X-ray diffraction studies of lecithin bilayers.

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, …, s_n. 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.