Balancing population size and genetic information in parentage analysis studies

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.