SHARP and FRANCIS: ENERGETICS MODEL FOR YELLOWFIN TUNA POPULATION 



in turn a function of the length of the individuals 

 (see Figure 3). In Magnuson's (1973) relation- 

 ships the variables necessary for a solution for 

 the minimum velocity are I and the density of the 

 fish. Magnuson (1973) provided data for fish 

 density (in the form of empirically derived multi- 

 pliers) by weight class for several species in- 

 cluding yellowfin tuna. We have extrapolated 

 his data to fit our size distribution with an asymp- 

 totic lower limit of fish density at 1.06 g/cm^ 

 reached by 120-cm fish. 



We are assuming that the animals have their 

 pectoral fins 75% extended all of the time that 

 they are in nonfeeding-flight behavior, hence 

 Ci = 0.75, and that the keel surface is 85% ef- 

 fective so that Cj , = 0.85. This results in a fish 



that is swimming somewhat faster on the average 

 than its Vjoo or minimum velocity. These values 

 are "best guess" estimates and as such, repre- 

 sent only minor changes in the appropriate di- 

 rection as opposed to using absolute minimum 

 energy utilization in the population simulation. 

 Magnuson's Vioo for a 50-cm yellowfin tuna is 

 50.91 cm/s. Solving for the "typical" velocity under 

 our "best guess" conditions results in a V^y^ of 

 58.29 cm/s. 



We have set a "typical" feeding-flight speed 

 at 3 m/s. This is an integrated average that in- 

 cludes all velocities above V^^^ and includes the 

 burst speed forays. Since the energy required 

 for different speeds is proportional to a cubic 

 function of the velocities, it should be noted 

 that the most probable velocity is less than 2 m/s, 

 since the energy requirements for a few short 

 bursts of up to 10 body lengths/s rapidly increase 

 the overall energy utilization. With this in mind. 



FORK LENGTH ICMI 



Figure 3. — The energy utilization (in kcal/day) for growth 

 (Eg), maintenance (£„,), and the total (Eg + E„ + E^ = ^total* 

 energy utilization are portrayed as functions of length 7. 



we have at^ibuted 95% of the day or 22.8 h of 

 the day to V^yp requirements and 5% or 1.2 h to 

 Vfeed behavior. This is not to say that the fish are 

 limited to 1.2 h/day of feeding but that on the 

 average the increased velocity due to external 

 stimuli are exhibited for this period. One sus- 

 pects that the feeding of large and small tuna is 

 entirely different in nature, but for simplicity and 

 since no data are available, it is not unreason- 

 able to assume that the relative effectiveness of 

 feeding is somewhat similar over the life history 

 of the animals. Based on these estimates we 

 hope to have contrived a "reasonable" fiction for 

 use in our model. The need for better estimates 

 is obvious. 



MODELING RESULTS 



The model ENSIM computes the caloric re- 

 quirement of each semestral cohort in the ex- 

 ploited population, by quarter of the fishing year. 

 Summary data are listed after each quarterly out- 

 put which differentiate the semester A cohort 

 caloric expenditure from that of the semester B 

 cohort, and a composite total expenditure is 

 listed (see Table 2). An annual summary for 1972 

 is also generated and an example is presented 

 in Table 3. 



Initial biomass and numbers, yield in weight 

 and numbers, gross growth, and average bio- 

 mass are tabulated for each quarter, and sum- 

 mary tables are generated for the individual 

 semestral cohorts as well as composite values. 

 The biomass of food ingested per day is gen- 

 erated for each cohort, assuming 1.00 kcal 

 (Paloheimo and Dickie 1966) are available per 

 gram food ingested. The minimum percent bio- 

 mass ingested per day with respect to the cohort 

 biomass is also calculated for each cohort (see 

 Figure 4). The caloric requirements for mainte- 

 nance, swimming (at V^yp, Vfeed); ^^^ growth are 

 tabulated by size of the average animal in each 

 cohort in the simulation by quarter (see Table 4). 



We have simulated the fishing years 1964-72 

 and included the best available estimates for 

 cohort strength, fishing effort, and availability 

 parameters. We have also simulated a nonex- 

 ploited population which was recruited at the 

 average level for the data from the last 5 yr which 

 includes all the population indicated or expected 

 from inside our study area (see Figure 5). From 

 Figure 5, the plot of the average annual biomass 

 estimate, one can readily see the effect of fishery 



43 



