An accurate formula to calculate exclusion power of marker sets in parentage assignment

Parentage assignment using genomic markers, usually microsatellites, is now widely used for research on population ecology and evolution [1], as well as in selective breeding, particularly for aquatic species. Indeed, maintaining pedigrees for these species is a challenge because of the very small size of individuals at hatching, which prevents physical tagging [2]. When developing a marker set for parentage assignment, it is important to be able to predict the assignment efficiency from a priori data. Exclusion probabilities are easily calculated from allele frequencies and are commonly used to quantify the efficiency of individual markers for parentage assignment. The most frequently used exclusion probability is the probability to exclude a random parent pair that is unrelated to the individual tested (named Q3 in [3], here Q3i for each locus i). Since a single locus is generally not sufficient to exclude all potential parent pairs, several loci have to be combined to reach an appropriate combined exclusion probability Q3, which is calculated as the product of the individual non-exclusion probabilities of all L loci:Then, the combined exclusion probability is raised to the power of the total number of potential parental pairs to be excluded. With N possible parent pairs (including the correct one), this number is N-1, and the probability to have all parent pairs excluded except the correct one is the theoretical probability of having a unique assignment [4,5]:However, experience shows that the predicted assignment rates using this formula are often too optimistic, especially in factorial designs, i.e. when the mating structure is unknown and thus all possible mother-father combinations must be taken into consideration [4,6]. It is then necessary to make two assumptions when applying formulae (1) and (2), i.e. (i) exclusion of the N-1 incorrect parent pairs represents N-1 independent tests and (ii) all excluded parents are unrelated to the offspring, which justifi