15


 The Generalized Stock Production Model (GSPM) as developed by Pella

and Tomlinson (1969) is composed of two functions. These are a popula-

tion growth function and a catch function. These functions are combined

in such a manner as to create a function relating sustainable yield to

fishing effort. The rate of change in any given fish population over

time can be expressed as a function of the population size by


 P(t) = HPm(t) KP(t) (2)

where H, K, m are constant parameters and P(t) is the time derivative of

population or biomass, P(t). Equation (2) is a general functional rep-

resentation of the sustainable yield function shown in Figure 2. For

populations to have an absolute maximum rate of growth or maximum sus-

tainable yield, the above equation must satisfy certain conditions on
 3
the parameters. These conditions are H, K < 0 if m > 1 and H, K > 0

if m < 1.

 Fishing effort is introduced into the GSPM by using the equation

 C(t) = qE(t)P(t) (3)

 where q is a constant, E(t) is fishing effort expended in time period t

 and C(t) is the time derivative of catch. This relationship is hypothe-

 sized under the assumption that effort units operate independently.

 Equation (3) can be seen to represent the production function for the

 fishery under non-equilibrium conditions. Equilibrium conditions are


 3The m parameter in equation (2) measures the skewness of the popu-
 lation growth function. A value of m = 2 leads to a symmetric function.
 As will be shown presently, a value of m = 1 is not permissable.