Center for Applied Mathematics Colloquium
In humans “the 1%” refers to inequality in wealth. Many animal and plant populations have similarly extreme inequality in lifetime reproductive success: a small fraction of the current generation produces most of the offspring that make up the next generation. Who gets to be one of these lucky few? Integrodifference equation models for structured populations, parameterized from empirical data, can be used to address questions like this. Assuming first that individuals are not intrinsically different, I consider two ways of identifying what distinguishes the lucky few: comparing life trajectories of lucky and unlucky, and comparing the impact of good outcomes at different ages, stages, or sizes. When there are persistent differences among individuals (e.g., different genotypes) we can ask how much of the variability in outcomes is due to sheer luck, rather than differences in individual quality. The role of luck often turns out to be surprisingly large. Time permitting, I will mention some open mathematical questions about these models.