Unbiased estimation of relative reproductive success of different groups: evaluation and correction of bias caused by parentage assignment errors

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Abstract
Parentage assignment is widely applied to studies on mating systems, population dynamics and natural selection. However, little is known about the consequence of assignment errors, especially when some parents are not sampled. We investigated the effects of two types of error in parentage assignment, failing to assign a true parent (type A) and assigning an untrue parent (type B), on an estimate of the relative reproductive success (RRS) of two groups of parents. Employing a mathematical approach, we found that (i) when all parents are sampled, minimizing either type A or type B error insures the minimum bias on RRS, and (ii) when a large number of parents is not sampled, type B error substantially biases the estimated RRS towards one. Interestingly, however, (iii) when all parents were sampled and both error rates were moderately high, type A error biased the estimated RRS even more than type B error. We propose new methods to obtain an unbiased estimate of RRS and the number of offspring whose parents are not sampled (zW(z)), by correcting the error effects. Applying them to genotypic data from steelhead trout (Oncorhynchus mykiss), we illustrated how to estimate and control the assignment errors. In the data, we observed up to a 30% assignment error and a strong trade-off between the two types of error, depending on the stringency of the assignment decision criterion. We show that our methods can efficiently estimate an unbiased RRS and zW(z) regardless of assignment method, and how to maximize the statistical power to detect a difference in reproductive success between groups.