Generalized Linear Latent Variable Models for Multivariate Count and Biomass Data in Ecology

Diverse bacterial consortia: key drivers of rhizosoil fertility modulating microbiome functions, plant physiology, nutrition, and soybean grain yield

Soybean cultivation in tropical regions relies on symbioses with nitrogen-fixing Bradyrhizobium and plant growth-promoting bacteria (PGPBs), reducing environmental impacts of N fertilizers and pesticides. We evaluate the effects of soybean inoculation with different bacterial consortia combined with PGPBs or microbial secondary metabolites (MSMs) on rhizosoil chemistry, plant physiology, plant nutrition, grain yield, and rhizosphere microbial functions under field conditions over three growing seasons with four treatments: standard inoculation of Bradyrhizobium japonicum and Bradyrhizobium diazoefficiens consortium (SI); SI plus foliar spraying with Bacillus subtilis (SI + Bs); SI plus foliar spraying with Azospirillum brasilense (SI + Az); and SI plus seed application of MSMs enriched in lipo-chitooligosaccharides extracted from B. diazoefficiens and Rhizobium tropici (SI + MSM). Rhizosphere microbial composition, diversity, and function was assessed by metagenomics. The relationships between rhizosoil chemistry, plant nutrition, grain yield, and the abundance of microbial taxa and functions were determined by generalized joint attribute modeling. The bacterial consortia had the most significant impact on rhizosphere soil fertility, which in turn affected the bacterial community, plant physiology, nutrient availability, and production. Cluster analysis identified microbial groups and functions correlated with shifts in rhizosoil chemistry and plant nutrition. Bacterial consortia positively modulated specific genera and functional pathways involved in biosynthesis of plant secondary metabolites, amino acids, lipopolysaccharides, photosynthesis, bacterial secretion systems, and sulfur metabolism. The effects of the bacterial consortia on the soybean holobiont, particularly the rhizomicrobiome and rhizosoil fertility, highlight the importance of selecting appropriate consortia for desired outcomes. These findings have implications for microbial-based agricultural practices that enhance crop productivity, quality, and sustainability.

Spatial versus spatio-temporal approaches for studying metacommunities: a multi-taxon analysis in Mediterranean and tropical temporary ponds

Prior research on metacommunities has largely focused on snapshot surveys, often overlooking temporal dynamics. In this study, our aim was to compare the insights obtained from metacommunity analyses based on a spatial approach repeated over time, with a spatio-temporal approach that consolidates all data into a single model. We empirically assessed the influence of temporal variation in the environment and spatial connectivity on the structure of metacommunities in tropical and Mediterranean temporary ponds. Employing a standardized methodology across both regions, we surveyed multiple freshwater taxa in three time periods within the same hydrological year from multiple temporary ponds in each region. To evaluate how environmental, spatial and temporal influences vary between the two approaches, we used nonlinear variation partitioning analyses based on generalized additive models. Overall, this study underscores the importance of adopting spatio-temporal analytics to better understand the processes shaping metacommunities. While the spatial approach suggested that environmental factors had a greater influence, our spatio-temporal analysis revealed that spatial connectivity was the primary driver influencing metacommunity structure in both regions. Temporal effects were equally important as environmental effects, suggesting a significant role of ecological succession in metacommunity structure.

Homogeneity pursuit and variable selection in regression models for multivariate abundance data

