Markov Chain Calculation of Inter-Individual Variance of Lifetime Fertility

Hal Caswell, Woods Hole Oceanographic Institution

Lifetime fertility is the number of offspring produced over a (usually female) individual's lifetime. Interindividual variation in lifetime fertility is considered essential for selection of traits related to reproduction. The familiar net reproductive rate, R_0, is the expectation of lifetime fertility. However, being an expectation, R_0 provides no information on variance in lifetime fertility. Empirical studies of lifetime fertility reveal high variance and positive skewness, often interpreted as an opportunity for selection. But observed variance must be compared to that generated by demographic processes alone. Here, I show how to calculate the variance and skewness in lifetime fertility using Markov chains with rewards. The method is applicable to any life cycle structure, in constant or variable environments. Here I present new results on variance in lifetime fertility in humans calculated from age-specific and ageXparity-specific fertility. The approach complements the information available from R_0 and completes the measurement of lifetime fertility.