POPULATION FACTORS AND SELECTED POPULATION PROBLEMS 



377 



producing 384 young. Under such conditions a 

 population is thriving."*' 



ORGANIZED PREDATION BY MAN 



The Problem of the "Optimal Yield" 



The problem of optimal yieldt can be 

 stated in this way: To what extent can a 

 particular population under specified con- 

 ditions be exploited (preyed upon), main- 

 tain itself within a certain size range, and 

 at the same time yield a reasonably high 

 catch to the exploiting agency? This, in 

 population terms, is one of the central 

 problems of conservation, for when an an- 

 swer is found, it is possible to predict the 

 most favorable ratio between the reconsti- 

 tution of a group in relation to exploita- 

 tion exerted against it. 



Russell (1942) is concerned with many 

 aspects of tlais matter from the point of 

 view of the fisheries biologist. "Put in a 

 nutshell [the problem] is this, that up to 

 a point you can increase yield by increas- 

 ing fishing, but after this maximum is 

 reached the more you fish the less weight 

 of fish you catch" (p. 75). The evidence 

 supporting this statement has already been 

 presented for haddock populations in the 

 chapter on grow^ form (p. 322; Fig. 

 116). 



The question of yield versus exploitation 

 was formulated in theoretical terms by 

 Russell (1931), who concerns himself with 

 the factors that determine the level of a 

 stock subjected to commercial fishing. In 

 a self-contained stock of fish of one partic- 

 ular species which is systematically fished 

 the fishing gear catches only those fishes 

 that have attained a certain length. The 

 fish population (S) thus can be divided 

 into those forms (Si) that are catchable 



** A comprehensive review, with an extensive 

 bibhography, of the predation problem in 

 populations of Vertebrates has been published 

 by Errington (1946). 



t Some of the more important references 

 about the optimal yield problem so far as com- 

 mercial, and largely marine, fishing is con- 

 cerned are those of Baranov (1916, 1925); 

 Russell (1931, 1942); Hjort, Jahn, and Ottestad 

 (1933); Thompson and Bell (1934) and 

 Thompson (1937); Graham (1935, 1948); 

 Ricker (1940a); Sette (1943), and Kesteven 

 ( 1947 ) . In our brief discussion we follow 

 largely the treatments of these investigators, 

 using Russell's summary ( 1942 ) as a general 

 guide. 



and those that are not. In the course of a 

 year's fishing the catchable stock changes 

 through death, through catching, of course, 

 and because some of the younger fishes 

 grow enough to enter the Si category. The 

 various factors pertaining to the tveight of 

 the stock at the end of this hypothetical 

 year (S:;) are as follows: 



S = the total stock (weight) 



Si = the starting catchable stock 



S2 = the catchable stock at the end of the 

 year 



A = the recruitment, i.e., the influx of 

 smaller fishes that attain catchable size 

 during the year 



G = the total growth increment of the sur- 

 viving individuals 



M = the natural mortaJity 



C = the year's total catch 



Those factors that increase the weight of 

 the stock are A + G; those that decrease 

 the stock are C + M. The following sim- 

 ple equation then can be written for the 

 weight of the stock at the end of the year: 



S2 = Si-f (A-fG) - (C + M) 



S2 therefore will be >, =, or < Si ac- 

 cording as (A + G) is >, =, or < (C H 

 M). Differently put, this means that (1) 

 if fishing takes more out of the catchable 

 population in a year, i.e., (C 4- M), than 

 is replaced by natural processes, i.e., (A + 

 G), the total weight of the catchable or 

 available population is reduced; (2) if loss 

 and gain balance each other, there will be 

 no change in the population; and (3) if 

 the natural replenishment exceeds loss ow- 

 ing to fishing effort and other mortahty, 

 the catchable stock at year's end will have 

 increased. 



A compHcation arises in that the popula- 

 tion may stabilize at different levels of 

 density. The level will depend primarily 

 upon the rate of capture, because this fac- 

 tor, operating through fishing mortality, de- 

 termines to a considerable extent the age 

 distribution of the stock. 



"We may expect rate of growth and rate of 

 recruitment to be affected to some extent by 

 the rate of capture. Thus if the rate of capture 

 is low, we may get an overcrowded stock, with 

 a slow rate of growth, and, probably, a slow 

 rate of recruitment, since there will be little 

 room for incoming stock. If the rate of capture 

 is increased, leaving more room for the stock 

 to grow and recruit itself, we may expect the 

 rate of growth and rate of recruitment to be 



