Parentage in natural populations: novel methods to detect parent-offspring pairs in large data sets

Parentage analysis in natural populations presents a valuable yet unique challenge because of large numbers of pairwise comparisons, marker set limitations and few sampled true parent-offspring pairs. These limitations can result in the incorrect assignment of false parent-offspring pairs that share alleles across multi-locus genotypes by chance alone. I first define a probability, Pr(delta), to estimate the expected number of false parent-offspring pairs within a data set. This probability can be used to determine whether one can accept all putative parent-offspring pairs with strict exclusion. I next define the probability Pr(phi|lambda), which employs Bayes' theorem to determine the probability of a putative parent-offspring pair being false given the frequencies of shared alleles. This probability can be used to separate true parent-offspring pairs from false pairs that occur by chance when a data set lacks sufficient numbers of loci to accept all putative parent-offspring pairs. Finally, I propose a method to quantitatively determine how many loci to let mismatch for study-specific error rates and demonstrate that few data sets should need to allow more than two loci to mismatch. I test all theoretical predictions with simulated data and find that, first, Pr(delta) and Pr(phi|lambda) have very low bias, and second, that power increases with lower sample sizes, uniform allele frequency distributions, and higher numbers of loci and alleles per locus. Comparisons of Pr(phi|lambda) to strict exclusion and CERVUS demonstrate that this method may be most appropriate for large natural populations when supplemental data (e.g. genealogies, candidate parents) are absent.