Apr 30
Math/Stats Colloquium: Pratima Hebbar, Grinnell College
Title: Long-time behavior of some birth-death models.
Abstract: Birth-death processes are a classical model in probability to study evolution of biological populations. Francis Galton, the half-cousin of Charles Darwin, and the infamous originator of the eugenics movement in the Victorian era, first proposed a birth-death process to investigate the extinction of aristocratic family names in England. We will introduce Galton-Watson processes, discuss some long established results regarding survival vs. extinction. We then study some generalizations of this population model. The first generalization allows individuals that have differing traits. The second generalization allows individuals to undergo spatial displacement in addition to reproduction. This model is crucial in understanding how species spread across heterogeneous, fast changing landscapes, and is applicable to wildlife conservation in the context of climate change, urban planning, and the study of infectious diseases.