2021/09/13 by Wirtz, Johannes, Guindon, Stéphane
#FOS: Biological sciences #FOS: Mathematics #Populations and Evolution (q-bio.PE) #Probability (math.PR)
paper · doi:10.48550/arxiv.2109.05833
We revisit the spatial λ-Fleming-Viot process introduced in [1]. Particularly, we are interested in the time T0 to the most recent common ancestor for two lineages. We distinguish between the case where the process acts on the entire two-dimensional plane, and on a finite rectangle. Utilizing a differential equation linking T0 with the physical distance between the lineages, we arrive at simple and reasonably accurate approximation schemes for both cases. Furthermore, our analysis enables us to address the question of whether the genealogical process of the model "comes down from infinity", which has been partly answered before in [2].