The Use of Species Accumulation Functions for the Prediction of Species Richness

We develop a stochastic theory of the accumulation of new species in faunistic or floristic inventories. Differential equations for the expected list size and its variance as a function of the time spent collecting are presented and solved for particular cases. These particular cases correspond to different models of how the probability of adding a new species changes with time, the size of the list, the complexity of the area sampled, and other parameters. Examples using field data from butterflies and mammals are discussed, and it is argued that the equations relating sampling effort with size of the list may be useful for conservation purposes because they should lend formality to comparisons among lists and because they may have predictive power by extrapolating the asymptotic size of the lists. The suitability of different models to a variety of field situations is also discussed.