A pathway for multivariate analysis of ecological communities using copulas

Anderson, Marti J.; Valpine, Perry de; Punnett, Andrew; Miller, Arden

doi:10.1002/ece3.4948

Cited by 34 publications

(48 citation statements)

References 112 publications

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“…(2015) and Morueta-Holme et al (2016). However, some care has to be taken with this interpretation (Dormann et al, 2018 Gaussian copulas, as used here, have exciting potential in ecology for the analysis of multivariate non-normal data (Anderson et al, 2019). For example the algorithm used to construct GCGMs here is quite general, and can be used to fit any desired covariance model on iteratively reweighted data (Popovic et al, 2018).…”

Section: Bicmentioning

confidence: 99%

Untangling direct species associations from indirect mediator species effects with graphical models

et al. 2019

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Ecologists often investigate co‐occurrence patterns in multi‐species data in order to gain insight into the ecological causes of observed co‐occurrences. Apart from direct associations between the two species of interest, they may co‐occur because of indirect effects, where both species respond to another variable, whether environmental or biotic (e.g. a mediator species). A wide variety of methods are now available for modelling how environmental filtering drives species distributions. In contrast, methods for studying other causes of co‐occurence are much more limited. “Graphical” methods, which can be used to study how mediator species impact co‐occurrence patterns, have recently been proposed for use in ecology. However, available methods are limited to presence/absence data or methods assuming multivariate normality, which is problematic when analysing abundances. We propose Gaussian copula graphical models (GCGMs) for studying the effect of mediator species on co‐occurence patterns. GCGMs are a flexible type of graphical model which naturally accommodates all data types, for example binary (presence/absence), counts, as well as ordinal data and biomass, in a unified framework. Simulations demonstrate that GCGMs can be applied to a much broader range of data types than the methods currently used in ecology, and perform as well as or better than existing methods in many settings. We apply GCGMs to counts of hunting spiders, in order to visualise associations between species. We also analyse abundance data of New Zealand native forest cover (on an ordinal scale) to show how GCGMs can be used analyse large and complex datasets. In these data, we were able to reproduce known species relationships as well as generate new ecological hypotheses about species associations.

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Section: Bicmentioning

confidence: 99%

Untangling direct species associations from indirect mediator species effects with graphical models

et al. 2019

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“…We provide a basic introduction to copula concepts in the “Background on copulas” section below (section 2). Readers can find additional abbreviated (Genest & Favre 2007; Anderson et al 2018) and comprehensive (Nelsen 2006; Joe 2014; Mai & Scherer 2017) introductions elsewhere. Copulas have already been used very effectively in a few studies to illuminate ecological phenomena (Valpine et al 2014; Anderson et al 2018; Popovic et al 2018), but such usage is still rare.…”

Section: Introductionmentioning

confidence: 99%

Copulas and their potential for ecology

Ghosh

Sheppard

Holder

et al. 2019

Preprint

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AbstractAll branches of ecology study relationships among and between environmental and biological variables. However, standard approaches to studying such relationships, based on correlation and regression, provide only a small slice of the complex information contained in the relationships. Other statistical approaches exist that provide a complete description of relationships between variables, based on the concept of the copula; they are applied in finance, neuroscience and other fields, but rarely in ecology. We here explore the concepts that underpin copulas and examine the potential for those concepts to improve our understanding of ecology. We find that informative copula structure in dependencies between variables is common across all the environmental, species-trait, phenological, population, community, and ecosystem functioning datasets we considered. Many datasets exhibited asymmetric tail associations, whereby two variables were more strongly related in their left compared to right tails, or vice versa. We describe mechanisms by which observed copula structure and asymmetric tail associations can arise in ecological data, including a Moran-like effect whereby dependence structures between environmental variables are inherited by ecological variables; and asymmetric or nonlinear influences of environments on ecological variables, such as under Liebig’s law of the minimum. We also describe consequences of copula structure for ecological phenomena, including impacts on extinction risk, Taylor’s law, and the stability through time of ecosystem services. By documenting the importance of a complete description of dependence between variables, advancing conceptual frameworks, and demonstrating a powerful approach, we aim to encourage widespread use of copulas in ecology, which we believe can benefit the discipline.

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“…Another recent and promising development in ecology is copula models (Anderson, Valpine, Punnett, & Miller, ; Popovic, Hui, & Warton, ; Popovic, Warton, Thomson, Hui, & Moles, ).…”

Section: Discussionmentioning

confidence: 99%

“…Anderson et al () highlighted a combination of the model‐ and distance‐based approaches. They proposed a copula model of ecological count data (see Hofert, Kojadinovic, Mächler, & Yan, , for an introduction to copula models), which consists of (a) fitting a copula model to the data, (b) simulating new count data with this copula, and (c) visualizing the centroids of the actual data and of the simulated data sets in a metric multidimensional scaling.…”

Section: Discussionmentioning

confidence: 99%

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

Jupke

Schäfer

2020

Ecology and Evolution

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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.

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A pathway for multivariate analysis of ecological communities using copulas

Cited by 34 publications

References 112 publications

Untangling direct species associations from indirect mediator species effects with graphical models

Untangling direct species associations from indirect mediator species effects with graphical models

Copulas and their potential for ecology

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

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