BKD infection for a mixture individual was randomly determined by sampling from potential source

Populations and implementation of more genetic markers, one can expect differences to diminish between mixture model estimates and estimates that condition on preliminary IA. Even so, mixture modeling will continue to enjoy the strongest theoretical foundation and some degree of superior statistical performance as long as uncertainty exists in IA. In this study, we seek the same statistical robustness for ecological and phenotypic trait inference that has been demonstrated for mixture modeling as compared to IA. We extend the Bayesian genetic mixture model to incorporate parameters associated with phenotypic traits. The conditional maximum likelihood model of Bromaghin et al. is incorporated into a Bayesian framework. Again, the conceptual advantage of this approach is the utilization of all available information in a mixture sample, along with its uncertainty, and minimizing potential biases stemming from conditioning on prior estimates of population membership. The performance of the Bayesian mixture model is assessed through comparison with that of IA using the maximum a posteriori rule. Under the MAP rule, we assign the individual to the group of source populations for which the posterior source probability is maximal, with application of various minimum probability thresholds. To achieve the overarching goals above, we consider two diverse example applications, reanalyzing recently published data in light of simulation results. Finally, we make recommendations for specific methods based on their performance under various distributions of the ecological/phenotypic trait and genetic distance among populations. Although we draw heavily on Pacific salmon research, we emphasize the general applicability of our analyses and especially the diversity of genetic and non-genetic traits that can be examined. Our analysis is relevant to all marker classes. Applications are limited only by available baseline data for known-origin individuals. We expect increasing interest in our methods as those data become available for more taxa. We constructed two sets of known BKD infections rates among the six reporting groups, one in which the infection rates were positively correlated with genetic similarity among reporting groups, and a second set which was negatively correlated. In the positive case, we hypothesized that both methods would perform equally well, as any errors in assignment would be between reporting groups with similar infection rates. In the negative case, however, assignment errors would most likely occur between reporting groups with dissimilar infection rates, which would bias their estimation. A measure of genetic differentiation was computed for each pair of reporting groups. Genetic differentiation between population pairs, FST, was calculated with GENEPOP, version 4.1.0. The average FST among all unique pairs of populations in each pair of reporting groups was computed as a measure of differentiation.

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