Bayes and Empirical Bayes approaches to addressing stock structure questions using mtDNA data, with an illustrative application to North Pacific minke whales

Abstract

Bayesian methods using mtDNA data are developed to compare single- and multiple-stock hypotheses. The likelihood of the data is assumed to be multinomial and the multivariate prior for the probability of an individual having a particular haplotype is assumed to be of the Dirichlet-b form. The values for the parameters of this prior are either determined using an Empirical Bayes approach or assumed to be distributed according to a log-normal hyper-prior (the ‘Full Bayes’ approach). The Empirical and Full Bayes methods are examined using simulation. The performance of the Empirical Bayes method is found to be much worse than that of the Full Bayes method. Illustrative comparisons for North Pacific minke whales based on the latter method confirm previous results that sub-areas 6 and 7 contain different stocks. Results of the application of this method to the mtDNA data for the sub-areas to the east of Japan, although generally uninformative, are nevertheless consistent with analyses based on hypothesis testing using allozymes and mtDNA. The results from this method should, however, be used for management purposes with some caution. This is because, although some testing of the Full Bayes method has been completed and suggests that when applied to data for two stocks that differ substantially in haplotype frequency, or when sample sizes are large and there is only one stock, performance is adequate, in common with most other methods for analysing genetics data, its performance has yet to be fully evaluated.