Tsung-Jen Shen

Nonparametric estimation of Shannon's index of diversity when there are unseen species in sample

A biological community usually has a large number of species with relatively small abundances. When a random sample of individuals is selected and each individual is classified according to species identity, some rare species may not be discovered. This paper is concerned with the estimation of Shannon’s index of diversity when the number of species and the species abundances are unknown. The traditional estimator that ignores the missing species underestimates when there is a non-negligible number of unseen species. We provide a different approach based on unequal probability sampling theory because species have different probabilities of being discovered in the sample. No parametric forms are assumed for the species abundances. The proposed estimation procedure combines the Horvitz–Thompson (1952) adjustment for missing species and the concept of sample coverage, which is used to properly estimate the relative abundances of species discovered in the sample. Simulation results show that the proposed estimator works well under various abundance models even when a relatively large fraction of the species is missing. Three real data sets, two from biology and the other one from numismatics, are given for illustration.

PREDICTING THE NUMBER OF NEW SPECIES IN FURTHER TAXONOMIC SAMPLING

In evaluating the effectiveness of further sampling in species taxonomic surveys, a practical and important problem is predicting the number of new species that would be observed in a second survey, based on data from an initial survey. This problem can also be approached by estimating the corresponding expected number of new species. A. R. Solow and S. Polasky recently proposed a predictor (or estimator), with the form of a sum of many terms, that was derived under the assumption that all unobserved species in the initial sample have equal relative abundances. We show in this paper that the summation can be expressed as only one term. We provide a direct justification for the simplified estimator and connect it to an extrapolation formula based on a special type of species accumulation curve. Using the proposed justification, we show that, for large sample sizes, the estimator is also valid under an alternative condition, i.e., species that are represented the same number of times in the initial sample have equal relative abundances in the community. This condition is statistically justified from a Bayesian approach, although the estimator exhibits moderate negative bias for predicting larger samples in highly heterogeneous communities. In such situations, we recommend the use of a modified estimator that incorporates a measure of heterogeneity among species abundances. An example using field data from the extant rare vascular plant species patterns in the southern Appalachians is presented to compare the various methods. Corresponding Editor: A. R. Solow

AN INCIDENCE-BASED RICHNESS ESTIMATOR FOR QUADRATS SAMPLED WITHOUT REPLACEMENT

Most richness estimators currently in use are derived from models that consider sampling with replacement or from the assumption of infinite populations. Neither of the assumptions is suitable for sampling sessile organisms such as plants where quadrats are often sampled without replacement and the area of study is always limited. In this paper, we propose an incidence-based parametric richness estimator that considers quadrat sampling without replacement in a fixed area. The estimator is derived from a zero-truncated binomial distribution for the number of quadrats containing a given species (e.g., species i) and a modified beta distribution for the probability of presence-absence of a species in a quadrat. The maximum likelihood estimate of richness is explicitly given and can be easily solved. The variance of the estimate is also obtained. The performance of the estimator is tested against nine other existing incidence-based estimators using two tree data sets where the true numbers of species are known. Results show that the new estimator is insensitive to sample size and outperforms the other methods as judged by the root mean squared errors. The superiority of the new method is particularly noticeable when large quadrat size is used, suggesting that a few large quadrats are preferred over many small ones when sampling diversity.

Small-sample estimation of species richness applied to forest communities.

Many well-known methods are available for estimating the number of species in a forest community. However, most existing methods result in considerable negative bias in applications, where field surveys typically represent only a small fraction of sampled communities. This article develops a new method based on sampling with replacement to estimate species richness via the generalized jackknife procedure. The proposed estimator yields small bias and reasonably accurate interval estimation even with small samples. The performance of the proposed estimator is compared with several typical estimators via simulation study using two complete census datasets from Panama and Malaysia.

A general framework for predicting delayed responses of ecological communities to habitat loss

Although biodiversity crisis at different spatial scales has been well recognised, the phenomena of extinction debt and immigration credit at a crossing-scale context are, at best, unclear. Based on two community patterns, regional species abundance distribution (SAD) and spatial abundance distribution (SAAD), Kitzes and Harte (2015) presented a macroecological framework for predicting post-disturbance delayed extinction patterns in the entire ecological community. In this study, we further expand this basic framework to predict diverse time-lagged effects of habitat destruction on local communities. Specifically, our generalisation of KH’s model could address the questions that could not be answered previously: (1) How many species are subjected to delayed extinction in a local community when habitat is destructed in other areas? (2) How do rare or endemic species contribute to extinction debt or immigration credit of the local community? (3) How will species differ between two local areas? From the demonstrations using two SAD models (single-parameter lognormal and logseries), the predicted patterns of the debt, credit, and change in the fraction of unique species can vary, but with consistencies and depending on several factors. The general framework deepens the understanding of the theoretical effects of habitat loss on community dynamic patterns in local samples.

Postnatal growth and age estimation in Scotophilus kuhlii.

Adequate postnatal growth is important for young bats to develop skilled sensory and locomotor abilities, which are highly associated with their survival once independent. This study investigated the postnatal growth and development of Scotophilus kuhlii in captivity. An empirical growth curve was established, and the postnatal growth rate was quantified to derive an age-predictive equation. By further controlling the fostering conditions of twins, the differences in the development patterns between pups that received maternal care or were hand-reared were analyzed to determine whether the latter developed in the same manner as their maternally reared counterparts. Our results indicate that both forearm length and body mass increased rapidly and linearly during the first 4 weeks, after which the growth rate gradually decreased to reach a stable level. The first flight occurred at an average age of 39 days with a mean forearm length and body mass of 92.07% and 70.52% of maternal size, respectively. The developmental pattern of hand-reared pups, although similar to that of their maternally reared twin siblings, displayed a slightly faster growth rate in the 4th and 5th weeks. The heavier body mass of hand-reared pups during the pre-fledging period may cause higher wing loading, potentially influencing the flight performance and survival of the bats once independent.

Good-Turing frequency estimation in a finite population.

Good-Turing frequency estimation (Good, ) is a simple, effective method for predicting detection probabilities of objects of both observed and unobserved classes based on observed frequencies of classes in a sample. The method has been used widely in several disciplines, such as information retrieval, computational linguistics, text recognition, and ecological diversity estimation. Nevertheless, existing studies assume sampling with replacement or sampling from an infinite population, which might be inappropriate for many practical applications. In light of this limitation, this article presents a modification of the Good-Turing estimation method to account for finite population sampling. We provide three practical extensions of the modified method, and we examine performance of the modified method and its extensions in simulation experiments.