The simplest representation of the dynamics of a fish stock, represented in units of biomass, is that due to Russell:
where B is stock biomass, t denotes time (conventionally measured in years), G is somatic growth of individuals, R
is biomass increase due to recruitment (addition of young individuals to the stock), Y is yield (catch in weight) from fishing, and D is loss of biomass from deaths due to other causes. These are the four basic forces considered in models of fish population dynamics.
An equation parallel to eqn  can be written for stock size in numbers. Notably, it would omit the term expressing somatic growth.
Generally, external influences such as environmental forcing are either assumed unimportant or modeled as modifying one of the four basic forces. Because eqn  models a closed stock, migration in or out is excluded by definition. Stock mixture is usually modeled as exchange between two otherwise independent stocks.
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