A Bayesian framework for parentage analysis: The value of genetic and other biological data

We develop fractional allocation models and confidence statistics for paren tage analysis in mating systems. The models can be used, for example, to es timate the paternities of candidate males when the genetic mother is known or to calculate the parentage of candidate parent pairs when neither is kno wn. The models do not require two implicit assumptions made by previous mod els, assumptions that are potentially erroneous. First, we provide formulas to calculate the expected parentage, as opposed to using a maximum likelih ood algorithm to calculate the most likely parentage. The expected parentag e is superior as it does not assume a symmetrical probability distribution of parentage and therefore, unlike the most likely parentage, will be unbia sed. Second, we provide a mathematical framework for incorporating addition al biological data to estimate the prior probability distribution of parent age. This additional biological data might include behavioral observations during mating or morphological measurements known to correlate with parenta ge. The value of multiple sources of information is increased accuracy of t he estimates. We show that when the prior probability of parentage is known , and the expected parentage is calculated, fractional allocation provides unbiased estimates of the variance in reproductive success, thereby correct ing a problem that has previously plagued parentage analyses. We also devel op formulas to calculate the confidence interval in the parentage estimates , thus enabling the assessment of precision. These confidence statistics ha ve not previously been available for fractional models. We demonstrate our models with several biological examples based on data from two fish species that we study, coho salmon (Oncorhychus kisutch) and bluegill sunfish (Lep omis macrochirus), In coho, multiple males compete to fertilize a single fe male's eggs. We show how behavioral observations taken during spawning can be combined with genetic data to provide an accurate calculation of each ma le's paternity. In bluegill, multiple males and multiple females may mate i n a single nest. For a nest, we calculate the fertilization success and the 95% confidence interval of each candidate parent pair. (C) 2001 Academic P ress.