When building regression models for multivariate abundance data in ecology, it is important to allow for the fact that the species are correlated with each other. Moreover, there is often evidence species exhibit some degree of homogeneity in their responses to each environmental predictor, and that most species are informed by only a subset of predictors. We propose a generalized estimating equation (GEE) approach for simultaneous homogeneity pursuit (ie, grouping species with similar coefficient values while allowing differing groups for different covariates) and variable selection in regression models for multivariate abundance data. Using GEEs allows us to straightforwardly account for between-response correlations through a (reduced-rank) working correlation matrix. We augment the GEE with both adaptive fused lasso- and adaptive lasso-type penalties, which aim to cluster the species-specific coefficients within each covariate and encourage differing levels of sparsity across the covariates, respectively. Numerical studies demonstrate the strong finite sample performance of the proposed method relative to several existing approaches for modeling multivariate abundance data. Applying the proposed method to presence-absence records collected along the Great Barrier Reef in Australia reveals both a substantial degree of homogeneity and sparsity in species-environmental relationships. We show this leads to a more parsimonious model for understanding the environmental drivers of seabed biodiversity, and results in stronger out-of-sample predictive performance relative to methods that do not accommodate such features.

Abundance, biomass and species richness of macrozoobenthos along an intertidal elevation gradient

Ecology aims to comprehend species distribution and its interaction with environmental factors, from global to local scales. While global environmental changes affect marine biodiversity, understanding the drivers at smaller scales remains crucial. Tidal flats can be found on most of the world's coastlines and are particularly vulnerable to anthropogenic disturbances. They are important transient ecosystems between terrestrial and marine ecosystems, and their biodiversity provides important ecosystem services. Owing to this unique, terrestrial-marine transition, strong environmental gradients of elevation, sediment composition and food availability prevail. Here, we investigated which regional and local environmental factors drive the spatio-temporal dynamics of macrozoobenthos communities on back-barrier tidal flats in the East Frisian Wadden Sea. On the regional level, we found that species composition changed significantly from west to east on the East Frisian islands and that total abundance and species richness decreased from west to east. On the local abiotic level, we found that macrozoobenthos biomass decreased with higher elevation towards the salt marsh and that the total abundance of organisms in the sediment significantly increased with increasing mud content, while biodiversity and biomass were not changing significantly. In contrast to expectations, increasing Chl a availability as a measure of primary productivity did not result in changes in abundance, biomass or biodiversity, but extremely high total organic carbon (TOC) content was associated with a decrease in biomass and biodiversity. In conclusion, we found regional and local relationships that are similar to those observed in previous studies on macrozoobenthos in the Wadden Sea. Macrozoobenthos biomass, abundance and biodiversity are interrelated in a complex way with the physical, abiotic and biotic processes in and above the sediment.

On generalized latent factor modeling and inference for high-dimensional binomial data

We explore a hierarchical generalized latent factor model for discrete and bounded response variables and in particular, binomial responses. Specifically, we develop a novel two-step estimation procedure and the corresponding statistical inference that is computationally efficient and scalable for the high dimension in terms of both the number of subjects and the number of features per subject. We also establish the validity of the estimation procedure, particularly the asymptotic properties of the estimated effect size and the latent structure, as well as the estimated number of latent factors. The results are corroborated by a simulation study and for illustration, the proposed methodology is applied to analyze a dataset in a gene-environment association study.

Consumer pressure and supplemental pollination mediate shrub facilitation of a native annual desert plant

Shrubs are important factors in the assembly of desert plant and animal communities. By providing shelter and resources to other plants and animals, shrubs can change plant-animal interactions including those with consumers and pollinators. Here, we test the hypothesis that shrubs facilitate the reproduction of other desert plants by influencing pollination and compensation for consumer pressure. We used the known benefactor Larrea tridentata as our focal shrub species and the flowering annual Malacothrix glabrata as a potential protege in the Mojave Desert. We tested the effects of facilitation (shrub microsite), consumer pressure (both artificial folivory and florivory), and pollination (ambient or supplemented) on flower and seed production of the annual M. glabrata. We found that floral production and seed mass were similar between microsites but that pollen was limited under shrubs in the absence of any other manipulation. Plants under shrubs produced more flowers and seeds than in the open when folivory and florivory treatments were applied. Malacothrix glabrata experienced a cost to association with L. tridentata in terms of pollen limitation but plants were better able to compensate for consumer pressure under shrubs through increased flower and seed production when damaged. Therefore, association with shrubs involves a reproductive trade-off between costs to pollination and benefits to compensation for consumer pressure.

