The coalescent process and background selection

Abstract

Abstract Gene trees or gene genealogies, which represent the history of a sample of genes from a population are fascinating objects whose statistical properties have recently been investigated under a few models (for example Kingman (1982), Tajima (1983), Slatkin (1989), Hudson (1990) and Hey (1991)). Different models can lead to gene trees with very different shapes and sizes. Examples of gene trees under three different models are shown in Fig. 4.1. Though gene trees are not directly observable entities, important observable quantities are indirectly related to them. It frequently aids our intuition, as well as mathematical analysis, to think about genetic variation as a by-product of gene genealogical (or coalescent) processes which generate gene trees. In fact, consideration of gene genealogies often leads to simple results concerning directly observable quantities. Incidentally, the gene genealogical approach also leads to efficient computer simulation algorithms for studying sampling distributions (Hudson 1990).