How sampling influences the statistical power to detect changes in abundance: An application to river restoration

Abstract

Assessing how populations respond to ecological restoration is particularly difficult because their abundance results from many sources of variation. In addition, abundance estimates depend on sampling efforts that are limited by financial or practical constraints. We used local abundance counts from the Rhône river restoration monitoring programme to quantify how sampling strategies and population characteristics influenced statistical power for detecting restoration effects. We first fitted observed changes in abundance of 13 fish taxa and 35 invertebrate taxa collected in microhabitats of four restored reaches of the Rhône river over 15 years, using a generalised linear mixed model. The model accounted for a restoration effect, random temporal variation between field surveys and spatial variation within surveys (i.e. microhabitat variation in abundance was assumed to follow a negative binomial distribution). We then used numerical simulations to calculate the statistical power (i.e. the probability of detecting a true change) and the type I error (the probability of detecting a non-existent change) associated with various hypotheses of restoration effect size, mean abundance and temporal and spatial variation. Model fits revealed that accounting for temporal variation is needed to reduce type I error associated with the effect of restoration. Significant abundance changes were observed for 27 of 104 (26%) of the taxa-reach combinations. When assuming temporal variation and population characteristics typical of our data sets, power simulations showed that the probability of detecting a moderate change (50-200%) in abundance was <38% in all tests. The average probability of detecting large changes (500-1000%) was 61%. In these conditions, power was increased by low spatial variation and high sampling effort. Large numbers of surveys (e.g. 16 instead of 4) increased the power by 20 points if surveys were balanced before and after restoration. Because our simulations covered a wide variety of population characteristics and sampling strategies, they can be used a priori to determine which sampling strategy is best adapted for detecting restoration effects from repeated abundance counts.