Delimitación conceptual

Measurement of home range size, shape, and an individual's use of that area, have become an increasingly important aspect of ecological and behavioural studies since Seton introduced the concept in 1909 (cited in Sanderson, 1966). The idea has been refined several times over the intervening decades, and is now broadly accepted as “...that area traversed by the individual in its normal activities of food gathering, mating and caring for young...” (Burt 1943, cited in White and Garrott, 1990). Home range measures are necessary when determining population densities, habitat use, spacing of individuals, and most importantly for this study, interactions between individuals. The amount of emphasis that is put on the words ‘normal activities’ needs to be defined for each study, as does the method of calculation. This definition also needs to include the time period of the study and the status of individuals eg. age or sex (Harris et al., 1990). The objectives of the study, the questions one has, and hypotheses to be tested, will determine these factors.

Home range is not all the area over which an animal moves in its lifetime, rather the area in which it normally moves. There are no generally accepted, objective, and biologically based, criteria for the selection of ‘normal’ point locations to be used in the calculation of a home range. White and Garrott (1990) identify two commonly used criteria; (i) a subjective evaluation by the observer (hardly objective and not repeatable by other researchers), and (ii) a probability level, eg. a 95% probability that the defined area will enclose a randomly selected single radio-location of the animal in question. The latter is objective, but also convenient - why 95 rather than 88%?

The majority of home range estimators require that locations be statistically independent. In most cases this is not possible, as a subsequent position of an animal is usually related to the present location. General rules of statistics are applied as much as possible, in that (i) a random sample of animals are chosen for tracking, and that any of them may be tracked at any time, and (ii) any point in time over the sampling period should have an equal chance of being sampled. Sampling interval can have a considerable influence on the home range estimate. Swihart and Slade (1985) found that, over a specified time frame, non statistical estimates (minimum polygons), became increasingly accurate as the number of observations increased, despite increasing autocorrelation. In contrast, bivariate normal estimators underestimated such ranges due to autocorrelation between locations. 2.3.1. Types of Home Range Estimator

There are 3 main types of home range estimator: 1. Minimum area polygons (MAP)

2. Bivariate normal estimators 3. Non-parametric methods 2.3.1.1. Minimum area polygons

These are the oldest, and most commonly used estimators (White and Garrott, 1990). There are several variations, the simplest of which is a polygon formed by joining all the outermost locations.

The method adjusts to any shaped area, is simple to calculate, and can cope with uniform distributions of animal locations. Disadvantages include, (i) an indefinite increase in home range size - there is always a probability that a subsequent location may be outside the area already defined, (ii) the method doesn't allow for autocorrelation as it assumes independence, and (iii) biologically incorrect ranges can be calculated - eg. a land animal living on the banks of a curved river may have the river included in its home range area.

Modifications to the basic method have been suggested. These include exclusion of outliers before data analysis, which can be time consuming as often all combinations of exclusion points need to be examined, (Kenward, 1987). Another variation is to use concave rather than convex polygons. Convex polygons join outer points at approximate angles of 180°, the interior angles between points for concave polygons may be 30°, but there are no objective criteria based on biological grounds (White and Garrott, 1990). (See Appendix II for figures describing range types)

2.3.1.2. Bivariate normal estimators

Bivariate normal models assume that animals move randomly about their home range, with the most probable locations being the centre - mean of the x and y coordinates. Jennrich and Turner (1969) generalised the shape to an ellipse. The method is not dependant on sample size - a 95% ellipse estimated from 100 points is expected to be the same size as one from 500. Home range size is more comparable between studies than is the case for polygon methods. Enhancements to the estimator include applying a weighting factor to each point based on its distance from the mean (Koeppl et al., 1977), or may take into account both distance and time of locations from the mean (Dunn and Gipson, 1977).

Bivariate models fail to adequately describe movements of many animal species as they do not move about randomly on a plane. Excursions from a centre of activity such as a den or nest - itself seldom in the centre of the range - are generally purposeful movements to food, water or mates. They are, however, easily calculated, and provide a probability estimate.

2.3.1.3. Non-parametric methods

Non-parametric techniques make fewer assumptions about the data distribution, or independence of points, but do not consider time, nor do they give confidence intervals (White and Garrott, 1990). The most commonly used method are harmonic means (Dixon and Chapman, 1980). Contours of area are calculated from a grid of nodes. Inclusion of a node within a probability contour are a function of its proximity to the radio triangulation locations. For example, if the reciprocal of the means to several locations from node A, is less than that from node B, then node A will be included inside a contour of higher probability of occurrence of the animal than B. Centres of activity are located in the areas of greatest activity, multiple centres can be defined, and no specific shapes are imposed on the estimator.

Other forms of non-parametric methods are grid cell counts and Fourier series. The former counts the number of locations found in each cell of a grid laid over the range area. The sum of the areas of the cells containing locations is taken as the estimate of home range. Disadvantages include difficulty in deciding the size of a grid cell - a coarse grid over-estimates range size - and problems with islands of cell locations. The islands are a result of sampling intensity, where an animal has moved some distance from one location to another, without being mapped in intervening cells. Subjective assessments such as including all cells in a line between the last 2 records are often made in these cases.

Fourier series smoothing is a result of an x-y plot with a ‘spike’ at each coordinate where the animal was located. A fourier transformation procedure mathematically analyses the spikes to produce a smoother surface representing the animal’s use of an area. Home range is then calculated as the smallest area encompassed by 95% (or any other %) of the volume of the surface. This type of estimate perform best when 50% or less of the volume is taken as the home range estimate, as the areas at the edge of the home range (eg. 95% volume) are poorly estimated because of a lack of data (White and Garrott, 1990). Non-parametric models have lower precision than other types because fewer assumptions are made about the data. They ignore the time component of telemetric data, and most lack confidence intervals.

2.3.2. Summary

Home ranges are important and useful biological measures, but are often poorly defined. Rigid statistical methods either cannot, or have not, been applied to many of the estimators. Each model has been shown to have strengths and weaknesses. The techniques vary in precision, strength of the assumptions required, and biological relevance in various habitats. Home range is a function of time as well as space, and appropriate sampling methods are required to avoid bias. The autocorrelation which exists between consecutive locations must be considered if a random sample of the animals time is not taken. Home range estimates should be recognised as the estimates and data summaries which they are, and measures more specific to the research objectives, such as differences in distributions of animal locations, employed when indicated.