Inconsistent response of taxonomic groups to space and environment in mediterranean and tropical pond metacommunities

The metacommunity concept provides a theoretical framework that aims at explaining organism distributions by a combination of environmental filtering, dispersal, and drift. However, few works have attempted a multitaxon approach and even fewer have compared two distant biogeographical regions using the same methodology. We tested the expectation that temperate (mediterranean-climate) pond metacommunities would be more influenced by environmental and spatial processes than tropical ones, because of stronger environmental gradients and a greater isolation of waterbodies. However, the pattern should be different among groups of organisms depending on their dispersal abilities. We surveyed 30 tropical and 32 mediterranean temporary ponds from Costa Rica and Spain, respectively, and obtained data on 49 environmental variables. We characterized the biological communities of bacteria and archaea (from the water column and the sediments), phytoplankton, zooplankton, benthic invertebrates, amphibians and birds, and estimated the relative role of space and environment on metacommunity organization for each group and region, by means of variation partitioning using generalized additive models. Purely environmental effects were important in both tropical and mediterranean ponds, but stronger in the latter, probably due to their larger limnological heterogeneity. Spatially correlated environment and pure spatial effects were greater in the tropics, related to higher climatic heterogeneity and dispersal processes (e.g., restriction, surplus) acting at different scales. The variability between taxonomic groups in the contribution of spatial and environmental factors to metacommunity variation was very wide, but higher in active, compared with passive, dispersers. Higher environmental effects were observed in mediterranean passive dispersers, and higher spatial effects in tropical passive dispersers. The unexplained variation was larger in the tropical setting, suggesting a higher role for stochastic processes, unmeasured environmental factors, or biotic interactions in the tropics, although this difference affected some actively dispersing groups (insects and birds) more than passive dispersers. These results, despite our limitations in comparing only two regions, provide support, for a wide variety of aquatic organisms, for the classic view of stronger abiotic niche constraints in temperate areas compared with the tropics. The heterogeneous response of taxonomic groups between regions also points to a stronger influence of regional context than organism adaptations on metacommunity organization.

Effect of nitrogen and glyphosate on the plant community composition in a simulated field margin ecosystem: Model-based ordination of pin-point cover data

The effect of nitrogen and glyphosate on the plant community composition was investigated in a simulated field margin ecosystem. The plant community composition was inferred from pin-point cover data using a model-based ordination method that is suited for modelling pin-point cover data. The mean structure of the ordination model is analogous to a standard linear model, which enabled us to estimate the mean effects of nitrogen and glyphosate and their interaction in the two-dimensional ordination space. There were significant effects of both nitrogen and glyphosate on the plant community composition and overall species diversity. The effects of nitrogen and glyphosate on the plant community composition differed significantly. Furthermore, the estimated combined effects of nitrogen and glyphosate indicated that nitrogen and glyphosate enforced the effect of each other on the plant community composition by synergistic interactions. Addition of nitrogen and glyphosate was found to favor a plant community that was dominated by perennial grasses, and there was a tendency for glyphosate to select for plant communities in which annual plants were more frequent. The results suggest that using the notion of plant functional types and specific knowledge of the degree of glyphosate tolerance may be effective for predicting the effect of glyphosate on the community composition.

