Francis K. C. Hui

The arcsine is asinine: the analysis of proportions in ecology

The arcsine square root transformation has long been standard procedure when analyzing proportional data in ecology, with applications in data sets containing binomial and non-binomial response variables. Here, we argue that the arcsine transform should not be used in either circumstance. For binomial data, logistic regression has greater interpretability and higher power than analyses of transformed data. However, it is important to check the data for additional unexplained variation, i.e., overdispersion, and to account for it via the inclusion of random effects in the model if found. For non-binomial data, the arcsine transform is undesirable on the grounds of interpretability, and because it can produce nonsensical predictions. The logit transformation is proposed as an alternative approach to address these issues. Examples are presented in both cases to illustrate these advantages, comparing various methods of analyzing proportions including untransformed, arcsine- and logit-transformed linear models and logistic regression (with or without random effects). Simulations demonstrate that logistic regression usually provides a gain in power over other methods.

Plant functional traits have globally consistent effects on competition

Phenotypic traits and their associated trade-offs have been shown to have globally consistent effects on individual plant physiological functions, but how these effects scale up to influence competition, a key driver of community assembly in terrestrial vegetation, has remained unclear. Here we use growth data from more than 3 million trees in over 140,000 plots across the world to show how three key functional traits—wood density, specific leaf area and maximum height—consistently influence competitive interactions. Fast maximum growth of a species was correlated negatively with its wood density in all biomes, and positively with its specific leaf area in most biomes. Low wood density was also correlated with a low ability to tolerate competition and a low competitive effect on neighbours, while high specific leaf area was correlated with a low competitive effect. Thus, traits generate trade-offs between performance with competition versus performance without competition, a fundamental ingredient in the classical hypothesis that the coexistence of plant species is enabled via differentiation in their successional strategies. Competition within species was stronger than between species, but an increase in trait dissimilarity between species had little influence in weakening competition. No benefit of dissimilarity was detected for specific leaf area or wood density, and only a weak benefit for maximum height. Our trait-based approach to modelling competition makes generalization possible across the forest ecosystems of the world and their highly diverse species composition.

So Many Variables: Joint Modeling in Community Ecology.

Technological advances have enabled a new class of multivariate models for ecology, with the potential now to specify a statistical model for abundances jointly across many taxa, to simultaneously explore interactions across taxa and the response of abundance to environmental variables. Joint models can be used for several purposes of interest to ecologists, including estimating patterns of residual correlation across taxa, ordination, multivariate inference about environmental effects and environment-by-trait interactions, accounting for missing predictors, and improving predictions in situations where one can leverage knowledge of some species to predict others. We demonstrate this by example and discuss recent computation tools and future directions.

Model‐based approaches to unconstrained ordination

Summary Unconstrained ordination is commonly used in ecology to visualize multivariate data, in particular, to visualize the main trends between different sites in terms of their species composition or relative abundance. Methods of unconstrained ordination currently used, such as non-metric multidimensional scaling, are algorithm-based techniques developed and implemented without directly accommodating the statistical properties of the data at hand. Failure to account for these key data properties can lead to misleading results. A model-based approach to unconstrained ordination can address this issue, and in this study, two types of models for ordination are proposed based on finite mixture models and latent variable models. Each method is capable of handling different data types and different forms of species response to latent gradients. Further strengths of the models are demonstrated via example and simulation. Advantages of model-based approaches to ordination include the following: residual analysis tools for checking assumptions to ensure the fitted model is appropriate for the data; model selection tools to choose the most appropriate model for ordination; methods for formal statistical inference to draw conclusions from the ordination; and improved efficiency, that is model-based ordination better recovers true relationships between sites, when used appropriately.

boral – Bayesian Ordination and Regression Analysis of Multivariate Abundance Data in r

Summary Model-based methods have emerged as a powerful approach for analysing multivariate abundance data in community ecology. Key applications include model-based ordination, modelling the various sources of correlations across species, and making inferences while accounting for these between species correlations. boral (version 0.9.1, licence GPL-2) is an r package available on cran for model-based analysis of multivariate abundance data, with estimation performed using Bayesian Markov chain Monte Carlo methods. A key feature of the boral package is the ability to incorporate latent variables as a parsimonious method of modelling between species correlation. Pure latent variable models offer a model-based approach to unconstrained ordination, for visualizing sites and the indicator species characterizing them on a low-dimensional plot. Correlated response models consist of fitting generalized linear models to each species, while including latent variables to account for residual correlation between species, for example, due to unmeasured covariates.

