370 



ANNUAL REPORT SMITHSONIAN INSTITUTION, 19 3 5 



changes in the fishery and the stock were explained, and a forecast 

 could be made from year to year of what any given amount of 

 fishing would yield. 



So important is the principle involved that a careful review will 

 be well worth while. It will be of interest to all biologists inter- 

 ested in population studies. 



The explanation of how fishing intensity affects the stock is clear- 

 est when the changes in a single age group of young are followed 

 in a series of hypothetical cases. A thousand young fish, coming 

 on the banks as 5-year-olds, may be chosen and their fate under 

 natural conditions followed. Natural mortality is not, perhaps, very 

 high, but, for simplicity's sake, it may be assumed to be 20 percent. 



Column 1 in table 1 represents the survivors in successive years, 

 the calculation being carried for but 6 years in the interest of 

 brevity. The weights at different ages are assumed ones, for the 

 sake of clarifying the illustration. The true ones are given in 

 table 4. 



In column 2 are given the average weights at successive ages if 

 growth is rapid enough just to balance the death rate, and in column 

 3 the resultant total weight of the group available in successive 

 years if natural mortality alone were operating. From this it is 

 seen that the fishermen who might take this group in its tenth year 

 would get as great a poundage as though they had taken it in its 

 fifth. In columns 4 and 5 a growth rate less than sufficient to bal- 

 ance the deaths is supposed. In such a case the fishermen would 

 lose a large poundage by waiting. In columns 6 and 7, a third case, 

 in which growth greatly exceeds loss by deaths, is shown. Delay 

 in this case would greatly profit the fishermen. 



It is plain that the balance between growth and natural death 

 determines whether it is profitable to take the fish early or late 

 in life. 



Table 1. — Hypothetical illustration showing how balance between groivth of 

 fishes and natural death rate determines whether it is profitable to take them 

 early or late in life 



Age 



5 years. 



6 years. 



7 years - 



8 years. 



9 years - 



10 years 



Surviv- 

 ors (mor- 

 tality 20 

 percent) 



(1) 



1,000 

 800 

 640 

 512 

 410 

 328 



Growth to balance 

 20 percent mor- 

 tality 



Average 

 weight 



(2) 



Poundu 

 4.00 

 5.00 

 6.25 

 7.80 

 9.77 

 12.20 



Total 

 weight 



(3) 



Pounds 

 4,000 

 4,000 

 4,000 

 4,000 

 4,000 

 4,000 



Growth equaling 



half the loss 



by death 



Average 

 weight 



(1) 



Pounds 

 4.00 

 4.50 

 5. 00 

 6.70 

 6.40 

 7.20 



Total 

 weight 



(5) 



Pounds 

 4,000 

 3,600 

 3,240 

 2,916 

 2,624 

 2,302 



Growth equaling 



twice the loss 



by death 



Average 

 weight 



(6) 



Pounds 

 4.00 

 6.00 

 9.00 

 13.50 

 20.23 

 30.34 



Total 

 weight 



(7) 



Pounds 

 4,000 

 4,800 

 6,760 

 6,912 

 8,294 

 9,953 



