Topographic complexity and the power to detect structural and functional changes in temperate reef fish assemblages: The need for habitat-independent sample sizes

Functional approaches have shown promising results to detect degradation in marine fish assemblages. However, background variability significantly affects the amplitude of change that is detectable by a monitoring plan, and failing to detect such changes can have devastating consequences and carry aggravated recovery costs due to unnoticed degradation. The present study aimed to understand the relationship between topographic complexity in temperate reefs and the power to detect variations in fish-based metrics. Underwater visual census of fish assemblages was performed using strip transects and a Monte Carlo simulation approach was used to generate a large number of replicates and simulate three alternative hypotheses representing different magnitudes of change. Statistical power to detect differences between null and alternative hypotheses was estimated through 10,000 Mann-Whitney tests for numbers of replicates ranging from 2 to 15. Power tended to vary with topographic complexity particularly with small and medium changes in metric values and when using small sample sizes. While power increased with complexity for most metrics, some showed decreasing trends. With a large effect, 5-15 transects were needed, depending on the metric, to stabilise power above 0.80 independently of habitat features. A power of 0.95, however, could not be achieved for most metrics in all sites, even when using 15 transects. The observation that the power to detect degradation and recovery in temperate reef fish seems to vary with habitat features means that a monitoring programme that is correctly planned for a particular area may not be directly applicable in a nearby reef. Adding to the need to maximise power in monitoring, this study highlights the need to take into account habitat variability in these calculations and estimate habitat-independent sample sizes that are appropriate for the scale and location of interest.