-CORRESPONDING NUMBER-PER-POUND EQUIVALENTS 

 (Headless) 



10 £ 



30 40 50 



AGE AT RECRUITMENT ijt/) 



{ Weeks) 



U< 



Figure 12. — Yield in weight per recruit against age at 

 recruitment for different levels of natural mortality (M) 

 in a population of pink shrimp. [F=0; 96, A"=0.07; 

 PP„ = 42.0 g. ; * indicates an observed as contrasted to 

 a hypothetical value.] 



describing growth. In contrast, greater variation 

 would be expected for natural mortality since it 

 may be readily conceived ,as the more sensitive 

 to and hence the more likely of the density- 

 dependent parameters to reflect even the most 

 subtle of environmental vagaries. In other words 

 the potentialities for growth in the individual are 

 largely predetermined within rather narrow limits 

 by the characteristics of the species; those for 

 natural mortality, which are enhanced through 

 great prolificness, largely by the environment. 



With this in mind, additional curves were 

 generated in like manner for four hypothetical and 

 successively lower values of the natural mortality 

 coefficient (fig. 12). These illustrate very clearly 

 what happens when, with respect, to some economic 

 standard /„, natural mortality becomes in- 

 creasingly compatible with growth. For any 

 magnitude of exploitation (F), maximum yields 

 will always occur at higher levels and at more 

 advanced recruitment ages as natural mortality 

 establishes itself at lower and lower levels. Under 

 the growth restrictions imposed here, postponing 

 initiation of exploitation would not be justified 

 unless the observed natural mortality rate were 

 on the order of 0.10 or less. It may be argued 

 now that even if the observed value for M (0.55) 

 constituted a gross overestimate of the true natural 



mortality, the associated error would have had to 

 be rather large before the general conclusion just 

 reached could be viewed with suspicion. The 

 present example also shows that with a natural 

 mortality of 0.05 (which is untenably low for 

 shrimp), the highest yield is obtained when age at 

 recruitment is increased to about 23 weeks, this 

 corresponding to a shrimp size of roughly 31-35, 

 headless-count. Dashed portions to the left of t p 

 arbitrarily designate the likely order and shape of 

 the yield curves for that part of the hypothetical 

 population not yet possessing economic worth. 



Effects of Variation in Rates of Growth and Exploitation 



To illustrate how changes in the critical factors 

 of growth and fishing mortality influence the yield 

 curve's shape and the position of its maximum 

 point, curves for selected (hypothetical) parameter 

 values are compared with those derived above for 

 observed values. If yield is described as a func- 

 tion of age at recruitment for varying rates of 

 growth (fig. 13 A), it will be noted that the effect 

 of a higher rate of growth than that observed is 

 an increase in amplitude of the yield curve and a 

 shift in its maximum point to the left, with what- 

 ever recruitment size is designated as the standard 

 minimum remaining the same as before. In other 

 words, every shrimp reaches the smallest ac- 

 ceptable size at an earlier age. Conversely, at a 

 given level of natural mortality, a lower rate of 

 growth tends to decrease curve amplitude and 

 move the point of maximum yield to the right, 

 the minimum marketable size again remaining 

 fixed but being attained at a later age. 



Exercising care to judge each new set of condi- 

 tions on its own merits, it appears that increased 

 rates of growth such as postulated in figure 13A 

 would still not be sufficient to justify any advance 

 of recruitment age where a high natural mortality 

 prevails. At a low mortality level, an advance of 

 recruitment age is indicated only when concurrent 

 growth is also of a low order. Hence, for a fixed 

 natural mortality, successively higher rates of 

 growth would merely dictate a retrogression in 

 recruitment age (but not size) if maximum yield is 

 to be achieved. This relationship implies no 

 change in minimum acceptable size at recruitment 

 but, instead, as in the observed situation where low 

 growth rate complements high natural mortality, a 

 greater overall yield by the age group involved 

 during its fishable life span. 



DYNAMICS OF A PENAEID SHRIMP POPULATION 



333 



