12


the population at a level of P1. This is the basis from which the
notion of sustainable yield derives. Before proceeding to a discussion

of sustainable yield, several aspects of the model in Figure 1 merit

comment. Under a given set of environmental conditions, a given popula-

tion will approach some natural equilibrium size. This equilibrium

occurs at the population size corresponding to the intersection of the

r(P) and h(P) functions. This population size is given by PN in the

diagram. The h(P) function is assumed to possess a unique maximum pro-

duction of mature progeny, corresponding to the underlying population,

P max As will be shown presently, the population size corresponding to
micax
the maximum production of mature progeny is not the same as that cor-

responding to maximum sustainable yield.

 Sustainable yield represents, for any given population level, the

 surplus production of mature progeny over that needed to just maintain

 the population at a fixed level. In terms of Figure 1, sustainable

 yield for any given population is then simply the difference between the

 h(P) function and the r(P) function. Mathematically, this can be

 represented by

 SY(Pi) = h(Pi) r(Pi) 0 < P< P (1)


 where SY(Pi) refers to sustainable yield corresponding to population Pi"

 Equation (1) defines a single valued function relating sustainable yield

 to population size. Figure 2 illustrates one possible shape of the

 sustainable yield function.2 This function can be seen to rise from a


 20ther possible shapes of the sustainable yield curve are discussed
 below.