Multiple species effects and spatial autocorrelation in detecting species associations

Abstract

Abstract. The traditional approach to the analysis of species association within a community, based upon co‐occurrence in sampling units such as quadrats, has been to test all pairs of species, using a 2 × 2 contingency table for each pair. It has long been recognised that all these tests are not independent of each other, but there is an additional problem in that the association between any particular pair may depend on the combination of the other species that are present or on the environmental factors that determine that combination. We use a 2k contingency table to examine this problem and find that pairwise associations are not independent of the other species. The second problem that we consider is the effect of spatial autocorrelation in the data which makes the statistical tests too liberal. In the absence of a derived solution for a deflation factor to correct the test statistic calculated from a 2k table, we describe a Monte Carlo approach that provides an approximate solution to this problem. In our data the amount of deflation that is necessary for a 2k table is small compared to the amount required for the 2 × 2 tables used to test pairwise association.

Classification of mesic and wet grasslands in northwest Croatia

“…the spatial autocorrelation issue (Dale et al 1991;Jongman et al 1997;Schiegg 2003). In order for two relevés not to be overly influenced by each other's seeds and clonal plants, 100 m was taken as the minimum distance between two relevés during the field research, with that distance being much greater in the majority of cases.…”

A New Method for Detecting Species Associations With Spatially Autocorrelated Data

“…By deflating the magnitude of the test statistic by the appropriate amount, depending on the degree of nonrandomness in the data, an estimate of the significance of the test statistic in the presence of autocorrelation is obtained. A limitation of Tavaré and Altham's (1983) method is that it is valid only when the within-species spatial patterns meet Markovian assumptions (Dale et al 1991). Dale et al (1991) extended Tavaré and Altham's (1983) approach and suggested a Monte Carlo procedure that can be applied to the analysis of multispecies 2 k contingency tables, where k is the number of species.…”

“…A limitation of Tavaré and Altham's (1983) method is that it is valid only when the within-species spatial patterns meet Markovian assumptions (Dale et al 1991). Dale et al (1991) extended Tavaré and Altham's (1983) approach and suggested a Monte Carlo procedure that can be applied to the analysis of multispecies 2 k contingency tables, where k is the number of species. Their method involves defining a null model which includes information on the spatial patterns of each species.…”

“…A number of statistical tests have been utilized for detecting species associations. These include correlation analysis (Greig-Smith 1983, O'Connor and Aarssen 1987, Myster and Pickett 1992, analysis by contingency table (Greig-Smith 1983, Dale et al 1991, variance tests (Schluter 1984, McCulloch 1985, and the use of cross-variograms (Rossi et al 1992). One major limitation of these tests is that they assume, for each species, within-species randomness of the spatial distribution patterns.…”

“…Patchy or clumped patterns, where an observation in one area makes it more likely that the same observation will also be made in neighboring areas, are said to exhibit positive spatial autocorrelation. With traditional tests of interspecific association the presence of positive spatial autocorrelation violates the assumption of within-species randomness, and results in an elevated Type I error rate, i.e., an increase in the risk of concluding a test statistic significant, even when the species are unassociated (Tavaré and Altham 1983, Dale et al 1991, Legendre 1993, Palmer and van der Maarel 1995. This feature of these tests is illustrated in the next section.…”