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Abstract
A variety of results for genealogical and line-of-descent processes that arise in
connection with the theory of some classical selectively neutral population genetics
models are reviewed. While some new results and derivations are included, the principle
aim is to demonstrate the central importance and simplicity of genealogical Markov
chains in this theory. Considerable attention is given to "diffusion time scale" approximations
of such genealogical processes. A wide variety of results pertinent to (diffusion
approximations of) the classical multiallele single-locus Wright-Fisher model and
its relatives are simplified and unified by this approach. Other examples where such
genealogical processes play an explicit role, such as the infinite sites and infinite
alleles models, are discussed.