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A pathway for multivariate analysis of ecological communities using copulas.

ABSTRACT: 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.

SUBMITTER: Anderson MJ

PROVIDER: S-EPMC6434552 | biostudies-literature | 2019 Mar

REPOSITORIES: biostudies-literature

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A pathway for multivariate analysis of ecological communities using copulas.

Anderson Marti J MJ de Valpine Perry P Punnett Andrew A Miller Arden E AE

Ecology and evolution 20190305 6

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 var ...[more]

PMID: 30962892

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Project description:Environmental exposures typically involve mixtures of pollutants, which must be understood to evaluate cumulative risks, that is, the likelihood of adverse health effects arising from two or more chemicals. This study uses several powerful techniques to characterize dependency structures of mixture components in personal exposure measurements of volatile organic compounds (VOCs) with aims of advancing the understanding of environmental mixtures, improving the ability to model mixture components in a statistically valid manner, and demonstrating broadly applicable techniques. We first describe characteristics of mixtures and introduce several terms, including the mixture fraction which represents a mixture component's share of the total concentration of the mixture. Next, using VOC exposure data collected in the Relationship of Indoor Outdoor and Personal Air (RIOPA) study, mixtures are identified using positive matrix factorization (PMF) and by toxicological mode of action. Dependency structures of mixture components are examined using mixture fractions and modeled using copulas, which address dependencies of multiple variables across the entire distribution. Five candidate copulas (Gaussian, t, Gumbel, Clayton, and Frank) are evaluated, and the performance of fitted models was evaluated using simulation and mixture fractions. Cumulative cancer risks are calculated for mixtures, and results from copulas and multivariate lognormal models are compared to risks calculated using the observed data. Results obtained using the RIOPA dataset showed four VOC mixtures, representing gasoline vapor, vehicle exhaust, chlorinated solvents and disinfection by-products, and cleaning products and odorants. Often, a single compound dominated the mixture, however, mixture fractions were generally heterogeneous in that the VOC composition of the mixture changed with concentration. Three mixtures were identified by mode of action, representing VOCs associated with hematopoietic, liver and renal tumors. Estimated lifetime cumulative cancer risks exceeded 10(-3) for about 10% of RIOPA participants. Factors affecting the likelihood of high concentration mixtures included city, participant ethnicity, and house air exchange rates. The dependency structures of the VOC mixtures fitted Gumbel (two mixtures) and t (four mixtures) copulas, types that emphasize tail dependencies. Significantly, the copulas reproduced both risk predictions and exposure fractions with a high degree of accuracy, and performed better than multivariate lognormal distributions. Copulas may be the method of choice for VOC mixtures, particularly for the highest exposures or extreme events, cases that poorly fit lognormal distributions and that represent the greatest risks.

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A pathway for multivariate analysis of ecological communities using copulas.

Publications

A pathway for multivariate analysis of ecological communities using copulas.

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