7 Specific Models 7.1 Coalescent Processes: Reversed Branching

Branching viewed backward is coalescence, the process of merging or clumping. It arises naturally in the structuring or formation of dispersed matter of various kinds and in various scales, from that of molecule aggregates in colloids (so-called micelles) to galaxies. It has been studied by physicists through computer simula-tion (e.g., Nilsson et al. 2000) and in a series of interesting mathematical articles by Aldous (1999). Evolution can be viewed as a grand multi-type branching process, with new species that arise through mutation (see Jagers 1991; Jagers et al. 1992; Taib 1992). The study of the origin of species is then time-reversed branching (i.e., coalescence). In genetics, the latter is also used to trace the roots of the genetic composition of populations and its development. It was within this area that the first pure coalescence model, the Kingman coalescent (1982a), was formulated as a reverse counterpart to the diffusion approximation of the renowned Wright–Fisher model (Fisher 1930; Wright 1931; see also Ewens 1979). The object of genetic models is thus population composition rather than size