Beyond Basic Diversity Estimates-Analytical Tools for Mechanistic Interpretations of Amplicon Sequencing Data

Understanding microbial ecology through amplifying short read regions, typically 16S rRNA for prokaryotic species or 18S rRNA for eukaryotic species, remains a popular, economical choice. These methods provide relative abundances of key microbial taxa, which, depending on the experimental design, can be used to infer mechanistic ecological underpinnings. In this review, we discuss recent advancements in in situ analytical tools that have the power to elucidate ecological phenomena, unveil the metabolic potential of microbial communities, identify complex multidimensional interactions between species, and compare stability and complexity under different conditions. Additionally, we highlight methods that incorporate various modalities and additional information, which in combination with abundance data, can help us understand how microbial communities respond to change in a typical ecosystem. Whilst the field of microbial informatics continues to progress substantially, our emphasis is on popular methods that are applicable to a broad range of study designs. The application of these methods can increase our mechanistic understanding of the ongoing dynamics of complex microbial communities.

mbDenoise: microbiome data denoising using zero-inflated probabilistic principal components analysis

The analysis of microbiome data has several technical challenges. In particular, count matrices contain a large proportion of zeros, some of which are biological, whereas others are technical. Furthermore, the measurements suffer from unequal sequencing depth, overdispersion, and data redundancy. These nuisance factors introduce substantial noise. We propose an accurate and robust method, mbDenoise, for denoising microbiome data. Assuming a zero-inflated probabilistic PCA (ZIPPCA) model, mbDenoise uses variational approximation to learn the latent structure and recovers the true abundance levels using the posterior, borrowing information across samples and taxa. mbDenoise outperforms state-of-the-art methods to extract the signal for downstream analyses.

Multivariate generalized linear mixed models for continuous bounded outcomes: Analyzing the body fat percentage data

We propose a multivariate regression model to handle multiple continuous bounded outcomes. We adopted the maximum likelihood approach for parameter estimation and inference. The model is specified by the product of univariate probability distributions and the correlation between the response variables is obtained through the correlation matrix of the random intercepts. For modeling continuous bounded variables on the interval (0,1) we considered the beta and unit gamma distributions. The main advantage of the proposed model is that we can easily combine different marginal distributions for the response variable vector. The computational implementation is performed using Template Model Builder, which combines the Laplace approximation with automatic differentiation. Therefore, the proposed approach allows us to estimate the model parameters quickly and efficiently. We conducted a simulation study to evaluate the computational implementation and the properties of the maximum likelihood estimators under different scenarios. Moreover, we investigate the impact of distribution misspecification in the proposed model. Our model was motivated by a data set with multiple continuous bounded outcomes, which refer to the body fat percentage measured at five regions of the body. Simulation studies and data analysis showed that the proposed model provides a general and rich framework to deal with multiple continuous bounded outcomes.

Top predator introduction changes the effects of spatial isolation on freshwater community structure

Current conceptual metacommunity models predict that the consequences of local selective pressures on community structure increase with spatial isolation when species favored by local conditions also have higher dispersal rates. This appears to be the case of freshwater insects in the presence of fish. The introduction of predatory fish can produce trophic cascades in freshwater habitats because fish tend to prey upon intermediate predatory taxa, such as predatory insects, indirectly benefiting herbivores and detritivores. Similarly, spatial isolation can limit dispersal and colonization rates of predatory insects more strongly than of herbivores and detritivores, thus generating similar cascading effects. Here we tested the hypothesis that the effect of introduced predatory fish on insect community structure increases with spatial isolation by conducting a field experiment in artificial ponds that manipulated the presence/absence of fish (the redbreast tilapia) at three different distances from a source wetland. Our results showed that fish have direct negative effects on the abundance of predatory insects but probably have variable net effects on the abundance of herbivores and detritivores because the direct negative effects of predation by fish may offset indirect positive ones. Spatial isolation also resulted in indirect positive effects on the abundance of herbivores and detritivores but this effect was stronger in the absence rather than in the presence of fish so that insect communities diverged more strongly between fish and fishless ponds at higher spatial isolation. We argue that an important additional mechanism, ignored in our initial hypothesis, was that as spatial isolation increases fish predation pressure upon herbivores and detritivores increases due to the relative scarcity of predatory insects, thus dampening the positive effect that spatial isolation confers to lower trophic levels. Our results highlight the importance of considering interspecific variation in dispersal and multiple trophic levels to better understand the processes generating community and metacommunity patterns.

