The Estimation of Parental Genotypes by the Analysis of a Fixed Number of Their Offspring

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When genotypes are cryptic in adult organisms but visible in young life-stages, it is possible to estimate the genotypes in parents after the examination of a fixed number of their offspring. Thus, in Drosophila, males collected in the wild can be crossed to females of a homozygous laboratory stock, and the identification for genotype of seven larvae is largely enough to guarantee a correct diagnosis of the two alleles of the father (P = 0.984). On the other hand, when collected females were inseminated in nature, it should be possible to determine the constitution both the female and her mate, after the analysis of a sufficient number of their offspring. Nevertheless, exact formulas for the probabilities of correct diagnoses of parental genotypes in this case have not yet been published. In this paper we derive such formulas, and illustrate their application. The conclusion we draw from our calculations is that, unless 13 larvae are examined among the offspring, the probability of misdiagnosis is over the 0.05 level. Of course, the errors produced become greater as smaller offspring numbers are analyzed. But in the case of one locus with two alleles, we have derived formulas to correct the observed number of matings and estimate its actual number in the sample, for any offspring sample size. After these corrections, we have been able to calculate estimates of relative mating frequencies in the sampled population, together with their associated errors, which can be subsequently used in studies of adult fitness components, mainly in those dealing with sexual selection.

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