Statistical Estimation and Model Selection of Species-Accumulation Functions

Abstract:  Soberón and Llorente (1993) proposed pure-birth stochastic processes as theoretical models for species-accumulation curves, and these processes have frequently been used to describe the progress of biological inventories. We describe, in algorithmic form, an alternative statistical analysis based on a likelihood approach ( Díaz-Francés & Gorostiza 2002 ) that provides mathematical rigor to the ideas in Soberón and Llorente (1993) and improves the estimation of the models by incorporating the facts that the variance of the error is not constant and that the observations are correlated. Additionally, we used the likelihood ratios between candidate models as an objective procedure for model selection, allowing comparison between the goodness of fit of various models. The software for these statistical methods can now be downloaded off the Internet. We used two examples of butterfly data sets to illustrate the use of the methods and the software.