Island-sharing by archipelago species

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Abstract
Diamond (1975) formulated “assembly rules” for avian species on islands in an archipelago, which made a successful colonisation depend essentially on which other species were present. Critically examining these rules, Connor and Simberloff (1979) maintained that, in the Vanuatu (New Hebrides) archipelago, the field data on species distribution was quite compatible with a null hypothesis, in which species colonise at random with no species interaction. Their work was in turn criticised (Diamond and Gilpin (1982), Gilpin and Diamond (1982)) and a vigorous controversy has ensued. Here we contribute a method in which a simple but hitherto neglected statistic is used as a probe: the number of islands shared by a pair of species, with its first and second moments. The matrix of these sharing values is given as a simple product of the incidence matrix, and its properties are examined — first, for the field data, and then in the random ensemble used by Connor and Simberloff (1979). It is shown that their constraints hold constant the mean number shared, so that any fall in the number that one pair of species share, due to their excluding each other, must imply a rise in the number shared by some other species pair-i.e., an aggregation. Turning to the second moment of the numbers shared, it is shown that its value in the Vanuatu field data exceeds the largest value to be found in a sample of 1000 matrices, these latter being constructed so that they obey the Connor and Simberloff constraints but are otherwise random. This indicates that exclusion and/or aggregation effects are present in the actual distribution of species, which are not catered for by the null hypothesis. The observed distribution thus emerges as much more exceptional than found by Connor and Simberloff (1979), and even by Diamond and Gilpin (1982), when examining the same ensemble. The reason for this disagreement are sought, and some cautions are offered, supported by numerical evidence, concerning the use of the chi-square test when the data points involved are mutually dependent.