2 problems

Multitype coalescent speed conjecture. Provided the conditions of the theorem establishing coming down from infinity hold, the ordinary differential equation

For each fixed sample size $k\ge1$, let $(\Pi_t^{k,N},t\ge0)$ be the ancestral partition process of a population of size $N$, restricted to the sample, and let $(\Pi_t^k,t\ge0)$ de…