Pella Tomlinson model

In the Schaefer production model, the production curve is symmetrical about BMsY. In the Pella-Tomlinson (generalized) production model, the production curve may be symmetrical or skewed in either direction (Figure 5). Fletcher's form of that model replaces eqn [36] with dBt Bt

where m is MSY, n determines the shape of the production curve, and 7 is a function of n:

At n = 1, where eqn [41] has a removable singularity, the Pella-Tomlinson model is known as the Fox model. At n = 2, it is the Schaefer model.

In the Pella-Tomlinson model, yield (the analog to eqn [39]) must be solved by numerical approximation, as no analytical solution to the corresponding catch equation is known. The parametrization of eqn [40] does not include r, because when n < 1, r is infinite, implying an extremely resilient population. The consequences of that theoretical property in modeling actual populations is unknown.

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