Detecting Fitness Difference in the Wild: Power Analysis and Its Application to Salmonid Species

Accumulating evidence suggests that there are large heterogeneities in reproductive fitness in the wild. Of special interest in fishery science is when fish are reared in captivity and released for natural reproduction. While empirical studies started revealing surprisingly large differences in reproductive fitness between wild and hatchery fish, it is also common that 10 or even 20% of fitness difference turns out to be statistically non-significant, by which researchers can say nothing definitive. However, theoretical evolutionary biology suggests that >10% of fitness difference should have a major evolutionary consequence. To bridge the gap between the empirical studies and the theoretical prediction, we conducted power analysis on several statistical tests, assuming two hypothetical groups of fish with different reproductive fitness. Our preliminary results indicate that a popular permutation test is rather too conservative, and transformations of the fitness distribution increase the power and a risk of high false positive rates. I discuss how in practice we can take advantage of the power analysis with real-world examples of salmonid fish populations.