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A simplified model for the growth of a population is studied in which randomeffects arise because reproducing individuals have a certain probability ofsurviving until the next breeding season and hence contributing to the nextgeneration. The resulting Markov chain is that of a branching process with aknown generating function. For parameter values leading to non-extinction, anapproximating diffusion process is obtained for the population size.  Results are obtained for the number of offspring $r_h$ and the initialpopulation size $N_0$ required to guarantee a given probabilty of survival. Forlarge probabilities of survival, increasing the initial population size from$N_0=1$ to $N_0=2$ gives a very large decrease in required fecundity butfurther increases in $N_0$ lead to much smaller decreases in $r_h$. For smallprobabilities (< 0.2) of survival the decreases in required fecundity when$N_0$ changes from 1 to 2 are very small. The calculations have relevance tothe survival of populations derived from colonizing individuals which could beany of a variety of organisms.

Density independent population growth with random survival