Power of Stable isotope techniques to detect size-based feeding in marine fishes

Abstract

Stable isotope techniques are now the most frequently applied method to investigate size-based variation in fish trophic position (TP), and data suggest changes in TP with body size are common. However, of 131 collated investigations of the relationship between body size and δ15N for inshore coastal fishes, approximately 60% were non-significant. The present study tests whether non-significant trends reflect a true feeding pattern, a lack of statistical power, or a function of both. Results suggest none of these studies for which correlation coefficients were available, achieved enough statistical power to rigorously assess observed slopes. The sample size required to detect statistically significant trends of different magnitude, given assumptions of dispersion and observed data on body size range sampled, was then assessed. Even under lenient assumptions of below average dispersion and uniform sampling effort across the sampled body size range, <10% of the statistical tests classifying trends as non-significant had the power to detect a slope corresponding to a 0.25 change in TP over 80% of maximum length (proportional length range: Lmax) throughout life. Therefore non-significant trends in δ15N are predominantly the result of poor power, and no conclusion can be drawn as to associated fish trophodynamics. Analysis here suggests that size-based feeding studies should aim to sample over 40% Lmax range of the population, as the sample size required to maintain sufficient statistical power diminishes almost exponentially with increasing body size range. Researchers should strive to minimise other sources of variation as linear increases in dispersion lead to virtually linear increases in sample size necessary to maintain power. Finally, a key component of hypothesis testing for size-based feeding should be not just whether a trend is significant, but whether sampling is adequate to detect a minimum ecologically relevant threshold slope. This will separate tests that lack power from those where size-independent feeding is a true feeding mode.