Successional syndromes of saplings in tropical secondary forests emerge from environment-dependent trait-demography relationships

Identifying generalisable processes that underpin population dynamics is crucial for understanding successional patterns. While longitudinal or chronosequence data are powerful tools for doing so, the traditional focus on community-level shifts in taxonomic and functional composition rather than species-level trait-demography relationships has made generalisation difficult. Using joint species distribution models, we demonstrate how three traits-photosynthetic rate, adult stature, and seed mass-moderate recruitment and sapling mortality rates of 46 woody species during secondary succession. We show that the pioneer syndrome emerges from higher photosynthetic rates, shorter adult statures and lighter seeds that facilitate exploitation of light in younger secondary forests, while 'long-lived pioneer' and 'late successional' syndromes are associated with trait values that enable species to persist in the understory or reach the upper canopy in older secondary forests. Our study highlights the context dependency of trait-demography relationships, which drive successional shifts in sapling's species composition in secondary forests.

Stock delineation of striped snakehead, Channa striata using multivariate generalised linear models with otolith shape and chemistry data

Otoliths are commonly used to discriminate between fish stocks, through both elemental composition and otolith shape. Typical studies also have a large number of elemental compositions and shape measures relative to the number of otolith samples, with these measures exhibiting strong mean–variance relationships. These properties make otolith composition and shape data highly suitable for use within a multivariate generalised linear model (MGLM) framework, yet MGLMs have never been applied to otolith data. Here we apply both a traditional distance based permutational multivariate analysis of variance (PERMANOVA) and MGLMs to a case study of striped snakehead (Channa striata) in India. We also introduce the Tweedie and gamma distributions as suitable error structures for the MGLMs, drawing similarities to the properties of Biomass data. We demonstrate that otolith elemental data and combined otolith elemental and shape data violate the assumption of homogeneity of variance of PERMANOVA and may give misleading results, while the assumptions of the MGLM with Tweedie and gamma distributions are shown to be satisfied and are appropriate for both otolith shape and elemental composition data. Consistent differences between three groups of C. striata were identified using otolith shape, otolith chemistry and a combined otolith shape and chemistry dataset. This suggests that future research should be conducted into whether there are demographic differences between these groups which may influence management considerations. The MGLM method is widely applicable and could be applied to any multivariate otolith shape or elemental composition dataset.

The Poisson-Lognormal Model as a Versatile Framework for the Joint Analysis of Species Abundances

Joint Species Distribution Models (JSDM) provide a general multivariate framework to study the joint abundances of all species from a community. JSDM account for both structuring factors (environmental characteristics or gradients, such as habitat type or nutrient availability) and potential interactions between the species (competition, mutualism, parasitism, etc.), which is instrumental in disentangling meaningful ecological interactions from mere statistical associations. Modeling the dependency between the species is challenging because of the count-valued nature of abundance data and most JSDM rely on Gaussian latent layer to encode the dependencies between species in a covariance matrix. The multivariate Poisson-lognormal (PLN) model is one such model, which can be viewed as a multivariate mixed Poisson regression model. Inferring such models raises both statistical and computational issues, many of which were solved in recent contributions using variational techniques and convex optimization tools. The PLN model turns out to be a versatile framework, within which a variety of analyses can be performed, including multivariate sample comparison, clustering of sites or samples, dimension reduction (ordination) for visualization purposes, or inferring interaction networks. This paper presents the general PLN framework and illustrates its use on a series a typical experimental datasets. All the models and methods are implemented in the R package PLNmodels, available from cran.r-project.org.

