Estimating species richness from quadrat sampling data: a general approach

We consider the problem of estimating the number of species (denoted by S) of a biological community located in a region divided into n quadrats. To address this question, different hierarchical parametric approaches have been recently developed. Despite a detailed modeling of the underlying biological processes, they all have some limitations. Indeed, some assume that n is theoretically infinite; as a result, n and the sampling fraction are not a part of such models. Others require some prior information on S to be efficiently implemented. Our approach is more general in that it applies without limitation on the size of n, and it can be used in the presence, as well as in the absence, of prior information on S. Moreover, it can be viewed as an extension of the approach of Dorazio and Royle (2005, Journal of the American Statistical Association 100, 389-398) in that n is a part of the model and a prior distribution is placed on S. Despite serious computational difficulties, we have perfected an efficient Markov chain Monte Carlo algorithm, which allows us to obtain the Bayesian estimate of S. We illustrate our approach by estimating the number of species of a bird community located in a forest.     

Nonparametric tests for continuous covariate effects with multistate survival data

SUMMARY: In clinical trials and observational studies, it is often of scientific interest to evaluate the effects of covariates on complex multistate event probabilities. With discrete covariates, nonparametric tests may be constructed using estimates of the relevant quantities. With continuous covariates, a common approach is to arbitrarily discretize the covariates, which may lead to substantial information loss. Another strategy is to formulate the covariate effects in a regression model. Model-based tests may have either low power or be biased under misspecification. We propose nonparametric tests not requiring arbitrary discretization. The tests involve integrals of estimates continuously indexed by dichotomizations of the covariates. General asymptotic results are derived under null and alternative hypotheses, and verified using empirical process theory in several special cases. The tests are consistent under stochastic ordering, which arises naturally with multistate data. A novel nonparametric measure of covariate effect is studied as a natural byproduct of the testing procedure. Simulation studies and two real data analyses demonstrate the gains of the new testing procedure over those based either on categorization or on regression models.     

Distance-based tests for homogeneity of multivariate dispersions

Summary The traditional likelihood‐based test for differences in multivariate dispersions is known to be sensitive to nonnormality. It is also impossible to use when the number of variables exceeds the number of observations. Many biological and ecological data sets have many variables, are highly skewed, and are zero‐inflated. The traditional test and even some more robust alternatives are also unreasonable in many contexts where measures of dispersion based on a non‐Euclidean dissimilarity would be more appropriate. Distance‐based tests of homogeneity of multivariate dispersions, which can be based on any dissimilarity measure of choice, are proposed here. They rely on the rotational invariance of either the multivariate centroid or the spatial median to obtain measures of spread using principal coordinate axes. The tests are straightforward multivariate extensions of Levene's test, with P‐values obtained either using the traditional F‐distribution or using permutation of either least‐squares or LAD residuals. Examples illustrate the utility of the approach, including the analysis of stabilizing selection in sparrows, biodiversity of New Zealand fish assemblages, and the response of Indonesian reef corals to an El Niño. Monte Carlo simulations from the real data sets show that the distance‐based tests are robust and powerful for relevant alternative hypotheses of real differences in spread.     

Nonparametric variance estimation in the analysis of microarray data: a measurement error approach

We investigate the effects of measurement error on the estimationof nonparametric variance functions. We show that either ignoringmeasurement error or direct application of the simulation extrapolation,SIMEX, method leads to inconsistent estimators. Nevertheless,the direct SIMEX method can reduce bias relative to a naiveestimator. We further propose a permutation SIMEX method thatleads to consistent estimators in theory. The performance ofboth the SIMEX methods depends on approximations to the exactextrapolants. Simulations show that both the SIMEX methods performbetter than ignoring measurement error. The methodology is illustratedusing microarray data from colon cancer patients.     

