## Stochastic Models

The models so far discussed are deterministic models. This means that given certain initial conditions, there will only be one outcome. Stochastic models include the variation (i.e., the probabilistic nature) inherent in biological systems by representing one or more variables in the model as random variables. Stochastic variables can be based on a probability of occurrence (i.e., probability of breeding at any given time step, or probability of having a certain number of offspring during a given reproductive bout). These probabilities are generally assigned based on previous knowledge of the system. Random variables can also be chosen from a frequency distribution of historical

Age-class models are the fundamental models of single-species population ecology and can be modeled several different ways. Life tables are age-specific summaries of mortality rates operating on a cohort of individuals. The mortality schedule is generally calculated based on the known number of survivors in each age class and, when combined with the fertility schedule, can be used to calculate the net reproductive rate per generation (R0), the mean length of a generation (G), and the intrinsic capacity for increase (r). Compartment models are mathematical models and are commonly used to represent many different ecological systems. In age-structured compartment models, each age class is represented by a compartment or state variable. These models typically consist of systems of equations with the equation for each compartment. Because realized fecundity and survival rates change as organisms age, matrix models separate populations into different age classes with each age class having the potential to possess different fecundity and survival rates. Matrix models are similar to compartment models, but matrix models are almost exclusively solved using linear algebra. The models so far discussed are deterministic models. This means that given certain initial conditions, there will only be one outcome. Stochastic models include the variation (i.e., the probabilistic nature) inherent in biological systems by representing one or more variables in the model as random variables. Therefore, when a stochastic model is run, the resulting outcome is never exactly the same.

See also: Demography; Growth Models; Matrix Models; Parameters.

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