Predicting future discoveries of European marine species by using a non-homogeneous renewal process

Summary.  Predicting future rates of species discovery and the number of species remaining are important in efforts to preserve biodiversity, discussions on the rate of species extinction and comparisons on the state of knowledge of animals and plants of different taxa. Data on discovery dates of species in 32 European marine taxa are analysed by using a class of thinned temporal renewal process models. These models allow for both underdispersion and overdispersion with respect to the non-homogeneous Poisson process. An approach for implementing Bayesian inference for these models is described that uses Markov chain Monte Carlo simulation and that is applicable to other types of thinned process. Predictions are made on the number of species remaining to be discovered in each taxon.     

Bayesian non-parametric inference for species variety with a two-parameter Poisson–Dirichlet process prior

Summary.  A Bayesian non-parametric methodology has been recently proposed to deal with the issue of prediction within species sampling problems. Such problems concern the evaluation, conditional on a sample of size n , of the species variety featured by an additional sample of size m . Genomic applications pose the additional challenge of having to deal with large values of both n and m . In such a case the computation of the Bayesian non-parametric estimators is cumbersome and prevents their implementation. We focus on the two-parameter Poisson–Dirichlet model and provide completely explicit expressions for the corresponding estimators, which can be easily evaluated for any sizes of n and m . We also study the asymptotic behaviour of the number of new species conditionally on the observed sample: such an asymptotic result, combined with a suitable simulation scheme, allows us to derive asymptotic highest posterior density intervals for the estimates of interest. Finally, we illustrate the implementation of the proposed methodology by the analysis of five expressed sequence tags data sets.     

On Gini's diversity measure

The purpose of this paper is to investigate the optimal properties of Gini's diversity measure. It is shown that as number of species increase , Gini's diversity approaches asymptotically to unity.     

Spatial hidden Markov models and species distributions

A spatial hidden Markov model (SHMM) is introduced to analyse the distribution of a species on an atlas, taking into account that false observations and false non-detections of the species can occur during the survey, blurring the true map of presence and absence of the species. The reconstruction of the true map is tackled as the restoration of a degraded pixel image, where the true map is an autologistic model, hidden behind the observed map, whose normalizing constant is efficiently computed by simulating an auxiliary map. The distribution of the species is explained under the Bayesian paradigm and Markov chain Monte Carlo (MCMC) algorithms are developed. We are interested in the spatial distribution of the bird species Greywing Francolin in the south of Africa. Many climatic and land-use explanatory variables are also available: they are included in the SHMM and a subset of them is selected by the mutation operators within the MCMC algorithm.     

Testing list effects and diagnosing individual catchabilities in the Rasch model

The Rasch model is useful in the problem of estimating the population size from multiple incomplete lists. It is of great interest to tell whether there are list effects and whether individuals differ in their catchabilities. These two important model selection problems can be easily addressed conditionally. A conditional likelihood ratio test is used to evaluate the list effects and several graphical methods are used to diagnose the individual catchabilities, while neither the unknown population size nor the unknown mixing distribution of individual catchabilities is required to be estimated. Three epidemiological applications are used for illustration.     

Sequential sampling in the search for new shared species

In microbial sciences, as well as other disciplines, it is often valuable to sample communities in a sequential or group sequential manner, in order to determine their structure or their similarity. We develop sequential sampling procedures to accomplish this by first assuming that one observation is drawn with replacement from each population at a time. Suppose that the sampling is terminated after n pairs of observations and k shared species were discovered, and assume that we receive payoff h(k)−cn, where h(k) is non-decreasing and the sampling cost c is non-negative. Similar to Rasmussen and Starr (1979), we show that an optimal stopping rule exists if h(k+1)−h(k) is non-increasing. An analogous result holds for group sequential sampling. This leads to using an estimate of the probability of discovering new shared species as a stopping indicator for comparing two populations with respect to the similarity index. We show by simulation and real examples that this is a feasible approach which can help to reduce the sample size.     

Bayesian temporal density estimation with autoregressive species sampling models

We propose a novel Bayesian nonparametric (BNP) model, which is built on a class of species sampling models, for estimating density functions of temporal data. In particular, we introduce species sampling mixture models with temporal dependence. To accommodate temporal dependence, we define dependent species sampling models by modeling random support points and weights through an autoregressive model, and then we construct the mixture models based on the collection of these dependent species sampling models. We propose an algorithm to generate posterior samples and present simulation studies to compare the performance of the proposed models with competitors that are based on Dirichlet process mixture models. We apply our method to the estimation of densities for the price of apartment in Seoul, the closing price in Korea Composite Stock Price Index (KOSPI), and climate variables (daily maximum temperature and precipitation) of around the Korean peninsula.     

