An Accumulation Rate Curve Estimator for Total Species

Abstract In this paper we present an estimator for total species that is based on modelling an accumulation rate curve. The proposed approach calculates the curve for the rate of arrival of new species conditional on the observed data and projectes it forward using parametric functions with varying rates of decay. The individual fits are integrated to obtain estimates for undetected species and a weighted estimate is obtained by optimizing a loss function subject to a set of restrictions. Confidence intervals are obtained using a parametric bootstrap of aggregate counts, with the underlying count covariances estimated from a regularized mixture distribution fit to the observed count data. A technique to adjust the point estimate for bias is also discussed. The method is tested using a simulation study and two data examples. The results indicate that the proposed method is robust in a majority of cases and largely outperforms existing methods in bias and mean squared error. Performance is especially improved when the proportion of unobserved species is high. Confidence interval coverage probabilities are noticeably better compared to existing methods and conservative interval widths are maintained. The bias adjustment technique is also shown to be effective in reducing mean squared error.