Calculating association indices in captive animals: Controlling for enclosure size and shape

• Studies using an association index often fail to account for enclosure size and shape.
• We propose a correction for such indices which controls for enclosure size and shape.
• Our simple R script can be used to determine chance encounters in any area.
• Shape did not affect the probability of a chance encounter in large areas.

Indices of association are used to quantify and evaluate social affiliation among animals living in groups. Association models assume that physical proximity is an indication of social affiliation; however, individuals seen associating might simply be together by chance. This problem is particularly pronounced in studies of captive animals, whose movements are sometimes severely spatially restricted relative to the wild. Few attempts have been made to estimate – and thus control for – chance encounters based on enclosure size and shape. Using geometric probability and Geographic Information Systems, we investigated the likely effect of chance encounters on association indices within dyads (pairs of animals), when different distance criteria for defining associations are used in shapes of a given area. We developed a simple R script, which can be used to provide a robust estimate of the probability of a chance encounter in a square of any area. We used Monte Carlo methods to determine that this provided acceptable estimates of the probability of chance encounters in rectangular shapes and the shapes of six actual zoo enclosures, and we present an example of its use to correct observed indices of association. Applying this correction controls for differences in enclosure size and shape, and allows association indices between dyads housed in different enclosures to be compared.