Estimating Inbreeding Rates in Natural Populations: Addressing the Problem of Incomplete Pedigrees.

Mark P Miller, Susan M Haig, Jonathan D Ballou, E Ashley Steel

Understanding and estimating inbreeding is essential for managing threatened and endangered wildlife populations. However, determination of inbreeding rates in natural populations is confounded by incomplete parentage information. We present an approach for quantifying inbreeding rates for populations with incomplete parentage information. The approach exploits knowledge of pedigree configurations that lead to inbreeding coefficients of F = 0.25 and F = 0.125, allowing for quantification of Pr(I|k): the probability of observing pedigree I given the fraction of known parents (k). We developed analytical expressions under simplifying assumptions that define properties and behavior of inbreeding rate estimators for varying values of k. We demonstrated that inbreeding is overestimated if Pr(I|k) is not taken into consideration and that bias is primarily influenced by k. By contrast, our new estimator, incorporating Pr(I|k), is unbiased over a wide range of values of k that may be observed in empirical studies. Stochastic computer simulations that allowed complex inter- and intra-generational inbreeding produced similar results. We illustrate the effects that accounting for Pr(I|k) can have in empirical data by revisiting published analyses of Arabian oryx (Oryx leucoryx) and Red deer (Cervus elaphus). Our results demonstrate that incomplete pedigrees are not barriers for quantifying inbreeding in wild populations. Application of our approach will permit a better understanding of the role that inbreeding plays in the dynamics of populations of threatened and endangered species and may help refine our understanding of inbreeding avoidance mechanisms in the wild.