Detecting Specific Populations in Mixtures

Mixed stock analysis (MSA) estimates the relative contributions of distinct populations in a mixture of organisms. Increasingly, MSA is used to judge the presence or absence of specific populations in specific mixture samples. This is commonly done by inspecting the bootstrap confidence interval of the contribution of interest. This method has a number of statistical deficiencies, including almost zero power to detect small contributions even if the population has perfect identifiability. We introduce a more powerful method based on the likelihood ratio test and compare both methods in a simulation demonstration using a 17 population baseline of sockeye salmon, Oncorhynchus nerka, from the Kenai River, Alaska, watershed. Power to detect a nonzero contribution will vary with the population(s) identifiability relative to the rest of the baseline, the contribution size, mixture sample size, and analysis method. The demonstration shows that the likelihood ratio method is always more powerful than the bootstrap method, the two methods only being equal when both display 100% power. Power declines for both methods as contribution declines, but it declines faster and goes to zero for the bootstrap method. Power declines quickly for both methods as population identifiability declines, though the likelihood ratio test is able to capitalize on the presence of 'perfect identification' characteristics, such as private alleles. Given the baseline-specific nature of detection power, researchers are encouraged to conduct a priori power analyses similar to the current demonstration when planning their applications.