17


function. Using this function, the natural rate of increase as a func-

tion of population size can be expressed by

 P(t) = K1 P(t) [M P(t)] (7)


where K and M are constants and all other terms are defined as above.

It can be easily shown that this equation corresponds to equation (2)

of the GSPM with m = 2, H = -K1, and K = -K1M. Thus, it becomes appar-

ent that the basis of the Schaefer model is merely a specific form of

the GSPM, with parameter m = 2. The Schaefer model also provides an

equation expressing equilibrium catch as a function of fishing effort.

Utilizing equation (3) once again as the non-equilibrium catch function,

the function


 C = qE (M E) (8)
 K1


can be derived. As before, the appropriate redefinition of constants

(H = -K1, K = -KIM) illuminates the fact that equation (8) is merely a

specific form of equation (6) with m = 2.

 The above has shown the widely used Schaefer model to be a special

 case of the Generalized Stock Production Model. In part, one of the

 primary goals of developing the GSPM was aimed at relaxing the con-

 straint of the symmetric yield function generated by the Schaefer model
 (Pella and Tomlinson, 1969). Figure 3 presents several possible equi-

 librium yield functions that are possible utilizing the GSPM. It can be

 seen that the shape of the equilibrium yield function takes a wide

 variety of shapes as m varies.