Sampling theory for species abundances in certain biological populations

The sampling theory of Fisher's logarithmic distribution, discussed in Wani (1978), is extended to the class of power-series distributions.     

A Similarity Measure Based on Species Proportions

ABSTRACT

There are several indices for measuring the similarity of two populations, including the ratio of the number of shared species to the number of distinct species (Jaccard's index) and the conditional probability of observing a shared species (Smith et al., 1996 Smith , W. , Solow , A. R. , Preston , P. E. ( 1996 ). An estimator of species overlap using a modified beta-binomial model. Biometrics 52 : 1472 – 1477 . [CSA] [CROSSREF] [Crossref], [Web of Science ®] , [Google Scholar]). However, these indices only take into account the number of species and species proportions of shared species. In this article, we propose a new similarity index which includes the species proportions of both the shared and non shared species in each population, and also propose a Nonparametric Maximum Likelihood Estimator (NPMLE) for this index. Bootstrap and delta methods are used to evaluate the standard errors of the NPMLE. Based on a loss function, we also compare a class of nonparametric estimators for the proposed index in various situations.     

Comparison of three estimators of the number of species

We consider estimation of the number of cells in a multinomial distribution. This is one version of the species problem: there are many applications, such as the estimation of the number of unobserved species of animals; estimation of vocabulary size, etc. We describe the results of a simulation comparison of three principal frequent-ist' procedures for estimating the number of cells (or species). The first procedure postulates a functional form for the cell probabilities; the second procedure approxi mates the distribution of the probabilities by a parametric probability density function; and the third procedure is based on an estimate of the sample coverage, i.e. the sum of the probabilities of the observed cells. Among the procedures studied, we find that the third (non-parametric) method is globally preferable; the second (functional parametric) method cannot be recommended; and that, when based on the inverse Gaussian density, the first method is competitive in some cases with the third method. We also discuss Sichel's recent generalized inverse Gaussian-based procedure which, with some refine ment, promises to perform at least as well as the non-parametric method in all cases.     

Estimating bird species richness from capture and count data

We used capture-recapture methods to estimate bird species richness from mist-net and point-count data from a study area in Campeche, Mexico. We estimated species richness separately for each survey technique for two habitats, forest and pasture, in six sampling periods. We then estimated richness based on species' detections by either technique, and estimated the proportion of species detected by each technique that are not part of the population sampled by the other technique. No consistent differences existed between richness estimates from count data and from capture data in the two habitats. In some sampling periods, over 50% of the richness estimate from one survey technique may be species that are not sampled by the other technique, suggesting that one technique may not be adequate to estimate total species richness and that comparing estimates from areas sampled by different techniques may not be valid.     

Red listing: deciding which species are at risk

Darwin explained how species began. Today we may be witnessing the sixth great extinction. Conservationists rely on the so-called "red list" of most-threatened species, but the red list has been criticised as arbitrary, subjective and based on inadequate data. David Keith looks at the science and the statistics of the red list.     

A Multiple-community Overlap Measure Based on a Probabilistic Approach

Species diversity indices are designed to measure the species diversity of a community and to compare the species distribution structure of two communities. The Shannon and Simpson indices are for describing one community, and the Jaccard and Morisita indices are for comparing two communities. Only a few indices allow the simultaneous comparison of three or more communities. In this study, we propose a multiple-community similarity index based on a probabilistic approach, and compare it with other multiple-community indices. Empirical examples are considered as a demonstration of the proposed similarity indices.     

The poisson-inverse gaussian disiribuiion as a model for species abundance

An inverse Gaussian mixture of Poisson distributions(the P-IG distribution) is considered as a model for species abundance data,, Minimum chi-square and maximum likelihood methods of estimation for the zero-truncated P-IG distribution are developed, Ihe performance of the P-IG distribution is illustrated and discussed for several well-known sets of insect abundance data.     

On estimating the conditional probability of discovering a new species

Based on a capture-recapture sample of size $i;n+k,n≥ l,k ≥ 0, from a population of an unknown number of distinct species (or classes), the problem of estimating the total probability of the species unobserved in the first n selections is considered. As the estimand depends on both the unknown parameters and the data, the standard theory of estimation is inadequate for this problem A suitable definition of sufficiency is introduced and used to prove a Rao-Blackwell type result and discuss uniformly minimum mean squared error unbiased estimation. An alternative proof for an inadmissibility result is presented. The new proof gives more insight and a method for deriving improved estimators. The theoretical developments may be useful in other problems concerning inferences about random parametric functions.     

