Species richness estimation from probabilities of observing new species
A new species richness estimator applicable to probability sampling with fixed-area (a) plots in a finite-area (A) population is presented and tested in simulated sampling from three stem-mapped forest compartments, and from six large collections of forest inventory data. The estimator of richness is the average number of species per plot times the sum—over the N = A/n plots in a population—of the probability (pm) of observing a new species in the mth plot (m = 1,…, N). A Cauchy distribution function is used to capture trends in pm. The parameters of the Cauchy distribution were estimated by optimizing a weighted maximum likelihood function. In comparison to five presumed best alternative estimators, the new estimator was ‘average’ with respect to bias, but best in terms of average root mean squared error. Taking the average of the estimates of richness produced by the five alternate and the new estimator would, generally, keep bias below 15 %. With relatively large sample sizes, the bias is moderately small (<10 %).