A null model for detecting nonrandom patterns of species richness along spatial gradients

I present a null model that can be used for detecting nonrandom patterns of species richness along spatial gradients, such as latitude and elevation. Because estimates of species richness along a single spatial gradient are n onindependent, tests of statistical inference should not be applied. The nu ll model described here circumvents this problem of nonindependence by rand omly placing the actual range width of each species along the gradient. The simulated richness curve generated in this way can be compared to an "aver age" random curve composed of many such simulations. The comparison involve s measuring the mean displacement (D) of the simulated curve from the avera ge random curve. By repeating these steps a specified number of times, one can obtain a distribution of D values. The displacement of the actual speci es richness curve from the average random curve can also be determined and compared to the distribution of D values of the simulated random curves. Th is comparison allows one to determine whether the actual curve is random. T he null model was found to be very powerful (power > 0.96) for curves consi sting of at least 10 richness estimates from a total pool of 20 or more spe cies.