There has been an ongoing controversy over how to decide whether the distribution of species is "random" - i.e., whether it is not greatly different from what it would be if species did not interact. We recently showed (Roberts and Stone (1990)) that in the case of the Vanuatu (formerly New Hebrides) avifauna, the number of islands shared by species pairs was incompatible with a "random" null hypothesis. However, it was difficult to determine the causes or direction of the community's exceptionality. In this paper, the latter problem is examined further. We use Diamond's (1975) notion of checkerboard distributions (originally developed as an indicator of competition) and construct a C-score statistic which quantifies "checkerboardedness". This statistic is based on the way two species might colonise a pair of islands; whenever each species colonises a different island this adds 1 to the C-score. Following Connor and Simberloff (1979) we generate a "control group" of random colonisation patterns (matrices), and use the C-score to determine their checkerboard characteristics. As an alternative mode of enquiry, we make slight alterations to the observed data, repeating this process many times so as to obtain another "control group". In both cases, when we compare the observed data for the Vanuatu avifauna and the Antillean bat communities with that given by their respective "control group", we find that these communities have significantly large checkerboard distributions, making implausible the hypothesis that their species distributions are a product of random colonisation.