  1. Sample size estimation through power analysis is a fundamental tool in
planning an ecological study, yet there are currently no well-established
procedures for when multivariate abundances are to be collected. A power
analysis procedure would need to address three challenges: designing a
parsimonious simulation model that captures key community data properties;
measuring effect size in a realistic yet interpretable fashion; and ensuring
computational feasibility when simulation is used both for power estimation and
significance testing. 2. Here we propose a power analysis procedure that
addresses these three challenges by: using for simulation a Gaussian copula
model with factor analytical structure, fitted to pilot data; assuming a common
effect size across all taxa, but applied in different directions according to
expert opinion (to "increaser", "decreaser" or "no effect" taxa); using a
critical value approach to estimate power, which reduces computation time by a
factor of 500 with little loss of accuracy. 3. The procedure is demonstrated on
pilot data from fish assemblages in a restoration study, where it was found
that the planned study design would only be capable of detecting relatively
large effects (change in abundance by a factor of 1.5 or more). 4. The methods
outlined in this paper are available in accompanying R software (the ecopower
package), which allows researchers with pilot data to answer a wide range of
design questions to assist them in planning their studies.
