On Testing the MacArthur-Wilson Model with Data on Rates

Abstract

The MacArthur-Wilson equilibrium theory of island biogeography makes various predictions about how island area and distance from a source of colonists affect immigration, extinction, and turnover rates. These predictions (table 1) can vary depending on whether absolute or relative rates are used; the relative rates divide absolute rates by some function of the number of species on the island in question to "control" for differences in species number. The relative rates, because they are ratios of variables, are subject to artifacts of ratio correlation; in particular, were area or distance strongly correlated with species number, as is typical, artifactual correlations between relative rates and area or distance would result, confounding the testing of MacArthur-Wilson predictions. An alternative method of controlling for variation in species number is to include species number as a separate independent variable in multiple regressions having the absolute rates as dependent variables. For a large set of data on orb spiders, this method was shown more consistent and conclusive than regressions having the relative rates as dependent variables. The absolute-rate method is recommended for testing MacArthur-Wilson predictions about area and distance.