Given a birth-death process which ends up with a given population size m after a certain time t, I am estimating the size of the population n before this by exponentiating the Q matrix of the corresponding CTMC to find the probabilities of reaching m after time t from various starting points.
After estimating this earlier population size n, I want to estimate how many of those n members of that population have survived to be part of the current population of size m.
How could I go about making this estimation?