Relative influence of size,connectivity and disturbance history on plant species richness and assemblages in fragmented grasslands

Questions: What is the relative influence of size, connectivity and disturbance history on plant species richness and assemblages of fragmented grasslands? What is the contribution of small fragments to the conservation of native species pool of the region? Location: Tandilia's Range, Southern Pampa, Argentina. Methods: Cover of plants was registered within 24 fragments of tall‐tussock grassland remnants within an agricultural landscape using modified Whittaker nested sampling. We analysed the influence of site variables related to disturbance history (canopy height, litter thickness) and fragment variables (size, connectivity) on species richness (asymptotic species richness, slope of the species–area curve) as well as on species assemblages by multiple regressions analysis and canonical correspondence analyses, respectively. Cumulative area was used for analysing whether small fragments or large fragments are more important to species diversity in the landscape. Results: Asymptotic species richness was significantly influenced by site variables, in particular by Paspalum quadrifarium's canopy height, but not by fragment variables. Species assemblages were also affected by site variables (12.2% of total variation), but no additional portion of the species assemblage variability was significantly explained by fragment size and connectivity. Sampling of several small fragments rendered more exotic and native species than sampling of few large fragments of the same total area. Conclusions: Our results agree with previous studies reporting low sensitivity of species diversity to size and isolation of grassland fragments in fragmented landscapes and high sensitivity of species diversity to local variables. The higher capture of regional native species pool by small grassland fragments than by few larger ones of equivalent accumulated area highlights the value of small fragments for conservation.     

Data-dependent permutation techniques for the analysis of ecological data

Two distribution-free permutation techniques are described for the analysis of ecological data. These methods are completely data dependent and provide analyses for the commonly-encountered completely-randomized and randomized-block designs in a multivariate framework. Euclidean distance forms the basis of both techniques, providing consistency with the observed distribution of data in many ecological studies.Abbreviations MRPP= Multiresponse permutation procedure - MRBP= Ibid, randomized block analog     

运用稀疏法分析物种丰富度的海拔梯度分布格局:以样方实测乔木种数据为例

植物物种丰富度随山地海拔梯度的变化格局是生物多样性研究的热点之一.基于种-面积关系的任何模型对群落物种数目所作估计,其精度都依赖于样本的代表性、抽样尺度以及所涉及的分类群.作者以秦岭南坡森林群落样方实测的乔木种数据为例,借鉴群落最小面积(minimum area,MA)的概念及其确定方式,利用稀疏法(rarefacti...     

Scale‐dependent biases in species counts in a grassland

Abstract. Numbers of plant species were recorded in species‐rich meadows in the Bílé Karpaty Mts., SE Czech Republic, with the aim to evaluate the sampling error made by well‐trained observers. Five observers recorded vascular plants in seven plots ranging from 9.8 cm² to 4 m² independently and were not time‐limited. In larger plots a discrepancy of 10–20% was found between individual estimates, in smaller plots discrepancy increased to 33%, on average. The gain in observed species richness by combining records of individual observers (in comparison with the mean numbers estimated by single observers) decreased from the smallest plot (27–82% for two to five observers) to the largest one (13–25%). However, after misidentified and suspicious records were eliminated, the gain was much lower and became scale‐independent; two observers added 12% species, on average, and the increase by combining species lists made by three or more observers was negligible (3% more on average). It is concluded that most discrepancies between individual observers were caused by misidentification of rare seedlings and young plants. We suggest that in species‐rich meadows plants should be recorded by at least three observers together and that they should consult all problematic plant specimens together in the field, to minimize errors.     

Some alternatives to asymptotic tests for the analysis of pharmacogenetic data using nonlinear mixed effects models

