title: Estimating the species accumulation curve using mixtures.
abstract: As a significant tool in ecological studies, the species accumulation curve or the collector's curve is the graph of the expected number of detected species as a function of sampling effort. The problem of estimating the species accumulation curve based on an empirical data set arising from quadrat sampling is studied in a nonparametric binomial mixture model. It will be shown that estimating the species accumulation curve not only is independent of the unknown number of species but also includes estimating the number of species as a limiting case. For the purpose of interpolation, moment-based estimators, associated with asymptotic confidence intervals, are developed from several points of view. A likelihood-based procedure is developed for the purpose of extrapolation, associated with bootstrap confidence intervals. The proposed methods are illustrated by ecological data sets.
authors: Department of Statistics, University of California, Riverside, California 92521, USA. cmao@stat.ucr.edu
authors: Chang Xuan
authors: CX
authors: Mao
authors: Robert K
authors: RK
authors: Colwell
authors: Jing
authors: J
authors: Chang
mesh_terms: D000818:Animals; D001699:Biometry; D001717:Birds; D016000:Cluster Analysis; D003198:Computer Simulation; D016001:Confidence Intervals; D004463:Ecology / Q000379:methods*; D016013:Likelihood Functions; D008954:Models, Biological; D015233:Models, Statistical; D008962:Models, Theoretical; D009010:Monte Carlo Method; D011156:Population Density; D018709:Statistics, Nonparametric