Exact confidence regions for species assignment based on DNA markers

Assignment of individuals to correct species or population of origin based on a comparison of allele profiles has in recent years become more accurate due to improvements in DNA marker technology. A method of assessing the error in such assignment problems is présentés. The method is based on the exact hypergeometric distributions of contingency tables conditioned on marginal totals. The result is a confidence region of fixed confidence level. This confidence level is calculable exactly in principle, and estimable very accurately by simulation, without knowledge of the true population allele frequencies. Various properties of these techniques are examined through application to several examples of actual DNA marker data and through simulation studies. Methods which may reduce computation time are discussed and illustrated.     

Tuning parameter selection for a penalized estimator of species richness

Our goal is to estimate the true number of classes in a population, called the species richness. We consider the case where multiple frequency count tables have been collected from a homogeneous population and investigate a penalized maximum likelihood estimator under a negative binomial model. Because high probabilities of unobserved classes increase the variance of species richness estimates, our method penalizes the probability of a class being unobserved. Tuning the penalization parameter is challenging because the true species richness is never known, and so we propose and validate four novel methods for tuning the penalization parameter. We illustrate and contrast the performance of the proposed methods by estimating the strain-level microbial diversity of Lake Champlain over three consecutive years, and global human host-associated species-level microbial richness.     

Hybrid Dirichlet mixture models for functional data

Summary.  In functional data analysis, curves or surfaces are observed, up to measurement error, at a finite set of locations, for, say, a sample of n individuals. Often, the curves are homogeneous, except perhaps for individual-specific regions that provide heterogeneous behaviour (e.g. 'damaged' areas of irregular shape on an otherwise smooth surface). Motivated by applications with functional data of this nature, we propose a Bayesian mixture model, with the aim of dimension reduction, by representing the sample of n curves through a smaller set of canonical curves. We propose a novel prior on the space of probability measures for a random curve which extends the popular Dirichlet priors by allowing local clustering: non-homogeneous portions of a curve can be allocated to different clusters and the n individual curves can be represented as recombinations (hybrids) of a few canonical curves. More precisely, the prior proposed envisions a conceptual hidden factor with k -levels that acts locally on each curve. We discuss several models incorporating this prior and illustrate its performance with simulated and real data sets. We examine theoretical properties of the proposed finite hybrid Dirichlet mixtures, specifically, their behaviour as the number of the mixture components goes to ∞ and their connection with Dirichlet process mixtures.     

A modified bootstrap procedure for cluster sampling variance estimation of species richness

Variance estimators for probability sample-based predictions of species richness (S) are typically conditional on the sample (expected variance). In practical applications, sample sizes are typically small, and the variance of input parameters to a richness estimator should not be ignored. We propose a modified bootstrap variance estimator that attempts to capture the sampling variance by generating B replications of the richness prediction from stochastically resampled data of species incidence. The variance estimator is demonstrated for the observed richness (SO), five richness estimators, and with simulated cluster sampling (without replacement) in 11 finite populations of forest tree species. A key feature of the bootstrap procedure is a probabilistic augmentation of a species incidence matrix by the number of species expected to be ‘lost’ in a conventional bootstrap resampling scheme. In Monte-Carlo (MC) simulations, the modified bootstrap procedure performed well in terms of tracking the average MC estimates of richness and standard errors. Bootstrap-based estimates of standard errors were as a rule conservative. Extensions to other sampling designs, estimators of species richness and diversity, and estimates of change are possible.     

A statistical social network model for consumption data in trophic food webs

We adapt existing statistical modeling techniques for social networks to study consumption data observed in trophic food webs. These data describe the feeding volume (non-negative) among organisms grouped into nodes, called trophic species, that form the food web. Model complexity arises due to the extensive amount of zeros in the data, as each node in the web is predator/prey to only a small number of other trophic species. Many of the zeros are regarded as structural (non-random) in the context of feeding behavior. The presence of basal prey and top predator nodes (those who never consume and those who are never consumed, with probability 1) creates additional complexity to the statistical modeling. We develop a special statistical social network model to account for such network features. The model is applied to two empirical food webs; focus is on the web for which the population size of seals is of concern to various commercial fisheries.