Nonlinear mixed effects models allow investigating individual differences in drug concentration profiles (pharmacokinetics) and responses. Pharmacogenetics focuses on the genetic component of this variability. Two tests often used to detect a gene effect on a pharmacokinetic parameter are (1) the Wald test, assessing whether estimates for the gene effect are significantly different from 0 and (2) the likelihood ratio test comparing models with and without the genetic effect. Because those asymptotic tests show inflated type I error on small sample size and/or with unevenly distributed genotypes, we develop two alternatives and evaluate them by means of a simulation study. First, we assess the performance of the permutation test using the Wald and the likelihood ratio statistics. Second, for the Wald test we propose the use of the F-distribution with four different values for the denominator degrees of freedom. We also explore the influence of the estimation algorithm using both the first-order conditional estimation with interaction linearization-based algorithm and the stochastic approximation expectation maximization algorithm. We apply these methods to the analysis of the pharmacogenetics of indinavir in HIV patients recruited in the COPHAR2-ANRS 111 trial. Results of the simulation study show that the permutation test seems appropriate but at the cost of an additional computational burden. One of the four F-distribution-based approaches provides a correct type I error estimate for the Wald test and should be further investigated.     

Latitudinal patterns in European ant assemblages: variation in species richness and body size

Using published distributions of 65 species from the British Isles and northern Europe, we show that ant assemblages change with latitude in two ways. First, as commonly found for many types of organisms, the number of ant species decreased significantly with increasing latitude. For Ireland and Great Britain, species richness also increased significantly with region area. Second, although rarely demonstrated for ectotherms, the body size of ant species, as measured by worker length, increased significantly with increasing latitude. We found that this body-size pattern existed in the subfamily Formicinae and, to a lesser extent, in the Myrmicinae, which together comprised 95% of the ant species in our study area. There was a trend for formicines to increase in size with latitude faster than myrmicines. We also show that the pattern of increasing body size was due primarily to the ranges of ant species shifting to higher latitudes as their body sizes increased, with larger formicines becoming less represented at southerly latitudes and larger myrmicines becoming more represented at northerly latitudes. We conclude by discussing five potential mechanisms for generating the observed body-size patterns: the heat-conservation hypothesis, two hypotheses concerning phylogenetic history, the migration-ability hypothesis, and the starvation-resistance hypothesis.     

Permutation‐based inference for the AUC: A unified approach for continuous and discontinuous data

We investigate rank‐based studentized permutation methods for the nonparametric Behrens–Fisher problem, that is, inference methods for the area under the ROC curve. We hereby prove that the studentized permutation distribution of the Brunner‐Munzel rank statistic is asymptotically standard normal, even under the alternative. Thus, incidentally providing the hitherto missing theoretical foundation for the Neubert and Brunner studentized permutation test. In particular, we do not only show its consistency, but also that confidence intervals for the underlying treatment effects can be computed by inverting this permutation test. In addition, we derive permutation‐based range‐preserving confidence intervals. Extensive simulation studies show that the permutation‐based confidence intervals appear to maintain the preassigned coverage probability quite accurately (even for rather small sample sizes). For a convenient application of the proposed methods, a freely available software package for the statistical software R has been developed. A real data example illustrates the application.     

Incorporation of clustering effects for the Wilcoxon rank sum test: a large-sample approach

The Wilcoxon rank sum test is frequently used in statistical practice for the comparison of measures of location when the underlying distributions are far from normal or not known in advance. An assumption of the ordinary rank sum test is that individual sampling units are independent. In many ophthalmologic clinical trials, the Early Treatment for Diabetic Retinopathy Scale (ETDRS) is a principal endpoint used for measuring the level of diabetic retinopathy. This is an ordinal scale, and it is natural to consider the Wilcoxon rank sum test for the comparison of the level of diabetic retinopathy between treatment groups. However, under this design, unlike the usual Wilcoxon rank sum test, the subject is the unit of randomization, but the eye is the unit of analysis. Furthermore, a person will tend to have different, but correlated, ETDRS scores for fellow eyes. Thus, we propose a correction to the variance of the Wilcoxon rank sum statistic that accounts for clustering effects and that can be used for both balanced (same number of subunits per cluster) or unbalanced (different number of subunits per cluster) data, both in the presence or absence of ties, with p-value adjusted accordingly. In this article, we present large-sample theory and simulation results for this test procedure and apply it to diabetic retinopathy data from type I diabetics in the Sorbinil Retinopathy Trial.     

