Fractional parentage analysis and a scale-free reproductive network of brown trout

In this study, we developed a method of fractional parentage analysis using microsatellite markers. We propose a method for calculating parentage probability, which considers missing data and genotyping errors due to null alleles and other causes, by regarding observed alleles as realizations of random variables which take values in the set of alleles at the locus and developing a method for simultaneously estimating the true and null allele frequencies of all alleles at each locus. We then applied our proposed method to a large sample collected from a wild population of brown trout (Salmo trutta). On analyzing the data using our method, we found that the reproductive success of brown trout obeyed a power law, indicating that when the parent-offspring relationship is regarded as a link, the reproductive system of brown trout is a scale-free network. Characteristics of the reproductive network of brown trout include individuals with large bodies as hubs in the network and different power exponents of degree distributions between males and females.