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 meets these challenges with accompanying R software (ecopower). Our simulation model uses a Gaussian copula model, and expert opinion is leveraged to simplify effect size specification into “increasers”, “decreasers” or “no effect” taxa. Computational issues are addressed by using a critical value approach, reducing computation time from days to minutes. The procedure is demonstrated by estimating the sample size required to detect changes for fish abundances.