A multiple-site dissimilarity measure for species presence/absence data and its relationship with nestedness and turnover

Multiple-site dissimilarity may be caused by two opposite processes of meta-community organization, such as species nestedness and turnover. Therefore, discriminating among these contributions is necessary for linking multiple-site dissimilarity to ecosystem functioning. This paper introduces a measure of multiple-site dissimilarity or beta diversity for presence/absence data that is based on information on species absences from the species × sites matrix. It is also shown that the newly proposed dissimilarity index can be additively partitioned into species nestedness and turnover.     

Nonparametric scanning tests of homogeneity for hierarchical models with continuous covariates

In many applications of hierarchical models, there is often interest in evaluating the inherent heterogeneity in view of observed data. When the underlying hypothesis involves parameters resting on the boundary of their support space such as variances and mixture proportions, it is a usual practice to entertain testing procedures that rely on common heterogeneity assumptions. Such procedures, albeit omnibus for general alternatives, may entail a substantial loss of power for specific alternatives such as heterogeneity varying with covariates. We introduce a novel and flexible approach that uses covariate information to improve the power to detect heterogeneity, without imposing unnecessary restrictions. With continuous covariates, the approach does not impose a regression model relating heterogeneity parameters to covariates or rely on arbitrary discretizations. Instead, a scanning approach requiring continuous dichotomizations of the covariates is proposed. Empirical processes resulting from these dichotomizations are then used to construct the test statistics, with limiting null distributions shown to be functionals of tight random processes. We illustrate our proposals and results on a popular class of two-component mixture models, followed by simulation studies and applications to two real datasets in cancer and caries research.     

Patterns in species richness,species density,and evenness in groundfish assemblages on the continental slope of the U.S. Pacific coast

For many taxa, diversity, often measured as species richness, decreases with latitude. In this report patterns of diversity (species richness, species diversity, and evenness) in groundfish assemblages were investigated in relation to depth (200–1200 m) and latitude (33–47°N) on the continental slope of the U.S. Pacific coast. The data originated from the 1999–2002 upper continental slope groundfish surveys conducted by the National Marine Fisheries Service. When the data were pooled across depths, species density and evenness were found to decline with latitude. All three diversity measures declined with depth, with the lowest overall diversity in the 600- to 900-m depth range where longspine thornyhead Sebastolobus altivelis constituted close to 70% of the catch. When latitudinal gradients were examined within four depth zones (200–300 m, 400–500 m, 600–900 m, and 1000–1200 m) more complex patterns emerged. At depth species richness and evenness were inversely correlated with latitude as longspine thornyhead dominated catches to the north. However, in shallower areas of the slope, species richness and evenness were positively correlated with latitude. Latitudinal patterns of diversity in the deeper zones and when pooled across depths were positively correlated with temperature and broadly consistent with the Ambient Energy hypothesis discussed by Willig et al. [Annu Rev Ecol System 34:273–309 (2003)].     

Global patterns of fern species diversity: An evaluation of fern data in GBIF

Despite that several studies have shown that data derived from species lists generated from distribution occurrence records in the Global Biodiversity Information Facility (GBIF) are not appropriate for those ecological and biogeographic studies that require high sampling completeness, because species lists derived from GBIF are generally very incomplete, Suissa et al. (2021) generated fern species lists based on data with GBIF for 100 km × 100 km grid cells across the world, and used the data to determine fern diversity hotspots and species richness–climate relationships. We conduct an evaluation on the completeness of fern species lists derived from GBIF at the grid–cell scale and at a larger spatial scale, and determine whether fern data derived from GBIF are appropriate for studies on the relations of species composition and richness with climatic variables. We show that species sampling completeness of GBIF is low (<40%) for most of the grid cells examined, and such low sampling completeness can substantially bias the investigation of geographic and ecological patterns of species diversity and the identification of diversity hotspots. We conclude that fern species lists derived from GBIF are generally very incomplete across a wide range of spatial scales, and are not appropriate for studies that require data derived from species lists in high completeness. We present a map showing global patterns of fern species diversity based on complete or nearly complete regional fern species lists.