An accurate formula to calculate exclusion power of marker sets in parentage assignment
© Vandeputte; licensee BioMed Central Ltd. 2012
Received: 20 August 2012
Accepted: 19 November 2012
Published: 3 December 2012
In studies on parentage assignment with both parents unknown, the exclusion power of a marker set is generally computed under the hypothesis that the potential families tested are independent and unrelated samples. This tends to produce overly optimistic exclusion power estimates. In this work, we have developed a new formula that gives almost unbiased results at the population level.
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 justifies the use of probability Q 3 . However, in practice, these assumptions are never met. While the lack of independence between tests does not prevent formula (2) to yield good approximations, the second problem is generally overlooked.
with and p j the frequency of the j th allele of locus i in the population. Combined probabilities over all loci, Q 1 and Q 3 can be calculated with formula (1).
It is then clear that the probability of having a unique assignment decreases exponentially as the number of potential parents increases, as already underlined by Wang []. However, the rate of decrease depends on whether term Q 1 or term Q 3 in formula (7) is most influential. Dodds et al. have already shown that Q 3i is always greater than Q 1i for a given locus regardless of the allelic frequencies.
In the work reported here, we studied the relative importance of Q 1 and Q 3 using idealized loci, with three, five or eight equally frequent alleles. Individual Q 1i values were 0.370 for a locus with three alleles, 0.595 for a locus with five alleles and 0.743 for a locus with eight alleles, while the values for Q 3i were 0.519 for a locus with three alleles, 0.772 with five alleles and 0.898 with eight alleles. In most cases, these values reflect microsatellites with low, moderate or high variability.
One important thing to note is that formula (7) does not assume a mating structure. This is because no mother-father combination is excluded a priori on the basis of pre-existing knowledge about mating structure and, thus, exclusion is performed on the basis of a full factorial design (Figure1), which is the general case when no mating structure is assumed. It may be possible to consider fewer combinations when the mating structure is known and thus, modify the exponents of Q 1 and Q 3 in formula (7), but this approach is not recommended since it limits the generality of the estimated assignment power.
Comparison of predicted and simulated exclusion power P u of idealized and real marker sets
Exclusion power P u
Type of markers
Size of factorial design (N f x N m )
Number of loci
Idealized markers (equally frequent alleles)
MV works in fish quantitative genetics at the INRA-Ifremer research group on sustainable fish breeding. One of the main tools used for fish quantitative genetics studies is parentage assignment with microsatellite markers, which he contributes to optimize.
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