Approximate analytical formulae for stochasticity in a birth - death process 1 Abhyudai Singh and João

Birth-death processes have been widely used for different biological applications, the most common of which is stochastic modeling of population dynamics. A review of these applications can be found in Novozhilov et al. (2006). In this letter we illustrate a method to obtain approximate formulae for the steady-state mean and variance, of a birth death process involving a single species with arbitrary polynomial birth-death rates. These quantities are useful measures of variability in a population due to demographic stochasticity. Recent work (Keeling, 2000) has also used the coefficient of variation, defined to be the standard deviation divided by the mean, as an extinction measure for the population.