11


both high and low populations, reaching a maximum at some intermediate

biomass. These three factors can be combined to yield a general func-

tional relationship between the population in time period t and mature

progeny in time period t + 1. This relationship is described by the

h(P) function shown in Figure 1. The h(P) function corresponds to the

actual production of mature progeny. For example, if the population at

time t is equal to P1, the mature progeny entering in the fishery will

be equal to MP,. The r(P) function is the replacement line representing

the production of progeny necessary to maintain the population at its

present level.



 r(P)








 C MP
 I I




 450 I I I
 I I


 p p* p p Population (t)
 1 max N



 Figure 1. Relationship between population size and mature
 progeny


 A population of P1 need only produce MPr progeny to maintain

 itself. The difference between MP1 and MPr (A B in Figure 1) cor-

 responds to a yield of fish which can be harvested while maintaining