Distributions Of Lifetime Reproductive Success Research Articles

Skewed distributions of lifetime reproductive success: beyond mean and variance

Lifetime reproductive performance is quantified here by the LRS (lifetime reproductive success), the random number of offspring an individual produces over its lifetime. Many field studies find that distributions of LRS among individuals are non-normal, zero-inflated and highly skewed. These results beg the question, what is the distribution of LRS predicted by demographic models when the only source of randomness is demographic stochasticity? Here we present the first exact analysis of the probability distribution of LRS for species described by age+stage models; our analysis starts with estimated vital rates. We illustrate with three examples: the Hadza, human hunter-foragers (age-only), the evergreen tree Tsuga canadensis (stage-only) and Roe deer, Capreolus capreolus (age+stage). For each we obtain the exact distribution of LRS, but also calculate and discuss the first three moments. Our results point to important questions about how such LRS distributions affect natural selection, and life history evolution.

Dynamic heterogeneity in life histories

Longitudinal data on natural populations have been analysed using multistage models in which survival depends on reproductive stage, and individuals change stages according to a Markov chain. These models are special cases of stage-structured population models. We show that stage-structured models generate dynamic heterogeneity: life-history differences produced by stochastic stratum dynamics. We characterize dynamic heterogeneity in a range of species across taxa by properties of the Markov chain: the entropy, which describes the extent of heterogeneity, and the subdominant eigenvalue, which describes the persistence of reproductive success during the life of an individual. Trajectories of reproductive stage determine survivorship, and we analyse the variance in lifespan within and between trajectories of reproductive stage. We show how stage-structured models can be used to predict realized distributions of lifetime reproductive success. Dynamic heterogeneity contrasts with fixed heterogeneity: unobserved differences that generate variation between life histories. We show by an example that observed distributions of lifetime reproductive success are often consistent with the claim that little or no fixed heterogeneity influences this trait. We propose that dynamic heterogeneity provides a 'neutral' model for assessing the possible role of unobserved 'quality' differences between individuals. We discuss fitness for dynamic life histories, and the implications of dynamic heterogeneity for the evolution of life histories and senescence.