Abstract: Estimating the number of species from multiple incidence-based subsamples is of great importance in ecological and environmental sciences. The problem is investigated in a mixture model of multivariate binomial densities. A sequence of algebraic lower bounds to the odds that a species is unseen in the survey is proposed. Estimating a lower bound leads to an estimator for the number of species. The nonparametric bootstrap method can be used to compute lower confidence limits. The asymptotic standard error for the first order estimator is provided. An example is investigated and a simulation experiment is carried out to assess the proposed estimators.
Key words and phrases: Biodiversity, truncated moment problem.