Hudson 1983, & gametes

[hyanwong]

Here's a useful quote from Hudson (1983a):

An ancestral gamete may contain directly ancestral genetic material at one or two loci. This directly ancestral genetic material at a locus will be referred to as an ancestral gene. If an ancestral gamete of generation t contains two ancestral genes, with probability r (the recombination rate), the gamete is the recombinant descendent of two ancestral gametes of generation t + 1. When any one of the ancestral gametes of generation t is the recombinant descendent of two ancestral gametes of generation t + 1, we say that the event RE has occurred in generation t + 1.

Note that (a) Hudson defines it all in terms of gametes, rather than individuals, which is helps get around the issues we were having with multiple recombinations in a single generation in a WF model (he explicitly uses a WF formulation, BTW) (b) he makes the distinction between events (which generate the process) and gametes/genomes (which are the things we record in the stucture). Here's another quote that makes the event/genome distinction, from the same paper:

When a CA event occurs, for example in generation t, two ancestral gametes are randomly chosen from the list and replaced by a single common ancestor gamete

[hyanwong]

Incidentally, Hudson doesn't even use the term coalescent in the 1983 paper (probably not in common use at that time). He uses MRCA instead.