Evaluation of paternity-testing data from the joint distribution of paternity index and rate of exclusion

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.

Paternity testing 3: exclusion probabilities

Blood typing with several blood systems is used in many countries to determine paternity or nonpaternity with respect to an alleged father. Various probabilities are usually presented, in particular: the conditional probability of excluding a random man as father given a particular mother-child phenotype combination, and the expected (unconditional) exclusion probability for all mother-child combinations can be calculated for a given blood system. Because these probabilities are of general interest in paternity studies, explicit formulae for the unconditional probabilities have been derived for some of the systems. Algorithms suitable for a microcomputer are given here for finding the exclusion probabilities for any system. These algorithms avoid the need for developing new formulae whenever a new system is introduced or a current system is extended through the addition of further alleles.

Paternity testing with genetic markers: are Y-linked genes more efficient than autosomal ones?

The average probability of exclusion for a Y-linked locus is computed and compared with that for an autosomal locus. It is shown that even if a Y-linked locus is only marginally polymorphic, it considerably enhances the chance of paternity exclusion in paternity dispute cases involving sons. For the positive identification of paternity, a Y-linked marker is not necessarily more ideal than an analogous autosomal marker since the discrimination of true fathers from random men not excluded from paternity (RMNEP) is still difficult on the basis of a paternity index. It is concluded that Y-linked markers are more efficient for paternity exclusions of male children, while for the positive identification of paternity their advantages over the autosomal markers are questionable.

Paternity testing. 2: Likelihood ratio tests

It is known that the so-called paternity index is also a likelihood ratio statistic for testing that an alleged father is the true father. Unfortunately the likelihood ratio test can sometimes lead to unsatisfactory results because of its dependence on the phenotype combinations of the mother and child. A new, conditional likelihood ratio test, which we call the ancillary test, is proposed in which statistical testing is carried out conditionally on the phenotypes of the mother and alleged father. An exact procedure is available which can be executed with reasonable facility on a microcomputer.