Optimal Yield 345 



the simplest situation with no modifying conditions the population 

 should be maintained at the inflection point of its growth curve since 

 at that point the largest increment is being added per unit of time 

 and the taking of this increment would represent the largest harvest 

 possible without inroad upon the breeding stock. We shall return 

 later to a discussion of special circumstances applying to particular 

 species that modify this basic relation and cause a different density 

 level of the population to be more favorable for the practical exploita- 

 tion of these species. 



To illustrate the basic principle let us imagine a flock of geese from 

 which we wish to obtain as many birds as possible for food. Suppose 

 that the flock originated from the establishment of one pair in a lim- 

 ited area and that the growth of the population followed the logistic 

 curve (Fig. 9.11) with values similar to those indicated in the lower 

 part of Table 18. The largest single yield would obviously be ob- 

 tained by allowing the flock to grow for 5 or 6 years and then shoot- 

 ing all or most of the birds. For a sustained harvest, however, only 

 the annual increment to the population should be taken; in this ex- 

 ample, 20 birds could be taken every year if the flock were allowed 

 to grow to 36 before harvesting. If a hunter considered exploiting 

 this flock without knowing its existing size and found that only 10 

 birds were added to the population each year, he would have to de- 

 termine whether the low growth rate was due to the population being 

 smaller or larger than the optimum. Low yield in any such popula- 

 tion may thus be caused by overexploitation— resulting in too small a 

 breeding stock, or in underexploitation— resulting in harmful crowding 

 of the breeding stock. The best conservation procedure often calls 

 for the reduction in size of a natural population. Recognizing this 

 fact, rangers now regularly cut back the populations of deer in national 

 parks whenever numbers become too large because of the absence of 

 wolves, panthers, or other natural enemies that otherwise would keep 

 the deer in check. Consequently, in exploiting a population, it is de- 

 sirable to ascertain whether density is above or below the level at 

 which increase is most rapid and, if possible, to adjust the size of the 

 population accordingly. 



As already suggested, several important modifying considerations 

 must be added to the underlying idea of the theory of optimal yield. 

 Up to this point we have discussed populations in terms of numbers 

 of individuals. Fishermen do not measure their catch by counting 

 the fish, but by weighing them; foresters evaluate their timber by its 

 volume, not by the number of trees. Thus, the growth in size of the 

 individuals must be taken into account as well as the increase in num- 



