Genetic distances Genetic distances, F-statistics and kinships

Utilisation and conservation of farm animal genetic resources 111

Chapter 5. Measuring genetic diversity in farm animals

measure of population subdivision and diferentiation. he estimation of F ST is deduced from the relationship: T S ST ST Het et H = F = Het 1 6 he expected heterozygosity in the total population Het T is calculated from the allele frequencies in the total population, p Ti , i.e. Het T = 1-Σ p Ti 2 Nagylaki, 1998. here are a number of variations on the way F ST is calculated. Weir and Cockerham 1984 and Robertson and Hill 1984 give diferent estimators of F ST from allele frequencies. he estimator of Robertson and Hill gives extra weight to rare alleles for conservation purposes. However, the variance of the estimator is greater and both estimators agree only when alleles have equal frequencies. Nagylaki 1998 argues that F ST will only be an appropriate measure of divergence of populations if the genetic diversity is low. For example: when we have N sub-populations of equal size, which do not share alleles at all, then 6 S S ST Het N Het N = F 1 1 1 Except when the populations are fully inbred Het S = 0, F ST will always be smaller than 1, even though the sub-populations are fully diferentiated. Moreover, when we have K sub-populations ixed for a locus with L K alleles, the average heterozygosity within populations will be 0 and hence F ST = 1, indicating complete diferentiation between sub-populations. However, L K means that complete diferentiation is only possible for L sub-populations. When K L complete diferentiation cannot be obtained and the F ST value of 1 is misleading.

2.3. Genetic similarities and kinships

While genetic distances and F-statistics are interested in diferences between populations or individuals, the measure on similarity is interested in resemblances between them. he genetic similarity measures the degree of relatedness, which is a complement to distance, hence 1 minus the similarity between two individuals or populations is roughly equal to the distance between them. Relatedness is usually expressed as coeicient of kinship. Relating coeicients of kinship to genetic diversity is straightforward. Over t generations, the loss in heterozygosity is directly related to the inbreeding coeicient: 112 Utilisation and conservation of farm animal genetic resources Herwin Eding and Jörn Bennewitz Het t Het = 1 – F where Het t is heterozygosity in generation t and Het in the founder generation, and F is the inbreeding coeicient relative to the founder generation. Kinship, also called coancestry f , is used to calculate the inbreeding coeicient and F X = f PQ , where f PQ is the coancestry of the parents P and Q of individual X. Twice the kinship, the coeicient of additive relationship is used to calculate the additive genetic variance σ² A. Because σ² A is proportional to heterozygosity, over t generations we have Falconer and Mackay, 1996; Gilligan et al., 2005: σ² A,t σ² A,0 = 1 – F here are many diferent estimators for relatedness. here are coancestry based estimators Toro et al., 2002; Eding and Meuwissen, 2001; Oliehoek et al., 2006 and two- and four-gene identity coeicient estimators Lynch and Ritland, 1999; Wang, 2002. Coancestry based estimators are more general in nature and perform well in a wide variety of population classes, while two- and four-gene identity coeicients show a substantial loss of eiciency in non-random mating populations Oliehoek et al., 2006. For these reasons we focus on coancestry based estimators of kinship. 2.3.1. Genetic similarities he most basic measure of relatedness is the genetic similarity. Genetic similarities are also known as allele sharing cf. Lynch, 1988. Basically any pair of individuals within or between populations is scored for common alleles for a number of loci. he total score is then averaged over loci to obtain the mean similarity between individuals. Further averaging over pairs of individuals gives the mean similarity between or within populations. here are two main methods to score genetic similarities with co-dominant polymorphic markers: the genic similarity Lynch, 1988 and the Malécot similarity Eding and Meuwissen, 2001. he diference between these two can be found in scoring of similar genotypes Table 5.1. While the genic similarity is the number of alleles shared by two individuals out of the total number of alleles e.g. 4 in diploid organisms, the Malécot similarity is the probability that an allele randomly drawn from one individual is the same as an allele randomly drawn from the other individual Malécot, 1948. he latter is derived from the deinition of the coeicient of kinship. Hence, if we assume that alleles can only be identical by descent that is: all similar alleles are copies from one and the same ancestral allele, the mean Malécot similarity calculated over multiple loci is expected to be equal to the coeicient of kinship.