An urn model for species richness estimation in quadrat sampling from fixed-area populations

A simple urn model species richness estimator applicable to quadrat sampling from a fixed-area sessile population composed of N quadrats is proposed. The urn model rests on the assumption that the proportion of quadrats with species that occurred in just one of the n sampled quadrats is proportional to the probability of discovering a new species if one quadrat is added to the sample. The urn model works by making one-step-ahead sequential predictions of new species discoveries for all N − n quadrats not in the original sample. The probability of a new discovery changes dynamically as predictions are made. The urn scheme is repeated a large number of times to yield a resampling distribution of richness from which the mean is obtained as the estimate of richness. The variance of the resampling distribution quantifies the prediction variance. Quantiles (0.025 and 0.975) of the resampling distribution were taken as the upper and lower limit of a 95 per cent confidence interval for the true richness. In simulated low-intensity quadrat sampling from 10 fixed-area populations of forest trees, the urn estimator had the lowest bias and root mean-squared errors and the best coverage of 95 per cent confidence intervals. Attractive ‘asymptotic’ properties of the urn model were demonstrated with three artificial benchmark populations.