Title: Do marine organisms hedge their bets? or A tragic tale of a diffusion approximation gone astray, with hope for redemption
Speaker: Robin Snyder (Associate Professor, Department of Biology, Case Western Reserve University)
Abstract: Many coastal marine organisms have a juvenile stage in which larvae drift on ocean currents until they have developed enough to settle and become adults. Ocean currents are turbulent, so larval dispersal is highly uncertain: many larvae never make it back to viable habitat. Many, many larvae are produced, so we still might hope to use the law of large numbers to treat population dynamics as deterministic. However, ocean eddies collect larvae into a relatively small number of bunches traveling as coherent groups, so that the number of independent tries is low: stochasticity matters. We used a diffusion approximation to examine the selection imposed on larval size by the stochasticity of larval dispersal. This approximation turns out to fail catastrophically under certain circumstances. I will present the original model, discuss why I think it fails, and what might be done instead. In short, come for the mathematical biology, stay for the schadenfreude, leave with the moral of the cautionary tale.