Concepts and Theory

The basic ideas underlying PVA are that there are some phenomena that are particularly relevant to the growth and decline of small populations and that the events generating such fluctuations are predictable only to a degree. These events include births and deaths of individuals in the population, the arrival of immigrants and the departure of emigrating individuals, changes in the environment that affect reproduction and survival, interactions with other organisms, the occurrence of rare environmental events like hurricanes or fires, and patterns of mating that lead to changes in average individual fitness including genetic inbreeding. PVA seeks to consider these factors in a probabilistic way by determining the likelihood of different possible population trajectories. Accordingly, PVA represents possible population trajectories with stochastic models in which one or more elements of the population growth process are determined by random variables drawn from probability distributions. Numerous approaches have been taken to model stochastic population growth, varying in their degree of sophistication, interpretability, and applicability. The four basic sources of uncertainty are reviewed below, followed by an outline of the different approaches to stochastic modeling and an elementary example.

1. Demographic stochasticity refers to uncertainty about population growth resulting from variation among individuals in the population. Individuals vary in their life spans, the timing of reproduction, and the number of offspring they produce. Sometimes demographic stochasticity is defined as the chance sequence of births and deaths and immigration/emigration events (also called 'vital rates') in the population. These are formally equivalent concepts. Some authors refer to effects of fluctuations in sex ratio as demographic stochasticity, particularly if the ratio of male to female offspring is represented by a random quantity.

2. Environmental stochasticity refers to random environmental fluctuations that affect average vital rates across all individuals in a population.

3. Allee effects are a class of nonlinear population dynamics characterized by decreased per capita population growth rate (equivalently, average individual fitness) at small population sizes. Allee effects typically result from mate limitation or cooperative behavior like foraging or colony defense.

4. Inbreeding depression refers to declines in average individual fitness in small population sizes due to mating by related individuals resulting in the expression of recessive traits and increased genetic load.

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