A mixing tree-valued process arising under neutral evolution with recombination

International audienceThe genealogy at a single locus of a constant size N population in equilibrium is given by the well-known Kingman's coalescent. When considering multiple loci under recombination, the ancestral recombination graph encodes the genealogies at all loci in one graph. For a continuous genome G, we study the tree-valued process (T N u)u∈G of genealogies along the genome in the limit N → ∞. Encoding trees as metric measure spaces, we show convergence to a tree-valued process with càdlàg paths. In addition, we study mixing properties of the resulting process for loci which are far apart