Species accumulation functions and pure birth processes

Abstract

Many authors in Ecology, following Soberón and Llorente (Conserv. Biol. 7(3) (1993) 480), model species accumulation functions as means of pure birth processes. Their approach has inconsistencies, but we show that it can be justified as an approximation, in the sense that given a species accumulation function S( t) of a proposed type, there exists a non-homogeneous pure birth process (PBP) whose mean is close to S( t). The variance of the PBP is basic for statistical inference and model assessment, but it is not known. We provide an upper bound for the variance that can be used in its place.