SHARP and FRANCIS: ENERGETICS MODEL FOR YELLOWFIN TUNA POPULATION 



Assuming the average caloric consumption by 

 the yellowfin tuna population per day to be 10% 

 of its caloric biomass, a somewhat higher than 

 realistic estimate, daily utilization in calories 

 would be 4.25 cal/m^ day. The results of the 

 ENSIM estimates of the total calories utilized per 

 year for the unexploited population was 14.96 x 

 10^^ cal/annum, so that the resulting utilization 

 per square meter day is given by: 



14.96 X 10^5 cal/annum _ 2.5 cal 



(365 day /annum) (1.696 x lO^^ m2) ~ m^ day 



The results of the simulations of the exploited 

 fishery for the years 1964-72 yield estimates of 

 less than 50% of this figure as the energy utili- 

 zation by the yellowfin tuna population. One 

 would expect the true values of caloric utiliza- 

 tion to lie somewhere in the range from approxi- 

 mately 1.5 cal/m^ day to the upper value of 4.25 

 cal/m^ day. 



With the primary productivity estimated to be 

 at an average level of 2.34 kcal/m^ day and forage 

 standing stock utilizable caloric values averaging 

 at a minimum of 1.00 kcal/m^, it seems hardly 

 likely that yellowfin tuna are food limited from the 

 40-cm recruitment size. 



This brings up the problem of how the east- 

 ern tropical Pacific yellowfin tuna population 

 is limited. This, of course, is best taken in per- 

 spective. Population limitation examples are 

 typically taken from terrestrial populations and 

 extrapolations made to ecosimilar strategies in 

 closed systems such as lakes and estuaries 

 where primary productivity is greatly affected 

 by season, and indeed can be determined to 

 be the limiting factor in population numbers 

 and biomass. 



In those marine animals where density de- 

 pendent growth functions are evidenced there is 

 generally a two-dimensional limitation imposed 

 such that crowding is likely to affect each indi- 

 vidual. For filter-feeding organisms, such as 

 herring and menhaden, the density dependent 

 function is easily conceptualized. 



One needs only to examine the relative abun- 

 dance of food available to highly mobile preda- 

 tory species which feed opportunistically on 

 organisms ranging in size from 1 to 30 cm, which 

 are available on a relatively continuous basis 

 in a tropical system, to see that dogma general 

 to terrestrial, estuarine, limnetic, two-dimen- 

 sional substrate tied, or filter-feeding animal 



ecology does not generally apply to the 40- to 

 140-cm yellowfin tuna. 



There are, however, several possibilities con- 

 cerning the survival of yellowfin tuna from larvae 

 to 40 cm which would certainly fit into the 

 schemes which typically limit species. Since they 

 are probably particulate feeders (e.g., do not 

 undergo ecometamorphoses at early ages from 

 filter feeders to predators), it can easily be seen 

 that they are victims of the availability of con- 

 centrations of food at smaller sizes because of 

 their relative lack of mobility. If a 40-cm tuna 

 requires 10-20% of its body weight per day to 

 maintain, as compared to 3-5% in large yellowfin 

 tuna, then one can hypothesize that the smaller 

 predators must consume even greater amounts 

 due to the pressures of very rapid growth, feed- 

 ing activity, and competition with peers, indicat- 

 ing that they are more likely severely affected 

 by density of both conspecifics and food than are 

 the larger sized fish. 



Another consideration is the size distribution 

 of the forage organisms. It is obvious that there 

 are considerably larger amounts of the smaller 

 food organisms than the bigger sizes, which 

 would perhaps indicate that the real density 

 competition pressures are on the intermediate 

 sizes (vis. 10-40 cm) as compared to the post- 

 larval sizes. This brings us to the next important 

 process, larval survival. 



Spawning Survival Versus 

 Population Biomass 



For our hypothesized unexploited population 

 of 600,000 metric tons of individuals from 40 to 

 140 cm fork length, we can calculate the requisite 

 number of postlarval survivors which must be 

 generated each year to maintain this stock at 

 equilibrium. Assuming 40-cm yellowfin tuna are 

 approximately 7 mo of age and that the survival 

 rate is constant for all ages after postlarval trans- 

 formation and is approximately equal to e"-^ on 

 an annual basis (Hennemuth 1961), the number 

 of postlarval survivors each year is given by the 

 relation 



A^, = A^4oe 



0.8(1) 



If A^4o is approximately 2.12 x 10'^ individuals 

 per year in cohort S^, and 2.06 x 10^ in cohort Sq, 

 then there are approximately 6.67 x 10'' sur- 

 vivors/yr. If we assume that they are aggregated 



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