Joint Estimation of Pedigrees and Effective Population Size Using Markov Chain Monte Carlo

Bursts of coalescence within population pedigrees whenever big families occur

We consider a simple diploid population-genetic model with potentially high variability of offspring numbers among individuals. Specifically, against a backdrop of Wright-Fisher reproduction and no selection, there is an additional probability that a big family occurs, meaning that a pair of individuals has a number of offspring on the order of the population size. We study how the pedigree of the population generated under this model affects the ancestral genetic process of a sample of size two at a single autosomal locus without recombination. Our population model is of the type for which multiple-merger coalescent processes have been described. We prove that the conditional distribution of the pairwise coalescence time given the random pedigree converges to a limit law as the population size tends to infinity. This limit law may or may not be the usual exponential distribution of the Kingman coalescent, depending on the frequency of big families. But because it includes the number and times of big families, it differs from the usual multiple-merger coalescent models. The usual multiple-merger coalescent models are seen as describing the ancestral process marginal to, or averaging over, the pedigree. In the limiting ancestral process conditional on the pedigree, the intervals between big families can be modeled using the Kingman coalescent but each big family causes a discrete jump in the probability of coalescence. Analogous results should hold for larger samples and other population models. We illustrate these results with simulations and additional analysis, highlighting their implications for inference and understanding of multilocus data.

Nearly unbiased estimator of contemporary effective mother size using within-cohort maternal sibling pairs incorporating parental and nonparental reproductive variations

In this study, we developed a nearly unbiased estimator of contemporary effective mother size in a population, which is based on a known maternal half-sibling relationship found within the same cohort. Our method allows for variance of the average number of offspring per mother (i.e., parental variation, such as age-specific fecundity) and variance of the number of offspring among mothers with identical reproductive potential (i.e., nonparental variation, such as family-correlated survivorship). We also developed estimators of the variance and coefficient of variation of contemporary effective mother size and qualitatively evaluated the performance of the estimators by running an individual-based model. Our results provide guidance for (i) a sample size to ensure the required accuracy and precision when the order of effective mother size is available and (ii) a degree of uncertainty regarding the estimated effective mother size when information about the size is unavailable. To the best of our knowledge, this is the first report to demonstrate the derivation of a nearly unbiased estimator of effective population size; however, its current application is limited to effective mother size and situations, in which the sample size is not particularly small and maternal half-sibling relationships can be detected without error. The results of this study demonstrate the usefulness of a sibship assignment method for estimating effective population size; in addition, they have the potential to greatly widen the scope of genetic monitoring, especially in the situation of small sample size.