Question: (c) subpopulations descending from distinct individuals develop independently. If pn(t ) denotes the probability that the population consists of n individuals at time t ,

(c) subpopulations descending from distinct individuals develop independently.

If pn(t ) denotes the probability that the population consists of n individuals at time t , show that

φ(z, t) =

∞X n=0 zn pn(t )

satisfies the partial differential equation

∂φ

∂t = (λz − μ)(z − 1)

∂φ

∂z + θ(z − 1)φ.

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