Balancing population size and genetic information in parentage analysis studies.

SUMMARY. In parentage analysis studies, the parameters of interest typically are not the parent assignments themselves, but population parameters such as variance in fertility, self-pollination rate, or average dispersal distances. The precision of parameter estimates is affected by two factors: the number of offspring under consideration, and the precision with which the offspring can be assigned to parents. When assignment of parents is based on genetic information, the confidence in assignments is affected by the number and polymorphism of the loci considered, and by the number of potential parents in the population. Studying larger populations may yield higher numbers of offspring, but since larger populations contain more potential parents, more (or more highly polymorphic) loci are necessary to attain a given level of confidence in the parent assignments. This article addresses how to relate the size of the population and the number of loci when designing a study. It is shown that the number of loci needed to assign all offspring unambiguously is proportional to the logarithm of the population size. In some cases, the constant of proportionality can be determined, eliminating the need for simulation-based projections. Population-wide measures of uncertainty in parent assignments are also introduced, and it is shown that holding uncertainty "steady" as the population size increases also requires increasing the number of loci proportional to the logarithm of the population size. Data from a study of self-pollination are used to illustrate the techniques suggested. Inference for many dispersal and fertility parameters would be straightforward if the true parents of each offspring in the population could be observed. For instance, suppose we were trying to estimate the proportion of seeds produced by selfpollination. If both parents of each seed were known, we would simply count the number of seeds where the mother and father were the same individual; estimating the proportion of selfpollination would be a simple binomial inference problem. However, in natural populations the identity of one or both parents (the true parent assignment) is typically unobservable. Instead, genetic markers can be used to obtain information about parent identities. (Genetic markers, also called loci, are specific portions of the genome that have variable content from individual to individual. The different possibilities for the content at a locus are called alleles.) When this strategy is used, a sample of offspring are "typed" (a process of determining what alleles are present) at several markers. The potential parents in the population (for example, all of the adults in the population, or all of the adults observed to flower in a particular year) are also typed. Since each offspring receives one allele from each of its parents at each locus, if enough markers are typed (without error), the pattern of allele sharing would allow one to determine which parents produced which offspring. The parameter estimation problem of interest, e.g., estimation of the self-pollination rate, would then become simple.