13


 MSY

 rJ

 1 SY






 SP P P2 Population
 0 0



 Figure 2. Quadratic sustainable yield function



level of zero at zero population to a unique maximum, and then back to

zero at the natural equilibrium level.

 The maximum point on the curve, maximum sustainable yield (MSY),
 I I


 1 2












occurs at population P This is precisely the same P as shown in

Figure 1. Thus, it can be seen that maximum sustainable yield occurs at

a population level which is smaller than that which produces the maximum

number of mature progeny, max in Figure 1.

 The form of the sustainable yield function in Figure 2, the

inverted U-shape, corresponds to any population that obeys a logistic

growth process. While other shapes are possible, there is no loss of

generality in considering the above curve. Before proceeding to a

mathematical discussion of biological stock production models, two

aspects of the above sustainable yield curve need mention. First,

inspection of Figure 2 reveals that the same sustainable yield can cor-

respond to two different population levels. For example, populations

PO and P2 both produce a sustainable yield of SYO. The importance of