A solution to the distribution problems arising in the studies of a two- sex population process (Q1060995)

The authors analyse a model of population growth involving two sexes in which the birth rates of both males and females depend only on the female population size. Using the Markov property of the process, the authors set up a partial differential equation for the probability generating function of the sizes of the two sexes. The resulting partial differential equation is then solved and an explicit formula for the covariance of the sizes of the male and female population is provided. The authors apparently do not seem to be aware of the usefulness of the backward equation technique [see \textit{M. S. Bartlett}, An introduction to stochastic processes (1955; Zbl 0068.118), p. 42] which would have resulted in considerable simplicity and calculational ease, particularly when higher order moments and correlations are needed.