Get lucky Variability in lifetime reproductive output

The number of offspring produced by an individual over their lifetime (lifetime reproductive output, or LRO) plays a key role in population biology. It is indicative of population growth or decline and is a proxy for individual fitness. Individuals differ widely in LRO; many individuals produce no offspring, while few individuals produce many. This variation is important because, if it has a genetic basis, it provides the material on which selection acts.
Across their life cycles, individuals experience a set of mortality and fertility rates. Even if these rates are identical for every individual in the same stage of the life cycle, there is a chance that one individual might survive, whereas another dies. One might successfully reproduce, whereas another fails. These chance processes generate variation in accumulated offspring over the life cycle despite individuals experiencing homogeneous rates. Variance in LRO is then entirely due to individual stochasticity. Understanding and analyzing this variance is the goal of my thesis.
This goal is accomplished by developing new theory to calculate the statistical properties of LRO using Markov chains with rewards (MCWR). MCWR models incorporate fertility and survival rates as probabilistic processes. These models are extended to include genuine differences between individuals at any stage in the life cycle; such differences represent heterogeneity. This thesis identifies the patterns in LRO driven by individual stochasticity in several comparative contexts, argues for a perspective of reproductive output beyond its mean, and shows how individual stochasticity and heterogeneity combine to determine the variance in LRO.