Density independent population growth with random survival

A simplified model for the growth of a population is studied in which random effects arise because reproducing individuals have a certain probability of surviving until the next breeding season and hence contributing to the next generation. The resulting Markov chain is that of a branching process with a known generating function. For parameter values leading to non-extinction, an approximating diffusion process is obtained for the population size. Results are obtained for the number of offspring rh and the initial population size N0 required to guarantee a given probabilty of survival. For large probabilities of survival, increasing the initial population size from N0 = 1 to N0 = 2 gives a very large decrease in required fecundity but further increases in N0 lead to much smaller decreases in rh. For small probabilities (¡ 0.2) of survival the decreases in required fecundity when N0 changes from 1 to 2 are very small. The calculations have relevance to the survival of populations derived from colonizing individuals which could be any of a variety of organisms.