, the methodology remains problematic and quasi-objective. On the other hand, if both axes in the histogram are log-transformed, the regression line typically becomes approximately linear over a broad part of the range of step lengths. This is a strong indication of a scale-free space use process (frequent fine-scale moves intermingled with fewer coarse-scale moves, in a mathematically fractal-compliant manner). Thus, while occasional sallies represent a stone in the shoe under the paradigmatic HR concept, the issue evaporates under the fractal HR concept.

Interestingly, many of the key ecological variables that are studied under the Burt paradigm (local intensity of space use, habitat preference, HR size, HR overlap, core areas, HR stability, etc.) have their quantifiable counterparts under the emerging “HR as a fractal” model. Unfortunately, the Burt legacy is hampering a broader exploration and critical evaluation of the latter.

REFERENCES

Burt, W.H., 1943. Territoriality and home range concepts as applied to mammals. J. Mammal. 24:346-352.