An accumulation rate curve estimator for total species

In this paper we present a total species estimator based on modelling the rate of change of a species accumulation curve (SAC). The proposed approach calculates an accumulation rate curve (ARC) for new species conditional on observed data and extrapolates it using parametric functions with varying rates of decay. The curve fits are integrated to obtain estimates for undetected species and a weighted estimate is calculated by optimizing a loss function subject to a set of restrictions. Confidence intervals are evaluated using a parametric bootstrap of aggregate counts, with the underlying count covariances estimated from a regularized mixture distribution fit to observed count data. A data smoothing technique and adjusting for bias are also discussed. The method is tested using a simulation study and applied to two example datasets. The results indicate that the proposed method is robust in a majority of cases and outperforms existing methods in bias and mean squared error. Performance is especially improved when the proportion of unobserved species is high. Confidence interval coverage is noticeably better compared to existing methods and conservative interval widths are maintained. The smoothing technique is also shown to be effective in reducing mean squared error under certain conditions.