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defined to be those levels of effort and population that yield a catch

equal to sustainable yield.

 The introduction of fishing into the GSPM necessitates that equa-

tion (2) be modified to


 P(t) = HPm(t) KP(t) qE(t)P(t) (4)

where all terms have been previously defined. Equation (4) implies the
rate of increase of any given population over time is decreased pre-

cisely by the rate at which fish are caught through fishing activity.

The imposition of the equilibrium conditions described above can be

accomplished by constraining P(t) = 0 in equation (4). This constraint,

in effect, requires that catch always equal sustainable yield. By solv-

ing the equation


 HPm(t) KP(t) E(t)P(t) = 0 (5)

 for P(t) and substituting the result into equation (3), the equilibrium
 effort yield function

 1

 C = qE(qE + m (6)


 is obtained. This equation represents the Generalized Stock Production
 Model relating equilibrium catch to fishing effort. Note that a value

 of m = 1 would make equation (6) undefined.
 The Schaefer model, which is a special case of the above model

 named after its originator, M. B. Schaefer, was developed in 1954
 (Schaefer, 1954). This model is based upon a logistic population growth