## Estimating Home Ranges

The simplest method of presenting the results of a trapping or telemetry study is to map all the positive records collected for each individual and draw a line around the outermost ones. The home range is defined as the area of the minimum convex polygon that includes all the locations known to have been visited. This method is simple and has a long history of use (Hayne 1949), but it often also includes large areas that are never visited, so grossly oversimplifies, and can actually muddy, the real picture (Powell 2000).

Minimum convex polygons are strongly influenced by extreme locations, those that are at the edges of where an animal travels, so missing an extreme point or including an exploratory trip can make a huge difference to estimates of an animal's home range. But in fact, almost all the studies of weasel home ranges that we review here have presented their results in terms of minimum convex polygons, because the simplest method is often the only one whose scrutiny the field data can bear.

A more important problem with minimum convex polygons is that they fail to use all of the hard-earned data from the interior of a home range, and they concentrate on the question of the size of the area an animal covers at the cost of more interesting questions about how it uses that area. For example, a weasel's

Figure 8.2 Attaching a tag onto the ear of an anesthetized stoat. (Redrawn from a photograph by C. D. McMillan.)

home range should really be described in all three dimensions of space plus the fourth dimension of time. Weasels of all species regularly explore the airspace both above the ground, by climbing trees, and underground, by running through burrows, and they use some parts of their home ranges much more often than other parts.

The best way to understand this complex pattern of use is to build a probability distribution of how a resident animal uses spaceāor, better yet (when someone figures out how to make one), a distribution showing how important the different parts of a home range are to its owner. For weasels, the question of how each uses the inside of its home range for foraging and avoiding larger predators is at least as important as the question of how it maintains its boundaries and interactions with other weasels outside.

If enough data are available, which requires successful radiotelemetry on a large number of individuals, new techniques for analyzing home ranges can begin to answer questions about how weasels move about on the ground most familiar to them. The simplest of these new methods is to divide the study area into small cells by drawing grid lines on a map and to count the number of times each animal was located within each cell. The result looks like a series of pillars rising from the map, and the height of each pillar shows the number of locations for that animal in each cell, thereby estimating how each animal divides its time across its home range (Powell 2000).

The next step is to use a fixed kernel estimator (the best method of analyzing home range data available at present) to convert the separate pillars into an undulating smooth surface (a utility distribution) whose highest spots are above the places the animal uses the most. It is easy to step from that to a probability distribution, showing the probability that the animal will be found in any given part of its home range. For example, in a nesting colony of burrowing seabirds in New Zealand, around 80% of the radio fixes from the stoats observed by Cuthbert and Sommer (2002) were located among seabird burrows, even though burrowed ground occupied on average only about 20% of each stoat's home range.

Utility distributions are demanding of data but extremely handy for analyzing home ranges. For example, superimposing an animal's utility distribution over a habitat map allows one to estimate the probability that the animal will be found in each habitat. Superimposing the utility distributions for two neighboring animals allows one to estimate how important the overlap is to them. If the overlap is in areas little used by each, it is probably of little importance to the animals, no matter how large its area. Cuthbert and Sommer's stoats tolerated a high degree of overlap in the 80% of their ranges outside the seabird colonies where they spent the least amount of time. If the overlap is in areas used much by both, the overlap is surely important, even if small. Unfortunately, the data requirements of kernel estimators are hard to meet, and few studies of weasels have attempted to use them.