How many sites? Methods to assist design decisions when collecting multivariate data in ecology

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.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 (if we would otherwise use 999 resamples to estimate each p-value) with minor loss of accuracy.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 1.7 or more).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.