A metagenomic alpha-diversity index for microbial functional biodiversity

Alpha-diversity indices are an essential tool for describing and comparing biodiversity. Microbial ecologists apply indices originally intended for, or adopted by, macroecology to address questions relating to taxonomy (conserved marker) and function (metagenome-based data). In this Perspective piece, I begin by discussing the nature and mathematical quirks important for interpreting routinely employed alpha-diversity indices. Secondly, I propose a metagenomic alpha-diversity index (MD) that measures the (dis)similarity of protein-encoding genes within a community. MD has defined limits, whereby a community comprised mostly of similar, poorly diverse protein-encoding genes pulls the index to the lower limit, while a community rich in divergent homologs and unique genes drives it toward the upper limit. With data acquired from an in silico and three in situ metagenome studies, I derive MD and typical alpha-diversity indices applied to taxonomic (ribosomal rRNA) and functional (all protein-encoding) genes, and discuss their relationships with each other. Not all alpha-diversity indices detect biological trends, and taxonomic does not necessarily follow functional biodiversity. Throughout, I explain that protein Richness and MD provide complementary and easily interpreted information, while probability-based indices do not. Finally, considerations regarding the unique nature of microbial metagenomic data and its relevance for describing functional biodiversity are discussed.

A general modeling framework for open wildlife populations based on the Polya tree prior

Wildlife monitoring for open populations can be performed using a number of different survey methods. Each survey method gives rise to a type of data and, in the last five decades, a large number of associated statistical models have been developed for analyzing these data. Although these models have been parameterized and fitted using different approaches, they have all been designed to either model the pattern with which individuals enter and/or exit the population, or to estimate the population size by accounting for the corresponding observation process, or both. However, existing approaches rely on a predefined model structure and complexity, either by assuming that parameters linked to the entry and exit pattern (EEP) are specific to sampling occasions, or by employing parametric curves to describe the EEP. Instead, we propose a novel Bayesian nonparametric framework for modeling EEPs based on the Polya tree (PT) prior for densities. Our Bayesian nonparametric approach avoids overfitting when inferring EEPs, while simultaneously allowing more flexibility than is possible using parametric curves. Finally, we introduce the replicate PT prior for defining classes of models for these data allowing us to impose constraints on the EEPs, when required. We demonstrate our new approach using capture-recapture, count, and ring-recovery data for two different case studies.

Community-level species' correlated distribution can be scale-independent and related to the evenness of abundance

The spatial distribution of species is not random; instead, individuals tend to gather, resulting in a non-random pattern. Previous studies used the independent negative binomial distribution (NBD) to model the distributional aggregation of a single species, in which the independence of the distribution of individuals of a species in different quadrats had been assumed. This way of analyzing aggregation will result in the scale-dependent estimation of the aggregation or shape parameter. However, because non-random (and therefore non-independent) distribution of individuals of a species in a finite area can be caused by either correlated or clumped distribution of individuals of a species between neighboring sites, an alternative model would assume that the distribution of individuals of a species over different sampling areas is multinomial. Here, we showed that, by assuming that regional species abundance followed a NBD while using a multinomial distribution to assign individuals of species in different non-overlapped sampling quadrats that are from a partition of the entire region (quantifying positive correlation or synchrony), the estimation of the shape parameter in this probabilistic model, which is the negative multinomial distribution (NMD), was scale-invariant (i.e., the estimated shape parameter is identical across different partitions of the study region). Accordingly, the estimation of the shape parameter was related to regional species distribution alone. This implied that, the shape parameter at the community level, using the NMD model, reflected the evenness of interspecific abundance. As a comparison, if the distribution of individuals of a single species followed independent NBDs as studied previously, the shape parameter would measure the evenness of intraspecific abundance (quantifying single-species' distributional aggregation). Moreover, our study highlighted the necessity for adjusting the model for the effects of unsampled species when studying community-level distributional patterns. Collectively, as long as a target area is partitioned into non-overlapping quadrats (no matter how their sizes vary), the proposed NMD model in this study, along with the independent NBDs model, can be jointly formulated as a framework to reconcile the scale-dependent debate on the shape parameter, unifying the relationship between inter- or intraspecific abundance and distributional patterns.

Analyzing differences between microbiome communities using mixture distributions

In this paper, we present a method to assess differences between microbiome communities that effectively models sparse count data and accounts for presence-absence bias frequently encountered when zeros are present. We assume that the observed data for each operational taxonomic unit is Poisson generated with the rate for each sample originating from an underlying rate distribution. We propose to model this distribution using a mixture model, specifying the components based on the posterior rate distribution of a count and estimating the optimal weights using a least squares objective function. The distribution incorporates varying resolutions of samples, a point mass for differentiating structural and nonstructural zeros, and a truncation point mass to account for high values that are too sparse to model. As mixture component specification is not always straightforward, a method to estimate a joint model from several mixture distributions using minimum distances of bootstrap iterates is proposed. Once the population rate distribution is approximated, we obtain sample-specific distributions by conditioning on the observed operational taxonomic unit count, resolution, and estimated mixture distribution and then use these to estimate pairwise distances for a permutation test. The method gives an accurate estimate of the true proportion of zeros for presence-absence, effectively models the distribution of low counts using the mixture distribution, and achieves good power for detecting differences in a variety of scenarios. The method is tested using a simulation study and applied to two microbiome datasets. In each case, the results are compared with a number of existing methods.

Rarefaction and extrapolation of species richness using an area-based Fisher's logseries

Fisher's logseries is widely used to characterize species abundance pattern, and some previous studies used it to predict species richness. However, this model, derived from the negative binomial model, degenerates at the zero‐abundance point (i.e., its probability mass fully concentrates at zero abundance, leading to an odd situation that no species can occur in the studied sample). Moreover, it is not directly related to the sampling area size. In this sense, the original Fisher's alpha (correspondingly, species richness) is incomparable among ecological communities with varying area sizes. To overcome these limitations, we developed a novel area‐based logseries model that can account for the compounding effect of the sampling area. The new model can be used to conduct area‐based rarefaction and extrapolation of species richness, with the advantage of accurately predicting species richness in a large region that has an area size being hundreds or thousands of times larger than that of a locally observed sample, provided that data follow the proposed model. The power of our proposed model has been validated by extensive numerical simulations and empirically tested through tree species richness extrapolation and interpolation in Brazilian Atlantic forests. Our parametric model is data parsimonious as it is still applicable when only the information on species number, community size, or the numbers of singleton and doubleton species in the local sample is available. Notably, in comparison with the original Fisher's method, our area‐based model can provide asymptotically unbiased variance estimation (therefore correct 95% confidence interval) for species richness. In conclusion, the proposed area‐based Fisher's logseries model can be of broad applications with clear and proper statistical background. Particularly, it is very suitable for being applied to hyperdiverse ecological assemblages in which nonparametric richness estimators were found to greatly underestimate species richness.