Corander et al A Bayesian method for Identification of stock mixtures from molecular marker data 



557 



Table 7 



Average numbers of allocations (over 20 replicates) to the 

 different stocks under an uneven sample size distribution: 

 TornW, ;! = 60, Simo, n=2Q. li, ;! = 30, Oulu. ;! = 5, Neva, 

 n = 10. Stocks correspond to five different rivers: Tornion- 

 joki (TornWl, Simojoki iSimol, lijoki (li). Oulujoki (Oului, 

 and Neva. The number of baseline individuals available 

 from each of the five stocks was 30. The column with the 

 heading "Other" refers to additional stocks inferred by 

 the method. The marker loci used for inference were ran- 

 domly sampled from the original nine microsatellites for 

 each replicate; in (A) seven loci were used, in (B) five loci 

 were used. 



Allocation 



Origin TornW Simo li Oulu Neva Other 



A TornW 44.5 



Simo 



li 



Oulu 



Neva 



TornW 

 Simo 

 li 

 Oulu 



Neva 



0.9 



2.8 

 0.3 

 0.0 



37.3 

 1.0 

 3.3 

 0.5 

 0.1 



3.2 

 17.8 

 1.6 

 0.1 

 0.0 



4.5 

 16.5 

 2.8 

 0.2 

 0.0 



7.6 

 0.9 

 24.7 

 0.2 

 0.0 



9.3 

 1.4 

 21.2 

 0.4 

 0.1 



4.3 

 0.4 

 0.9 

 4.5 

 0.0 



5.5 

 0.6 

 2.2 

 4.0 

 0.2 



0.2 

 0.0 

 0.1 

 0.0 

 10.0 



0.5 

 0.2 

 0.1 

 0.0 

 9.6 



0.0 

 0.1 

 0.0 

 0.0 

 0.0 



3.1 

 0.4 

 0.5 

 0.1 



0.2 



graphical location, can be incorporated into the analysis. 

 This information is incorporated by the pre-assignment of 

 individuals in the catch data to a priori sampling units, 

 when such are considered to be relevant for the species 

 under investigation. Such prior information is particu- 

 larly useful if the available molecular data are scarce 

 because it enhances the statistical power to detect correct 

 stock origins, as illustrated in our example analyses. 



Although the Bayesian method that we propose seems 

 to be a versatile tool for stock mixture identification, 

 certain modifications of the model would also provide 

 fruitful extensions for a variety of biological settings. 

 Current use of the auxiliary information necessitates 

 that the individuals assigned to the same sampling 

 unit represent with certainty the same origin. However, 

 the existence of such conclusive information cannot be 

 assumed in applications in general. There is still a pos- 

 sibility of incorporating information about a tendency 

 to a geographical clustering among the catch individu- 

 als with respect to the stock origin, through a suitable 

 modification of the prior distribution of the partitions. 

 In general, use of biological information concerning the 

 behaviour of a species, in combination with geographical 

 sampling information, provides a rich area for further 

 model development. In particular, this combination of 

 information highlights the potential use of the Bayesian 

 statistical framework because the relevant biological in- 

 formation can often be efficiently incorporated through 

 the prior distributions for the model parameters. 



Acknowledgments 



The authors thank Marja-Liisa Koljonen for providing 

 data about the microsatellite allele frequencies in Baltic 

 salmon stocks. This work was supported by the Centre 

 of Population Genetic Analyses, University of Oulu, 

 Finland (Academy of Finland, grant no. 53297), and by 

 Research funds of University of Helsinki, Finland. 



Literature cited 



Balding, D. J., and R. A. Nichols. 



1997. Significant genetic correlations among Caucasians 

 at forensic DNA loci. Heredity 78:583-589. 

 Beaumont, M. A., and B. Rannala. 



2004. The Bayesian revolution in genetics. Nat. Rev. 

 Genet. 5:251-261. 

 Corander, J., P. Waldmann, P. Marttinen, and M. J. Sillanpaa. 

 2003. BAPS 2: enhanced possibilities for the analy- 

 sis of genetic population structure. Bioinformatics 

 20:2363-2369. 



