Drivers of diversity in individual life courses: Sensitivity of the population entropy of a Markov chain

Individuals differ in their life courses, but how this diversity is generated, how it has evolved and how maintained is less understood. However, this understanding is crucial to comprehend evolutionary and ecological population dynamics. In structured populations, individual life courses represent sequences of stages that end in death. These sequences can be described by a Markov chain and individuals diversify over the course of their lives by transitioning through diverse discrete stages. The rate at which stage sequences diversify with age can be quantified by the population entropy of a Markov chain. Here, we derive sensitivities of the population entropy of a Markov chain to identify which stage transitions generate--or contribute--most to diversification in stage sequences, i.e. life courses. We then use these sensitivities to reveal potential selective forces on the dynamics of life courses. To do so we correlated the sensitivity of each matrix element (stage transition) with respect to the population entropy, to its sensitivity with respect to fitness {lambda}, the population growth rate. Positive correlation between the two sensitivities would suggest that the stage transitions that selection has acted most strongly on (sensitivities with respect to {lambda}) are also those that contributed most to the diversification of life courses. Using an illustrative example on a seabird population, the Thick-billed Murres on Coats Island, that is structured by reproductive stages, we show that the most influential stage transitions for diversification of life courses are not correlated with the most influential transitions for population growth. Our finding suggests that observed diversification in life courses is neutral rather than adaptive. We are at an early stage of understanding how individual level dynamics shape ecological and evolutionary dynamics, and many discoveries await.