To mix or not to mix: comparing the predictive performance of mixture models vs. separate species distribution models

Species distribution models (SDMs) are an important tool for studying the patterns of species across environmental and geographic space. For community data, a common approach involves fitting an SDM to each species separately, although the large number of models makes interpretation difficult and fails to exploit any similarities between individual species responses. A recently proposed alternative that can potentially overcome these difficulties is species archetype models (SAMs), a model-based approach that clusters species based on their environmental response. In this paper, we compare the predictive performance of SAMs against separate SDMs using a number of multi-species data sets. Results show that SAMs improve model accuracy and discriminatory capacity compared to separate SDMs. This is achieved by borrowing strength from common species having higher information content. Moreover, the improvement increases as the species become rarer.

Tuning Parameter Selection for the Adaptive Lasso Using ERIC

The adaptive Lasso is a commonly applied penalty for variable selection in regression modeling. Like all penalties though, its performance depends critically on the choice of the tuning parameter. One method for choosing the tuning parameter is via information criteria, such as those based on AIC and BIC. However, these criteria were developed for use with unpenalized maximum likelihood estimators, and it is not clear that they take into account the effects of penalization. In this article, we propose the extended regularized information criterion (ERIC) for choosing the tuning parameter in adaptive Lasso regression. ERIC extends the BIC to account for the effect of applying the adaptive Lasso on the bias-variance tradeoff. This leads to a criterion whose penalty for model complexity is itself a function of the tuning parameter. We show the tuning parameter chosen by ERIC is selection consistent when the number of variables grows with sample size, and that this consistency holds in a wider range of contexts compared to using BIC to choose the tuning parameter. Simulation show that ERIC can significantly outperform BIC and other information criteria proposed (for choosing the tuning parameter) in selecting the true model. For ultra high-dimensional data (p > n), we consider a two-stage approach combining sure independence screening with adaptive Lasso regression using ERIC, which is selection consistent and performs strongly in simulation. Supplementary materials for this article are available online.

The Effect of Seasonal Ambient Temperatures on Fire-Stimulated Germination of Species with Physiological Dormancy: A Case Study Using Boronia (Rutaceae)

Dormancy and germination requirements determine the timing and magnitude of seedling emergence, with important consequences for seedling survival and growth. Physiological dormancy is the most widespread form of dormancy in flowering plants, yet the seed ecology of species with this dormancy type is poorly understood in fire-prone vegetation. The role of seasonal temperatures as germination cues in these habitats is often overlooked due to a focus on direct fire cues such as heat shock and smoke, and little is known about the combined effects of multiple fire-related cues and environmental cues as these are seldom assessed in combination. We aimed to improve understanding of the germination requirements of species with physiological dormancy in fire-prone floras by investigating germination responses across members of the Rutaceae from south eastern Australia. We used a fully factorial experimental design to quantify the individual and combined effects of heat shock, smoke and seasonal ambient temperatures on germination of freshly dispersed seeds of seven species of Boronia, a large and difficult-to-germinate genus. Germination syndromes were highly variable but correlated with broad patterns in seed morphology and phylogenetic relationships between species. Seasonal temperatures influenced the rate and/or magnitude of germination responses in six species, and interacted with fire cues in complex ways. The combined effects of heat shock and smoke ranged from neutral to additive, synergistic, unitive or negative and varied with species, seasonal temperatures and duration of incubation. These responses could not be reliably predicted from the effect of the application of single cues. Based on these findings, fire season and fire intensity are predicted to affect both the magnitude and timing of seedling emergence in wild populations of species with physiological dormancy, with important implications for current fire management practices and for population persistence under climate change.

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

The joint modelling of many variables in community ecology is a new and technically challenging area with many opportunities for future developments. The possibility of extending joint models to deal with imperfect detection has been highlighted by Beissinger et al. as an important problem worthy of further investigation [1]. We agree, and previously pointed to this potential extension as an outstanding question [2], alongside models that can estimate phylogenetic repulsion or attraction, nonlinearity in the response to latent variables, and spatial or temporal correlation, because further developments in all these directions are needed.

Joint Selection in Mixed Models using Regularized PQL

ABSTRACT The application of generalized linear mixed models presents some major challenges for both estimation, due to the intractable marginal likelihood, and model selection, as we usually want to jointly select over both fixed and random effects. We propose to overcome these challenges by combining penalized quasi-likelihood (PQL) estimation with sparsity inducing penalties on the fixed and random coefficients. The resulting approach, referred to as regularized PQL, is a computationally efficient method for performing joint selection in mixed models. A key aspect of regularized PQL involves the use of a group based penalty for the random effects: sparsity is induced such that all the coefficients for a random effect are shrunk to zero simultaneously, which in turn leads to the random effect being removed from the model. Despite being a quasi-likelihood approach, we show that regularized PQL is selection consistent, that is, it asymptotically selects the true set of fixed and random effects, in the setting where the cluster size grows with the number of clusters. Furthermore, we propose an information criterion for choosing the single tuning parameter and show that it facilitates selection consistency. Simulations demonstrate regularized PQL outperforms several currently employed methods for joint selection even if the cluster size is small compared to the number of clusters, while also offering dramatic reductions in computation time. Supplementary materials for this article are available online.