A Generalized Linear Mixed Model Approach to Assess Emerald Ash Borer Diffusion

The Asian Emerald Ash Borer beetle (EAB, Agrilus planipennis Fairmaire) can cause damage to all species of Ash trees (Fraxinus), and rampant, unchecked infestations of this insect can cause significant damage to forests. It is thus critical to assess and model the spread of the EAB in a manner that allows authorities to anticipate likely areas of future tree infestation. In this study, a generalized linear mixed model (GLMM), combining the features of the commonly used generalized linear model (GLM) and a random effects model, was developed to predict future EAB spread patterns in Southern Ontario, Canada. The GLMM was designed to deal with autocorrelation in the data. Two random effects were established based on the geographic information provided with the EAB data, and a method based on statistical inference was proposed to identify the most significant factors associated with the distribution of the EAB. The results of the model showed that 95% of the testing data were correctly classified. The predictive performance of the GLMM was substantially enhanced in comparison with that obtained by the GLM. The influence of climatic factors, such as wind speed and anthropogenic activities, had the most significant influence on the spread of the EAB.

Should ecologists prefer model- over distance-based multivariate methods?

Ecological data sets often record the abundance of species, together with a set of explanatory variables. Multivariate statistical methods are optimal to analyze such data and are thus frequently used in ecology for exploration, visualization, and inference. Most approaches are based on pairwise distance matrices instead of the sites-by-species matrix, which stands in stark contrast to univariate statistics, where data models, assuming specific distributions, are the norm. However, through advances in statistical theory and computational power, models for multivariate data have gained traction. Systematic simulation-based performance evaluations of these methods are important as guides for practitioners but still lacking. Here, we compare two model-based methods, multivariate generalized linear models (MvGLMs) and constrained quadratic ordination (CQO), with two distance-based methods, distance-based redundancy analysis (dbRDA) and canonical correspondence analysis (CCA). We studied the performance of the methods to discriminate between causal variables and noise variables for 190 simulated data sets covering different sample sizes and data distributions. MvGLM and dbRDA differentiated accurately between causal and noise variables. The former had the lowest false-positive rate (0.008), while the latter had the lowest false-negative rate (0.027). CQO and CCA had the highest false-negative rate (0.291) and false-positive rate (0.256), respectively, where these error rates were typically high for data sets with linear responses. Our study shows that both model- and distance-based methods have their place in the ecologist's statistical toolbox. MvGLM and dbRDA are reliable for analyzing species-environment relations, whereas both CQO and CCA exhibited considerable flaws, especially with linear environmental gradients.

Evaluating and presenting uncertainty in model-based unconstrained ordination

Variability in ecological community composition is often analyzed by recording the presence or abundance of taxa in sample units, calculating a symmetric matrix of pairwise distances or dissimilarities among sample units and then mapping the resulting matrix to a low-dimensional representation through methods collectively called ordination. Unconstrained ordination only uses taxon composition data, without any environmental or experimental covariates, to infer latent compositional gradients associated with the sampling units. Commonly, such distance-based methods have been used for ordination, but recently there has been a shift toward model-based approaches. Model-based unconstrained ordinations are commonly formulated using a Bayesian latent factor model that permits uncertainty assessment for parameters, including the latent factors that correspond to gradients in community composition. While model-based methods have the additional benefit of addressing uncertainty in the estimated gradients, typically the current practice is to report point estimates without summarizing uncertainty. To demonstrate the uncertainty present in model-based unconstrained ordination, the well-known spider and dune data sets were analyzed and shown to have large uncertainty in the ordination projections. Hence to understand the factors that contribute to the uncertainty, simulation studies were conducted to assess the impact of additional sampling units or species to help inform future ordination studies that seek to minimize variability in the latent factors. Accurate reporting of uncertainty is an important part of transparency in the scientific process; thus, a model-based approach that accounts for uncertainty is valuable. An R package, UncertainOrd, contains visualization tools that accurately represent estimates of the gradients in community composition in the presence of uncertainty.

