Extending Joint Models in Community Ecology: A Response to Beissinger et al

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.

Assuming independence in spatial latent variable models: Consequences and implications of misspecification

Multivariate spatial data, where multiple responses are simultaneously recorded across spatially indexed observational units, are routinely collected in a wide variety of disciplines. For example, the Southern Ocean Continuous Plankton Recorder survey collects records of zooplankton communities in the Indian sector of the Southern Ocean, with the aim of identifying and quantifying spatial patterns in biodiversity in response to environmental change. One increasingly popular method for modeling such data is spatial generalized linear latent variable models (GLLVMs), where the correlation across sites is captured by a spatial covariance function in the latent variables. However, little is known about the impact of misspecifying the latent variable correlation structure on inference of various parameters in such models. To address this gap in the literature, we investigate how misspecifying and assuming independence for the latent variables' correlation structure impacts estimation and inference in spatial GLLVMs. Through both theory and numerical studies, we show that performance of maximum likelihood estimation and inference on regression coefficients under misspecification depends on a combination of the response type, the magnitude of true regression coefficient, and the corresponding loadings, and, most importantly, whether the corresponding covariate is (also) spatially correlated. On the other hand, estimation and inference of truly nonzero loadings and prediction of latent variables is consistently not robust to misspecification of the latent variable correlation structure.

Sampling beetle communities: Trap design interacts with weather and species traits to bias capture rates

Globally, many insect populations are declining, prompting calls for action. Yet these findings have also prompted discussion about sampling methods and interpretation of long-term datasets. As insect monitoring and research efforts increase, it is critical to quantify the effectiveness of sampling methods. This is especially true if sampling biases of different methods covary with climate, which is also changing over time. We assess the effectiveness of two types of flight intercept traps commonly used for beetles, a diverse insect group responsible for numerous ecosystem services, under different climatic conditions in Norwegian boreal forest. One of these trap designs includes a device to prevent rainwater from entering the collection vial, diluting preservatives and flushing out beetles. This design is compared to a standard trap. We ask how beetle capture rates vary between these traps, and how these differences vary based on precipitation levels and beetle body size, an important species trait. Bayesian mixed models reveal that the standard and modified traps differ in their beetle capture rates, but that the magnitude and direction of these differences change with precipitation levels and beetle body size. At low rainfall levels, standard traps catch more beetles, but as precipitation increases the catch rates of modified traps overtake those of standard traps. This effect is most pronounced for large-bodied beetles. Sampling methods are known to differ in their effectiveness. Here, we present evidence for a less well-known but likely common phenomenon-an interaction between climate and sampling, such that relative effectiveness of trap types for beetle sampling differs depending on precipitation levels and species traits. This highlights a challenge for long-term monitoring programs, where both climate and insect populations are changing. Sampling methods should be sought that eliminate climate interactions, any biases should be quantified, and all insect datasets should include detailed methodological metadata.

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.

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.

Empirically-based modeling and mapping to consider the co-occurrence of ecological receptors and stressors

Part of the ecological risk assessment process involves examining the potential for environmental stressors and ecological receptors to co-occur across a landscape. In this study, we introduce a Bayesian joint modeling framework for use in evaluating and mapping the co-occurrence of stressors and receptors using empirical data, open-source statistical software, and Geographic Information Systems tools and data. To illustrate the approach, we apply the framework to bioassessment data on stream fishes and nutrients collected from a watershed in southwestern Ohio. The results highlighted the joint model's ability to parse and exploit statistical dependencies in order to provide empirical insight into the potential environmental and ecotoxicological interactions influencing co-occurrence. We also demonstrate how probabilistic predictions can be generated and mapped to visualize spatial patterns in co-occurrences. For practitioners, we believe that this data-driven approach to modeling and mapping co-occurrence can lead to more quantitatively transparent and robust assessments of ecological risk.

How to make more out of community data? A conceptual framework and its implementation as models and software

Community ecology aims to understand what factors determine the assembly and dynamics of species assemblages at different spatiotemporal scales. To facilitate the integration between conceptual and statistical approaches in community ecology, we propose Hierarchical Modelling of Species Communities (HMSC) as a general, flexible framework for modern analysis of community data. While non-manipulative data allow for only correlative and not causal inference, this framework facilitates the formulation of data-driven hypotheses regarding the processes that structure communities. We model environmental filtering by variation and covariation in the responses of individual species to the characteristics of their environment, with potential contingencies on species traits and phylogenetic relationships. We capture biotic assembly rules by species-to-species association matrices, which may be estimated at multiple spatial or temporal scales. We operationalise the HMSC framework as a hierarchical Bayesian joint species distribution model, and implement it as R- and Matlab-packages which enable computationally efficient analyses of large data sets. Armed with this tool, community ecologists can make sense of many types of data, including spatially explicit data and time-series data. We illustrate the use of this framework through a series of diverse ecological examples.