Estimating abundance-based generalized species accumulation curves

An important but difficult problem in ecological studies is estimating species richness, i.e., the number of species in an assemblage based on an incomplete survey (Colwell and Coddington 1994). The same problem also arises from various other scientific fields (Bunge and Fitzpatrick 1993). In the survey, individuals are selected from the species assemblage and their species identities are recognized. The species accumulation curve (SAC) is the plot of the expected number of species against the measure of sampling effort, which serves a variety of purposes in ecological studies such as comparison among species assemblages and prediction of expected number of new species (e.g., Hurlbert 1971; Colwell and Coddington 1994; Shen et al. 2003; Mao 2005). The estimand of a nonparametric species richness estimator is also often plotted against the measure of sampling effort, called a generalized SAC and and used like the usual SAC (Colwell and Coddington 1994). Although estimating the usual SAC has been extensively studied (e.g., Mao 2005), little investigation has been made to estimate generalized SACs. A computationally intensive randomization procedure is usually used by ecologists and conservation biologists.