Intra-Archipelago Vertebrate Distributions: The Slope of the Species-Area Relation

This paper investigates the exponent, z, of the power function relating island species number to island area. Two methods used to fit the power function to species-area data are contrasted. In the past, the logarithm of the power function has been fit to species-area data by linear regression. However, the underlying regression model may be inappropriate, and, in any event, the residual sum of squares is minimized and predictive accuracy increases when the power function is fit directly by nonlinear regression. Theory predicts that z-values should fall in a narrow range and observed z-value are in close agreement. When the power function is fit by linear regression, the consistent magnitude of z-values may be due to statistical artifact (Connor and McCoy 1979). If the power function is fit by iterative, nonlinear regression, statistical artifact does not affect z-values and most observed z-values still fall within the predicted range. The equilibrium theory of island biogeography allows predictions about z-values. Equilibrium theory postulates that insular biota are determined by a dynamic balance between the immigration of species new to an island and the extinction of species which are already present. The effect of different immigration and extinction rates on z-values is examined after incorporating the relative immigration and extinction rates of terrestrial vertebrate taxa into an equilibrium model. Predicted and observed relative z-values are in close agreement. Data indicate that z-values are also affected by an archipelago's history of colonization. I use the equilibrium model to predict changes in z-values with time for archipelagos which were colonized solely by overwater dispersal and for archipelagos which were initially contiguous with their source fauna and were colonized overland.