Fractional paternity assignment: theoretical development and comparison to other methods.

There has recently been a burgeoning interest in the analysis of paternity patterns for natural populations because of its relevance to population genetic phenomena such as the distance between successful mates, relative male reproductive success and gene flow. In this paper we develop a method of analyzing populational patterns of paternity, the fractional paternity method, and compare its performance to two other commonly used methods of paternity analysis (simple exclusion and the most-likely methods). We show that the fractional method is the most accurate method for determining populational patterns of paternity because it assigns paternity to all progeny examined, and because it avoids biases inherent in the other paternity analysis methods when model assumptions are met. In particular, it avoids a systematic bias of the most-likely paternity assignment method, which has a tendency to over-assign paternity of progeny to certain male parents with a greater than average number of homozygous marker loci. We also demonstrate the effect of linkage of some of the marker loci on paternity assignment, showing how the knowledge of the linkage phase of male and female parents in the population can significantly improve the accuracy of the estimates of populational patterns of paternity. Knowledge of the linkage phase of individuals in a population is usually unknown and difficult to assess without progeny testing, which involves considerable labor. However, we show how the linkage phase of hermaphroditic individuals in a population can be obtained in conjunction with the paternity analysis if progeny can be obtained from each hermaphroditic individual in the population, thereby avoiding the problem of traditional progeny testing. Applications of the fractional paternity approach developed herein should contribute significantly to our understanding of the mating patterns in, and hence the evolution of, natural populations.