DOI: 10.5061/dryad.3s6rm0f
title: Data from: Effects of Poor Knights Islands Marine Reserve on demersal fish populations

description: 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.
description: Underwater visual census
 data from the Poor Knights Islands, New ZealandData consist of counts
 of abundances of each of p = 47 species in each of N = 56 sites at the
 Poor Knights Islands, New Zealand. At each site, divers performed a visual
 census in each of nine 25 m × 5 m transects, and these transect-level
 counts were summed to yield a single count value for each species at each
 site. There were three different times of sampling: September 1998 (15
 sites), March 1999 (21 sites) and September 1999 (20 sites). These times
 of sampling span the point in time when the Poor Knights Islands were
 classified as a no-take marine reserve (October 1998). The data were
 originally obtained as part of an ongoing monitoring programme of the
 status of fish communities for the Poor Knights Islands, funded by New
 Zealand’s Department of Conservation (DoC). Initial analyses of these data
 appear in the following report, which should be cited directly if these
 data are to be used in any other context. Willis, T.J. & Denny, C.M.
 (2000). Effects of Poor Knights Islands Marine Reserve on demersal fish
 populations. Report to the Department of Conservation, Research Grant No.
 2519, Leigh Marine Laboratory, University of Auckland, New
 Zealand.NZDOC.PKIMR_UVS.species_counts.1998_1999.csv