Changes in infaunal assemblage structure influence nutrient fluxes in sediment enriched by mussel biodeposition

Although many studies have described the influence of bivalve aquaculture on the benthic environment, effects on benthic functional diversity are poorly known, as are links with ecosystem processes. We investigated the response of a benthic ecosystem in terms of taxonomic and functional diversity (infauna >500 μm), biogeochemical indicators (organic matter content, redox potential, sulfides level, bacteria) and metabolism (nutrient fluxes), subjected to various levels of mussel biodeposition as a general model of organic enrichment. Results show that local benthic conditions may recover fairly quickly depending on environmental conditions whereas modifications of the benthic community structure persist over a longer time scale with an impact on benthic ecosystem functioning. Fauna-mediated oxidation of the sediment likely increased nitrogen recycling through nitrification whereas binding and release of phosphorus to the water column seems to be driven by more complex processes. Results highlight the importance of species identity (ecological traits) on biogeochemical cycling and solute exchange across the sediment-water interface, with implications for the ecological functioning of exploited areas.

Analyzing community structure subject to incomplete sampling: hierarchical community model vs. canonical ordinations

Recently developing hierarchical community models (HCMs) accounting for incomplete sampling are promising approaches to understand community organization. However, pros and cons of incorporating incomplete sampling in the analysis and related design issues remain unknown. In this study, we compared HCM and canonical redundancy analysis (RDA) carried out with 10 different dissimilarity coefficients to evaluate how each approach restores true community abundance data sampled with imperfect detection. We conducted simulation experiments with varying numbers of sampling sites, visits, mean detectability and mean abundance. Performance of HCM was measured by estimates of "expected" (mean) abundance ( λ ^ ij ) and realized abundance ( N ^ ij : direct estimate of site- and species-specific abundance). We also compared HCM and different types of RDA (normal, partial, and weighted), all performed with the same ten different dissimilarity coefficients, with unequal number of visits to sampling sites. In addition, we applied the models to a virtual survey carried out on the Barro Colorado Island tree plot data for which we know true community abundance. Simulation experiments showed that N ^ ij yielded by HCM best restored the underlying abundance of constituent species among 12 abundance estimates by HCM and RDA regardless if the sampling was equal or unequal. Mean abundance predominantly affected the performance of HCM and RDA while λ ^ ij yielded by HCM had comparable performance to percentage difference and Gower dissimilarity coefficients of RDA. Relative performance of RDA types depended on the combination of dissimilarity coefficients and the distribution of sampling effort. Best performance of N ^ ij followed by λ ^ ij , percentage difference and Gower dissimilarity were also observed for the analysis of tree plot data, and graphical plots (triplots) based on λ ^ ij rather than N ^ ij clearly separated the effects of two environmental covariates on the abundance of constituent species. Under our conditions of model evaluation and the method, we concluded that, in terms of assessing the environmental dependence of abundance, HCMs and RDA can have comparable performance if we can choose appropriate dissimilarity coefficients for RDA. However, since HCMs provide straightforward biological interpretations of parameter estimates and flexibility of the analysis, HCMs would be useful in many situations as well as conventional canonical ordinations.

Efficient estimation of generalized linear latent variable models

Generalized linear latent variable models (GLLVM) are popular tools for modeling multivariate, correlated responses. Such data are often encountered, for instance, in ecological studies, where presence-absences, counts, or biomass of interacting species are collected from a set of sites. Until very recently, the main challenge in fitting GLLVMs has been the lack of computationally efficient estimation methods. For likelihood based estimation, several closed form approximations for the marginal likelihood of GLLVMs have been proposed, but their efficient implementations have been lacking in the literature. To fill this gap, we show in this paper how to obtain computationally convenient estimation algorithms based on a combination of either the Laplace approximation method or variational approximation method, and automatic optimization techniques implemented in R software. An extensive set of simulation studies is used to assess the performances of different methods, from which it is shown that the variational approximation method used in conjunction with automatic optimization offers a powerful tool for estimation.

