Use of the Normal Generated Distribution for Estimating Population Survival
Journal of Theoretical Biology
Counting the individuals in a population before and after an annual period of environmental stress allows the proportion s of the initial population surviving the period to be computed. A series of such observations over n annual periods gives a sequence s1, s2, …, sn. A statistical model is formulated from axioms describing the survival process, and it is concluded that these observed values may usefully be regarded as realizations of a random variable that arises from the normal generated distribution (n.g.d.). Equations for estimating the n.g.d. parameters ζ and τ2 from observed survival proportions by the method of moments and maximum likelihood are given. The distributions of parameter estimates ζ and τ2 are obtained and discussed in the context of testing hypotheses comparing survival among different populations. Finally, the dependence of the n.g.d. upon parameters ζ and τ2 is examined in terms of altering survival, either by population self-regulation mechanisms or man-induced controls. The intent is to provide insight into the relationship between the n.g.d. and its supporting axioms and, more generally, basic knowledge of population processes.
H. C. Romesburg. 1976. Use of the Normal Generated Distribution for Estimating Population Survival. Journal of Theoretical Biology, 61:447-457.