Abstract
The formulation and estimation of species accumulation curve (SAC) for a single community have been extensively discussed in ecological literature. The expected SAC describes how the expected number of observed species changes when the number of sampling individuals is increased. This thesis focuses on extending SAC to shared species accumulation curve in two communities as shared species richness plays an important role to quantify the similarity and dissimilarity among multiple communities. This thesis focuses on two communities case, an estimator for the shared species accumulation curve including rarefaction and extrapolation is proposed, that is, the focus is on how the estimated expected number of shared species changes when the number of sampling individuals changes. Biological diversity includes three aspects: species diversity, phylogenetic diversity and functional diversity. The shared species accumulation curve only considers species abundance distributions within each community and species abundances for shared species. This thesis also extends this framework to the phylogenetic diversity, that is, shared PD accumulation curve based on the Faith’s (1992) phylogenetic diversity (the sum of all branch lengths connecting all species in an assemblage). In addition, the thesis also extends the framework to the functional diversity, that is, shared FAD accumulation curve based on the functional attributed diversity (the total species pairwise distances) defined by Walker et al. (1999). To compare the estimator proposed in this thesis to the traditional empirical method, computer simulation results are reported, when compared with the traditional empirical method, the new proposed estimator exhibits substantial improvement in bias, RMSE and the coverage probability of 95% confidence interval. Finally, the estimators proposed in this thesis are illustrated with a dataset for Mexican Phyllostomid bat and a dataset for Brazilian rain forest trees.