A pathway for multivariate analysis of ecological communities using copulas

We describe a new pathway for multivariate analysis of data consisting of counts of species abundances that includes two key components: copulas, to provide a flexible joint model of individual species, and dissimilarity-based methods, to integrate information across species and provide a holistic view of the community. Individual species are characterized using suitable (marginal) statistical distributions, with the mean, the degree of over-dispersion, and/or zero-inflation being allowed to vary among a priori groups of sampling units. Associations among species are then modeled using copulas, which allow any pair of disparate types of variables to be coupled through their cumulative distribution function, while maintaining entirely the separate individual marginal distributions appropriate for each species. A Gaussian copula smoothly captures changes in an index of association that excludes joint absences in the space of the original species variables. A permutation-based filter with exact family-wise error can optionally be used a priori to reduce the dimensionality of the copula estimation problem. We describe in detail a Monte Carlo expectation maximization algorithm for efficient estimation of the copula correlation matrix with discrete marginal distributions (counts). The resulting fully parameterized copula models can be used to simulate realistic ecological community data under fully specified null or alternative hypotheses. Distributions of community centroids derived from simulated data can then be visualized in ordinations of ecologically meaningful dissimilarity spaces. Multinomial mixtures of data drawn from copula models also yield smooth power curves in dissimilarity-based settings. Our proposed analysis pathway provides new opportunities to combine model-based approaches with dissimilarity-based methods to enhance understanding of ecological systems. We demonstrate implementation of the pathway through an ecological example, where associations among fish species were found to increase after the establishment of a marine reserve.

A unified framework for unconstrained and constrained ordination of microbiome read count data

Explorative visualization techniques provide a first summary of microbiome read count datasets through dimension reduction. A plethora of dimension reduction methods exists, but many of them focus primarily on sample ordination, failing to elucidate the role of the bacterial species. Moreover, implicit but often unrealistic assumptions underlying these methods fail to account for overdispersion and differences in sequencing depth, which are two typical characteristics of sequencing data. We combine log-linear models with a dispersion estimation algorithm and flexible response function modelling into a framework for unconstrained and constrained ordination. The method is able to cope with differences in dispersion between taxa and varying sequencing depths, to yield meaningful biological patterns. Moreover, it can correct for observed technical confounders, whereas other methods are adversely affected by these artefacts. Unlike distance-based ordination methods, the assumptions underlying our method are stated explicitly and can be verified using simple diagnostics. The combination of unconstrained and constrained ordination in the same framework is unique in the field and facilitates microbiome data exploration. We illustrate the advantages of our method on simulated and real datasets, while pointing out flaws in existing methods. The algorithms for fitting and plotting are available in the R-package RCM.

Order selection and sparsity in latent variable models via the ordered factor LASSO

Generalized linear latent variable models (GLLVMs) offer a general framework for flexibly analyzing data involving multiple responses. When fitting such models, two of the major challenges are selecting the order, that is, the number of factors, and an appropriate structure for the loading matrix, typically a sparse structure. Motivated by the application of GLLVMs to study marine species assemblages in the Southern Ocean, we propose the Ordered Factor LASSO or OFAL penalty for order selection and achieving sparsity in GLLVMs. The OFAL penalty is the first penalty developed specifically for order selection in latent variable models, and achieves this by using a hierarchically structured group LASSO type penalty to shrink entire columns of the loading matrix to zero, while ensuring that non-zero loadings are concentrated on the lower-order factors. Simultaneously, individual element sparsity is achieved through the use of an adaptive LASSO. In conjunction with using an information criterion which promotes aggressive shrinkage, simulation shows that the OFAL penalty performs strongly compared with standard methods and penalties for order selection, achieving sparsity, and prediction in GLLVMs. Applying the OFAL penalty to the Southern Ocean marine species dataset suggests the available environmental predictors explain roughly half of the total covariation between species, thus leading to a smaller number of latent variables and increased sparsity in the loading matrix compared to a model without any covariates.