Testing for differences in spatial distributions from individual based data

Abstract

Spatial distribution is increasingly studied using individual based telemetric methods in lieu of, or supplementing, surveys. Distributions may be in two- or three-dimensions, or in an abstract space such as depth-temperature space. One of the most basic questions one might address when analyzing these data is whether the distributions of two species, populations, genders, age classes, or other units are different. However due to the inherent differences between survey and telemetric approaches, it is difficult for practitioners to find a simple and easily applied approach to answer this question. In contrast to surveys, telemetry collects a large amount of data about a small number of individuals. Methods must therefore account for the random effects of individual variation in a way not otherwise necessary. We will demonstrate, for example, that tests suitable for detecting differences in distributions from survey data can give false positives (type I errors) when faced with telemetry data. This is essentially because the test treats the large number of data points as a very high n, but in fact the small number of individuals makes the n very small. As a solution, we present a test for differences in distribution based on an existing test for survey data based upon randomizing the data at the level of individuals rather than observations.