Statistical comparison of proximity matrices: applications in animal behaviour

Animal behaviour studies often require the diagnosis and statistical evaluation of patterns among individuals of a group. However, association values derived for all pairs of individuals are mathematically interrelated and, hence, difficult to evaluate. A general method of matrix comparison, called the Mantel test, is described which accounts for such interdependencies. In this test, two square difference matrices are compared to determine whether a statistical association exists between corresponding elements. For example, distances in one of the matrices might represent differences in songs for each pair of a group of birds, while distances in the other matrix could be the geographic distances between each of the same bird pairs; the test would assess whether or not birds close to one another have songs that are more similar than those pairs that are located further apart geographically. Distances in the matrices can be of a variety of sorts (depending on the application), including for instance geographic distances, morphological differences, or behavioural differences. The test has wide applicability in studies of animal behaviour, and we present three examples. First, dialects of splendid sunbirds (Nectarinia coccinigaster) were investigated to determine whether local or regional patterns of geographic variation in song were present, and whether birds with similar dialects were concentrated within the same habitat. Second, dominance hierarchies of white-throated sparrows (Zonotrichia albicollis) and dark-eyed juncos (Junco hyemalis oreganus) were analysed by constructing appropriate hypothesis matrices that were contrasted against a matrix summarizing behavioural interrelationships of flock members. In the third application, involving progressions of yellow baboons (Papio cynocephalus), an approach was developed to assess whether members of a given sex occur adjacent (or at least closer) to one another in progression order more often than expected by chance, and also whether individuals of a given sex tend to be found at or near the end of a progression more frequently than predicted. Other possible applications of the Mantel test are discussed, and a detailed computational example is included.