Background reading part 1: Demographic Stochasticity

When a population declines, chance factors become more important. Two significant stochastic processes affect the probability that a population will persist. Environmental stochasticity is the unpredictable occurrence of unfavorable abiotic conditions. Physical factors such as fire, flood, and extreme weather may inflict significant mortality or depress reproductive success. As populations grow smaller, they are numerically more vulnerable to such events. The second random process, the one we are concerned with in this exercise, is known as demographic stochasticity. This phenomenon is the result of random changes in the demographic variables in small populations. As a population declines, chance events have a greater effect. Many demographic parameters such as ${\mathrm{l}}_x$ (the age-specific mortality rate), $b_x$ (the age-specific birth rate), and the multiplicative growth rate ($\lambda$), are variables that we present as mean values. Over time, these parameters vary simply by chance. We expect on average a proportion, ${\mathrm{l}}_x$, to survive in each age category. But this precise value will not necessarily occur each in time interval. When the population is very small, any chance deviation from expected value can have significant consequences.

For additional background information, please see Section 18.2 of Chapter 18, What Processes Lead to Extinction?