UW Aquatic & Fishery Sciences Quantitative Seminar

# Toshihide Kitakado

Assistant Professor

Department of Marine Biosciences, Faculty of Marine Science

Tokyo University of Marine Science and Technology

**Statistical genetic modeling and estimation with latent variables and their applications to fisheries populations**

## Abstract

To study the genetic structures of natural populations, samples are often taken from several localities. Sometimes, populations have continuous structures and consist of a large number of subpopulations. In such cases, assuming a metapopulation or an infinite-island model is a natural way to estimate the genetic differentiation between subpopulations. For this purpose, some statistical estimation methods for Fst such as the conventional maximum likelihood and pseudo-likelihood methods have been developed. However, these methods may cause underestimations of Fst when the number of sampling localities is small. It is possible to reduce the bias by modifying the estimation method. In this study, a statistical estimation using an integrated likelihood approach is proposed to obtain better estimation performance for Fst. In this method, the mean allele frequencies over populations are regarded as nuisance parameters and are eliminated by integration. To maximize the integrated likelihood function, two algorithms, a Monte Carlo EM algorithm and a Laplace approximation, are developed. The integrated likelihood method is applied to real data for Pacific herring, African elephants, and Channel Island foxes.

Besides the spatial differentiation in genetic composition over areas or localities, different genetic compositions can be observed in different temporal stages such as years, generation and so on. Such temporal changes in genetic composition can be observed in stock enhancement programs. For fisheries stocks that reduce their numbers, artificial release under the stock enhancement program is one of possible ways to recover the population levels. In these programs, it is important to assess mixing rates of released individuals in stocks. For this purpose, genetic stock identification has been applied. The allele frequencies in a composite population are expressed as a mixture of the allele frequencies in the natural and released populations. The estimation of mixing rates is possible, under successive sampling from the composite population, based on temporal changes in allele frequencies. The natural population is not generally observed. The allele frequencies in the natural population may be estimated from those of the composite population in the preceding year. However, it should be noted that these frequencies could vary between generations due to genetic drift. In this study, a new method for simultaneous estimation of mixing rates and genetic drift in a stock enhancement program is developed. The model of genetic variation acts a penalty against large genetic drift. The method is illustrated with application to real data on mud crab stocking.

## References

Kitakado, T., Kitada, S., Kishino, H. and Skaug, H.J. (2006) An integrated likelihood method for estimating genetic differentiation between populations, Genetics, 173, 2073-2082.

http://www.genetics.org/cgi/reprint/173/4/2073

Kitakado, T., Kitada, S., Obata, Y. and Kishino, H. (2006) Simultaneous estimation of mixing rates and genetic drift under successive sampling of genetic markers with application to the mud crab (Scylla paramamosain) in Japan, Genetics, 173, 2063-2072.

http://www.genetics.org/cgi/reprint/173/4/2063