Statistics of natural populations. III. Sequential sampling plans for the estimation of gene frequencies

In previous work several models have been developed for genetic surveys of natural populations. Parents of unknown genotype are collected from a natural population, polymorphic at a single genetic locus. From each of these N cryptic parents a number of offspring are identified for their genotype. Our problem is to select an efficient offspring sampling plan for estimating the frequency of an allele in the cryptic adult population based on the N family profiles of juvenile genotypes. A criterion called the information per unit cost of observation is introduced to evaluate sequential sampling plans, in which the number of offspring per family examined is random. Some simple, practical schemes for stopping the sampling of offspring from a collected parent are introduced; one example is stopping when: (i) the offspring are definitive about the parental genotype(s) for the first time; (ii) a fixed number of one genotype only is seen; or (iii) a fixed maximum feasible number of offspring have been genotyped. This sampling scheme is recommended. For each sampling scheme, the best linear unbiased estimator and the sequential maximum likelihood estimator of the allele frequency are characterized. From the moments of these estimators, it is then possible to tabulate efficient sequential sampling plans, which are better (in the sense of information per unit cost), just as simple, and less costly than corresponding fixed sampling plans in use.