Series Title: Some mathematical models of evolution
Lecture 2: Expanding populations
Speaker:Alison Etheridge, OBE FRS, Prof. of Probability and Head of the Department of Statistics, University of Oxford
This lecture is part of the IICD & Probability and Society Initiative Joint Seminar Series, mini-series on Some mathematical models of evolution.
The way in which a population expands its range, or the way in which a favored genetic type spreads through a population, is often modeled by the classical Fisher-KPP equation or its stochastic counterpart, both of which exhibit traveling wave solutions. At the front of the expanding wave, where there is little competition for space, individuals can reproduce quickly and produce large families. The advantage that the uncrowded nature of their environment gives them is such that they can even afford to carry some disadvantageous mutations, with the result that individuals in the front are inherently less fit than those in the bulk, an effect called expansion load. We investigate expansion load (mostly numerically), particularly in the presence of genetic drift.