Rate of coalescence of lineage pairs in the Spatial Λ-Fleming–Viot process

We revisit the Spatial $\Lambda$-Fleming–Viot process introduced in Barton and Kelleher (2010). Particularly, we are interested in the time $T_0$ to the most recent common ancestor for two lineages. We distinguish between the cases where the process acts on the two-dimensional plane and on a finite rectangle. Utilizing a differential equation linking $T_0$ with the physical distance between the lineages, we arrive at computationally efficient 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 Véber and Wakolbinger (2015).