The parent-offspring probability when sampling age-structured populations.

We consider two individuals sampled from an age-structured population, and derive the probability that these have a parent-offspring relationship. Such probabilities play an important role in the recently proposed close-kin mark-recapture methods. The probability is decomposed into three terms. The first is the probability of the parent being alive, the second term involves the mechanism by which individuals are sampled, and the third term is a contribution from the observed age of the parent. A stable age distribution in the population is assumed, and we provide an expression for how this distribution is perturbed by the information that an individual has given birth at a particular time point in the past or in the future. Calculations are performed from the perspective of the offspring, but we also make comparison to the situation where the perspective is put on the parent. Although the resulting probabilities are the same, the actual calculations differ, due to the asymmetry of a parent-offspring relationship.