Edwards: Associated tunas and dolphins in eastern tropical Pacific 



683 



where "8^ = 1380, and 128^ = 0.67. 

 Caloric cost of activity!^ was estimated as 



ACT,^ = PWR* 20650, 



where 20650 converts watts to calories/day. Power re- 

 quired to swim (PWR) was estimated as 



PWR = MP/(ME*PE), 



where MP is mechanical power required to overcome 

 drag, ME is mechanical efficiency, ^^ and PE is "pro- 

 peller efficiency" (efficiency of propulsion by flukes)^'^. 

 MP (in watts) was estimated as a function of total drag 

 (Dti in dynes) and velocity (VL; in c/sec) as 



MP = (Dt*L)/10^ 



where the factor 10^ converts the product Dt*L to 



watts. 



" Sa was assumed constant for all sizes of spotted dolphins. Given 

 an observed rate of 0.45mg 0, • g wet wt"' ■ hr ' for a spinner 

 dolphin Stenella longirostris weighing 68000 WW^ (Hampton and 

 Whittow 1976) and assuming 3.25 cal/mg 0„ (Elliot and Davidson 

 1975), then 2,386,800 (0.45*3.25*68000) calories are expended 

 daily in standard metabolism, and 83=1380 (2,386,800/68.000""). 

 The observed resting rate of oxygen consumption is consistent with 

 the range of resting rates (0.3-0.6 mg 0, ■ g wet wt ') reported 

 for bottlenose dolphins under various conditions (Hampton et al. 

 1971. Karandeeva et al. 1973, Hampton and Whittow 1976). 



'- Heusner (1982) presents convincing statistical arguments that intra- 

 specific relationships between basal (standard) metabolism and body 

 weight in adult mammals are better described by the 2/3 power 

 than the 3/4 power proposed by Kleiber (1961). Heusner's argu- 

 ment is based on observed differences between adults of similar 

 species (e.g., breeds of dog); but Huesner's curve is also more 

 realistic because it predicts a relatively higher weight-specific rate 

 in smaller (younger) animals of a given species. This is more con- 

 sistent with Kleiber's (1961) observation that younger animals tend 

 to have elevated weight-specific metabolic rates compared not only 

 with adults of the same species, but with small adults of similar 

 species. In young marine mammals, weight-specific standard 

 metabolic rate is often at least twice the standard rate of adults 

 (Ashwell-Erickson and Eisner 1981, Lavigne et al. 1982). The 

 parameterization above results in weight-specific estimates of S 

 that are 2.3-1.3 times higher in dolphins measuring 80-140 cm TL 

 than in adult dolphins (~190cmTL). This differs by 0-11% (increas- 

 ing with increasing size) from basal metabolic rates of juvenile 

 through adult seals of similar weight (Ashwell-Erickson and Eisner 

 1981). 



" Dolphins were assumed to swim steadily far enough below the sur- 

 face to eliminate the effects of surface drag (e.g., Hertel 1969). 

 This formulation ignores the costs of surfacing to breathe, and the 

 attendant increase in total distance swum to follow a sinusoidal 

 rather than a straight path through the water. Preliminary 

 estimates of these additional costs for individual dolphins of several 

 sizes, for reasonably realistic depths of dive and distance between 

 surfacings, ranged from 10 to 25% of steady swimming costs. As 

 this cost is relatively low, the dolphin model was not reformulated 

 to include these added costs of surfacing. 



"ME = 0.20. by analogy to observed muscle efficiencies of terres- 

 trial mammals. 



'■''PE = 0.85 by analogy to tunas (Magnuson 1978). 



Total drag was estimated as a function of drag due 

 to body, fins, and movements by flukes as 



Dt = (0.5*N*VL2*8„*Ct)/(1.0-FID), 



where N is density of seawater (1.025g/cm3), S^ is 

 wetted surface area of the body, Cj is coefficient of 

 total drag, and FID is (fin -1- induced) drag. FID^^ is ex- 

 pressed here as the fractional increase in estimated 

 total drag due to adding the effects of fins and moving 

 flukes. 



S„ is wetted surface area of the body, excluding flip- 

 pers, dorsal fin, and flukes, estimated as^^ 



S„ = 0.1636 *TL2i4. 



Surface areas of fins are excluded from this calcula- 

 tion because fin drag is incorporated into the equation 

 for total drag as an increase of 21% over drag esti- 

 mated from body dimensions alone. 



Ct was estimated from the formula for drag of sub- 

 merged streamlined bodies moving with constant 

 velocity 



Ct = Cf*[l + (1.5*(Da/TL)3'2) + (7*(D,/TL)3)] 



(Hoerner 1965, Webb 1975). Cf is the coefficient of 

 friction drag, and D^ is the maximum body diameter 

 (cm; derived from girth at axilla (Gg)) where 



Ga = Gaa 



■WWkgGab_ 



with Gaa = 25 and G^h = 0.28, based on measurements 

 of 50 spotted dolphins measuring 82-210cmTL. 



Cf was estimated from the equation for streamlined 

 bodies moving submerged at constant velocity in tur- 

 bulent flow as 



Cf = 0.072 Rl-1/5, 



where Rl is Reynolds number, estimated here as 



Rl = (TL*VL)/v, 



where v is kinematic viscosity ( = 0.01 8tokes) assum- 

 ing turbulent flow at the boundary layer (Webb 1975), 

 and VL is velocity (cm/sec), estimated as 



VL = VLa*TLVL\ 



■^FID was assumed = 0.21, based on the fraction of estimated total 

 (body -I- fin -I- induced) drag accounted for by (fin + induced) drag in 

 the 4-dolphin sample. 



"Based on measurements of wetted surface area in the 34-dolphin 

 sample. 



