Title:

Extreme first passage times, biological redundancy, and human reproduction

Abstract:

Why are women born with hundreds of thousands of primordial follicles when only a few hundred will ever grow and survive to ovulate a mature egg? Why do hundreds of millions of sperm cells search for the egg when only a single sperm cell is necessary for fertilization? The seeming vast oversupply and redundancy in these and other biological systems can be better understood using extreme first passage time (FPT) theory.

Generically, a FPT is the time it takes a random ``searcher'' to find a ``target.'' While FPT theory is often used to estimate timescales in biology, the overwhelming majority of studies focus on the time it takes a given single searcher to find a target. However, in many scenarios the more important timescale is the FPT of the fastest or slowest searcher(s) to find a target from a large group of searchers. These so-called extreme FPTs depend on rare events and are often orders of magnitude faster or slower than the FPT of a given single searcher. In this talk, I will describe recent mathematical results in extreme FPT theory and show how these results offer new explanations for biological redundancy, including the oversupply of female and male gametes.