Theoretical Population Biology 62, 181–197 (2002) doi:10.1006/tpbi.2002.1609 Wright–Fisher Revisited : The Case of Fertility Correlation Alexandre Sibert Laboratoire d’Anthropologie Biologique, CNRS FRE 2292, Mus ! ee de l’Homme, 17 Place du Trocadero, Mus ! eum National d’Histoire Naturelle 75116 Paris, France E-mail : sibert@mnhn:fr Fre ´ de ´ ric Austerlitz Laboratoire de G ! en ! etique et d’Am ! elioration des Arbres Forestiers, INRA, Cestas, France and E ´ velyne Heyer Laboratoire d’Anthropologie Biologique, CNRS FRE 2292, Mus ! ee de l’Homme, 17, Place du Trocad ! ero, Mus ! eum National d’Histoire Naturelle 75116 Paris, France Received November 1, 2001 We study the non-genetic inheritance of fertility from parents to offspring. For this purpose, we propose an exchangeable extension of the Wright–Fisher model. This extension allows us to introduce non-genetic fertility correlation in the forward in time process and to study its effects on the genealogies of individuals (or genes) samples. Since it is independent of the gene considered, this effect is uniform on the genome, even in diploid populations. For values of fertility correlation observed in human populations, we show that coalescence times are strongly but inhomogenously reduced and that the shape of gene genealogies is markedly unbalanced. Despite the fact that our simulations concern stationary populations, the former non-genetic effect is very similar to what has been described for populations of variable size such as populations passing through demographic bottleneck. However, additional strong tree imbalance due to non-genetic causes is reported here for the first time. & 2002 Elsevier Science (USA) Key Words: non-genetic fertility correlation; Wright–Fisher model; coalescent; tree topology. 1. INTRODUCTION The concept of neutrality in population genetics is sometimes ambiguous. As far as the original theory of coalescence (Kingman, 1982b) or its extensions (e.g., Slatkin and Hudson, 1991; Griffiths and Tavar ! e, 1994) are concerned, at least two definitions coexist. The first is derived from the historical definition that, under neutrality, the effect of demography and mutation can be separated, that is the genealogical process and the mutational process are independent (Donnelly and Tavar ! e, 1995). The second states that the individuals presentatagiventimeareexchangeableasregardstheir propensitytoreproduce,andthatanyotherinformation 181 0040-5809/02 $35.00 # 2002 Elsevier Science (USA) All rights reserved.