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

TL;DR

This paper introduces a new power analysis method for ecological multivariate data collection, using Gaussian copula models and a critical value approach, to help researchers plan effective study designs.

Contribution

It presents a novel, computationally efficient power analysis procedure tailored for multivariate ecological data, implemented in an R package.

Findings

The method accurately estimates power with reduced computation time.

Applied to fish assemblage data, it showed the study could detect large effects only.

The approach aids in designing studies with realistic effect detection capabilities.

Abstract

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.