Wright-Fisher revisited: the case of fertility correlation

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.