Data from: Effects of Poor Knights Islands Marine Reserve on demersal fish populations

PLEASE NOTE, THESE DATA ARE ALSO REFERRED TO IN SUBSEQUENT PUBLICATIONS.
PLEASE SEE Anderson et al. (2019) at https://doi.org/10.1002/ece3.4948 FOR
MORE INFORMATION. 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 modelled 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 an MCEM 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.