FISHERY BULLETIN: VOL. 78, NO. 1 



transient. The latter drops rapidly, proportionally 

 to the square root of time elapsed since arrival of 

 the larva. Substituting numerical values into 

 Equation (10), the oxygen flux can be compared 

 with oxygen requirements of larval anchovy to see 

 if the swimming motions are required for respira- 

 tion. 



The equivalent radius, a, of the larval anchovy 

 is found by equating the surface area of the larva 

 and the equivalent sphere. The larva, at this 

 yolk-sac stage, is described for diffusion purposes 

 as a sphere of radius q (the yolk sac) attached to an 

 almost flat ribbon of length Zj and average breadth 

 b. The combined surface area of the sphere and 

 ribbon is then taken to be equal to the area of the 

 equivalent sphere appearing in Equation (10). 

 Thus 



47ra2 = 2l^b + Anq^. 



(11) 



Using typical values for these parameters for 

 newly hatched larvae we obtain /j = 1.4 mm, b = 

 0.3 mm, and q = 0.3 mm (from drawings by E. H. 

 Ahlstrom, Senior Scientist, Southwest Fisheries 

 Center, NMFS, NOAA, La Jolla, CA 92038), i.e., a 

 = 0.0395 cm. The mass content of oxygen in sea- 

 water at 20° C is Co =7.8 x IQ-^ g/cm^^ (Prosser 

 1973), and the mass fraction is obtained by divid- 

 ing by the density of sea water, which then cancels 

 out in Equation (10). Finally, the diffusion 

 coefficient of oxygen is approximately equal for 

 freshwater and seawater (Riley and Skirrow 1965) 

 so that a reasonable value for 20° C is 1.8 x 10'^ 

 cm2/s (O'Brien et al. 1978), or D = 1.08 x lO'^ 

 cm^/min. Substituting all these values into Equa- 

 tion (10) we obtain 



J= (4.18 + 2.51 r'/2) 10-^ g/min (12) 



when the water is 100% saturated. Reducing the 

 oxygen content of the water causes the value of the 

 oxygen flux, J, to go down proportionally, i.e., by 

 multiplying J from Equation ( 12) by the fraction of 

 saturation. Some typical values of J appear in 

 Figure 2 with the percent of saturation as the 

 parameter. 



When the larva starts swimming, two changes 

 in the oxygen supply occur. First, the animal's 

 motion produces a convective local flow relative to 

 the body, thus bringing new, oxygen-rich water 

 closer and removing the respiratory waste prod- 

 ucts. Secondly, the absolute motion will bring the 

 larva to an area where the oxygen concentration is 



oo 



mm 



Figure 2.— Rate of oxygen transport (J) to motionless northern 

 anchovy larva by diffusion versus time (t). Broken part of curve 

 shows asymptotic value, after the initial transient has disap- 

 peared. Parameter is oxygen concentration in percentage of sat- 

 uration. 



still at the initial ambient value, starting the pro- 

 cess described by Equations (l)-(4) again. 



Following this reasoning, even relatively slight 

 motions causing just a local flow around the ani- 

 mal's body would suffice for respiratory functions. 

 Thus, actual swimming would not be required. 

 However, the yolk-sac larvae are increasingly 

 negatively buoyant with age (Hunter and Sanchez 

 1976), which causes them to sink. Therefore, ac- 

 tive absolute motion is necessary for the larva to 

 stay at a given depth for feeding and future school- 

 ing. 



When the larva is swimming, the process of 

 transport of oxygen changes to convective diffu- 

 sion, and as such is described by a different model 

 (Daykin 1965). Daykin's work dealt with station- 

 ary eggs in a moving river environment, but for 

 mass transfer purposes this is equivalent to a 

 larva (or egg) moving at constant speed relative to 

 the water. In the convective diffusion process 

 (Levich 1962; Daykin 1965), the mass transfer to 

 the larva can be roughly described by 



'^con = 47TaHc„-C^)k 



(13) 



112 



