A good description of stochastic population growth uses a discrete state space with population numbers taking on integer values. Demographic transitions like birth, death and growth are subject to two sources of variation. One is demographic stochasticity — in simple terms sampling randomness — and the other is environmental stochasticity or variation between individuals. Demographic stochasticity is caused by finite population size. The basic theory of population growth in fluctuating environments was first presented by Cohen (1977) and Tuljapurkar and Orzack (1980). Based on this theory Lande and Orzack (1988) derive a diffusion approximation for the logarithm of total population size in a population subject to density — independent fluctuations in vital rates. We describe, in the following discussion their development.
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