Abstract

Mathematical population genetics is only one of Kingman's many research interests. Nevertheless, his contribution to this field has been crucial, and moved it in several important new directions. Here we outline some aspects of his work which have had a major influence on population genetics theory.

AMS subject classification (MSC2010) 92D25

Introduction

In the early years of the previous century, the main aim of population genetics theory was to validate the Darwinian theory of evolution, using the Mendelian hereditary mechanism as the vehicle for determining how the characteristics of any daughter generation depended on the corresponding characteristics of the parental generation. By the 1960s, however, that aim had been achieved, and the theory largely moved in a new, retrospective and statistical, direction.

This happened because, at that time, data on the genetic constitution of a population, or at least on a sample of individuals from that population, started to become available. What could be inferred about the past history of the population leading to these data? Retrospective questions of this type include: “How do we estimate the time at which mitochondrial Eve, the woman whose mitochondrial DNA is the most recent ancestor of the mitochondrial DNA currently carried in the human population, lived? How can contemporary genetic data be used to track the ‘Out of Africa’ migration? How do we detect signatures of past selective events in our contemporary genomes?” Kingman's famous coalescent theory became a central vehicle for addressing questions such as these.