Abstract
The 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 $\mathbb G$, we study the tree-valued process $(T^N_u)_{u\in\mathbb{G}}$ of genealogies along the genome in the limit $N\to\infty$. Encoding trees as metric measure spaces, we show convergence to a tree-valued process with cadlag paths. In addition, we study mixing properties of the resulting process for loci which are far apart.
Citation
Andrej Depperschmidt. Étienne Pardoux. Peter Pfaffelhuber. "A mixing tree-valued process arising under neutral evolution with recombination." Electron. J. Probab. 20 1 - 22, 2015. https://doi.org/10.1214/EJP.v20-4286
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