Cambridge University Press, Advances in Applied Probability, 4(35), p. 1071-1089, 2003
Cambridge University Press, Advances in Applied Probability, 04(35), p. 1071-1089, 2003
DOI: 10.1017/s000186780001274x
Full text: Unavailable
We investigate the distribution of the coalescence time (most recent common ancestor) for two individuals picked at random (uniformly) in the current generation of a branching process founded t units of time ago, in both the discrete and continuous (time and state-space) settings. We obtain limiting distributions as t→∞ in the subcritical case. In the continuous setting, these distributions are specified for quadratic branching mechanisms (corresponding to Brownian motion and Brownian motion with positive drift), and we also extend our results for two individuals to the joint distribution of coalescence times for any finite number of individuals sampled in the current generation.