Birth-Death & Coalescent Theory

Kingman Coalescent (1982):
P(k→k-1 in dt) = C(k,2)/N_e dt
E[T_k] = N_e / C(k,2)
E[TMRCA] = 2N_e(1−1/n)

Birth-Death (Yule process):
dP_n/dt = λ(n−1)P_{n-1} − λnP_n

Diversification rate r = λ − μ
Expected clades: ~e^{rt}

Net: N(t) = N_0·e^{(λ−μ)t}