Comparing mixture estimates by parametric bootstrapping likelihood ratios

Wildlife managers and researchers often need to estimate the relative contributions of distinct populations in a mixture of organisms. Increasingly, there is interest in comparing these mixture contributions across space or time. Comparisons usually just check for overlap in the interval estimates for each population contribution from each mixture. This method inflates Type I error rates, has limited power due to its focus on marginal comparisons, and employs a fundamentally inappropriate measure of mixture difference. Given the difficulty of defining an appropriate measure of mixture difference, a powerful alternative is to compare mixtures using a likelihood ratio test. In applications where the standard asymptotic theory does not hold, the null reference distribution can be obtained through parametric bootstrapping. In addition to testing simple hypotheses, a likelihood ratio framework encourages modeling the change in mixture contributions as a function of covariates. The method is demonstrated with an analysis of potential sampling bias in the estimation of population contributions to the commercial sockeye salmon (Oncorhynchus nerka) fishery in Upper Cook Inlet, Alaska.