Pella and Masuda: Bayesian methods for analysis of stock mixtures from genetic markers 
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Population proportion 
Figure 2 
Histograms of samples from the posterior distribution of unknown proportions of summer 
populations of harbor porpoise (Gulf of Maine-Bay of Fundy, Gulf of St. Lawrence, New- 
foundland, and West Greenland) in the wintering group. 
sets of samples for each experiment — Bayes mode, Bayes 
mean, and conditional maximum likelihood (CML) esti- 
mate — and their standard errors were computed (Table 3). 
The main lesson of these simulations is that the Bayes 
method, as configured, performs reasonably well in the 
frequency sense, that is, under repeated sampling. The 
Bayes posterior mode seems to be a practical point es- 
timator for population proportions in stock mixtures: it 
was less biased than the Bayes posterior mean and the 
conditional maximum likelihood estimate when the ex- 
perimental conditions caused bias. As is characteristic of 
stock-mixture composition bias, uneven population contri- 
butions combined with large variation in estimated con- 
tributions were aggravating. When the populations con- 
tributed equally (stock mixture 4), bias was negligible for 
any estimator, given the large variation of estimated popu- 
lation proportions, but with unequal contributions (stock 
mixtures 1-3), the bias became increasingly severe be- 
cause the haplotypes were added to the populations and 
increased the variation in estimated contributions. Lower 
bias of the Bayes mode was not without cost because its 
variation among sets of samples was generally larger than 
that of the Bayes mean or conditional maximum likeli- 
hood estimate for the more-difficult third and fourth stock 
mixtures. 
Example 2: Sashin Creek steelhead ( Oncorhynchus mykiss) 
stock mixture Sashin Creek on Baranof Island in South- 
east Alaska contains a population of anadromous rainbow 
trout, or steelhead, in its lower portion. In addition, a self- 
sustaining population above a barrier waterfall was cre- 
ated in 1926 by a transplant from the lower to the upper 
portion (which includes two lakes). Although the falls was 
a barrier to upstream migration, migrating juveniles from 
the upper portion apparently survived the plunge to the 
lower river. Samples of mature adults returning from the 
ocean, obtained from the lower portion, were compared 
with similar samples from the upper population for allo- 
zymes (21 loci with 2-6 alleles per locus), microsatellites 
(10 loci with 3-26 alleles per locus), and mtDNA (5 haplo- 
types). An excess of homozygotes at loci (Wahlund effect) 
provided evidence that the samples came from a mixture 
of both populations. In particular, the allozyme, PGK2, 
appeared to be fixed (100%) in the upper population, yet 
the fixed allele represented less than 50% of the PGK2 
alleles in the stock-mixture sample from the lower por- 
tion. Biologists 3 were able to infer that roughly 25% of the 
stock mixture probably originated from the upper popula- 
3 Thrower, F. 2000. NMFS, Auke Bay Laboratory, Juneau, AK 
99801-8626. 
