Statistics of Natural Populations. II. Estimating an Allele Probability in Families Descended from Cryptic Mothers.

In population studies, adults are frequently difficult or inconvenient to identify for genotype, but a family profile of genotypes can be obtained from an unidentified female crossed with a single unidentified male. The problem is to estimate an allele frequency in the cryptic parental gene pool from the observed family profiles. For example, a worker may wish to estimate inversion frequencies in Drosophila; inversion karyotypes are cryptic in adults but visible in salivary gland squashes from larvae. A simple mixture model, which assumes the Hardy-Weinberg law, Mendelian laws and a single randomly chosen mate per female, provides the vehicle for studying three competing estimators of an allele frequency. A simple, heuristically appealing estimator called the Dobzhansky estimator is compared with the maximum likelihood estimator and a close relative called the grouped profiles estimator. The Dobzhansky estimator is computationally simple, consistent and highly efficient and is recommended in practice over its competitors.