HUNTER and SANCHEZ: CHANGES IN SWIM BLADDER INFLATION 



bladders. At night, larvae were occasionally neu- 

 trally buoyant but most were slightly negatively 

 buoyant. 



To develop an equation for expressing sinking 

 speed in terms of larval length and swim bladder 

 volume, the data on sinking speeds were grouped 

 into four classes of larval length: 10.0 to 11.9 mm, 

 N = 30; 12.0 to 13.9 mm, A^ = 41; 14.0 to 15.9 mm, 

 A'' = 54; and 16.0 to 17.9 mm, N = 14. A regression 

 of sinking speed on swim bladder volume for each 

 length class yielded the following slopes and 

 standard errors for the regression lines: -3.040, 

 SE = 2.339; -4.001, SE = 1.297; -4.8796, 

 SE = 0.616; and -5.070, SE = 1.680, respectively. 

 Covariance analysis of these data indicated that 

 the slopes were not different whereas the inter- 

 cepts for the regression lines were statistically 

 different (P = 0.01). Since no difference existed in 

 the slopes among the four groups, the common 

 slope from the covariance analysis, -4.769, 

 SE = 0.487, was used to express the relation 

 between sinking rate and swim bladder volume for 

 each length class (Figure 5, lower panel). When 

 adjusted for the common slope, the sinking rate 

 intercepts of the four regression lines showed a 

 precise linear relationship when plotted against 

 the midpoints of their respective length classes 

 (Figure 5, upper panel). The equation for the 

 intercept-length relationship was y = O.ISL - 1.51 

 where L is larval length (the midpoints of the 

 larval length classes) and y is the intercept for the 

 regression of sinking rate on swim bladder volume 

 (the sinking rate at F = in Figure 5). This 

 equation was combined with the common slope to 

 provide the equation given below: 



S = 0.18L- 1.51- 4.77 F 



where S = sinking speed in centimeters per sec- 

 ond 

 L = larval length in millimeters 

 V = swim bladder volume (outside 

 dimensions) in cubic millimeters. 



We examined the changes in sinking speed of 

 larvae from the time of hatching through the 

 development of the swim bladder. These changes 

 are of interest because they illustrate the timing 

 of swim bladder development, its effect on 

 buoyancy, and the advantage of a nightly inflation 

 cycle. Data for sinking rates for larvae 4.0 to 9.9 

 mm were grouped into 1-mm classes and the 

 means plotted at the midpoints of the class inter- 



002 004 006 008 010 012 014 

 SWIM BLADDER VOLUME (V) mm^ 



016 



Figure 5.- The relation in larval northern anchovy between 

 sinking speed (S), swim bladder volume ( V), and larval length (L). 

 Lower panel, regression lines show relation between sinking 

 speed and swim bladder volume for the four classes of larva! 

 length indicated in the figure, when a common slope of -4.769 is 

 used (see text). Upper panel, the regression of the y intercepts (S 

 at F = 0) of the four regression lines on larval length (midpoints 

 of the four length classes); equation for intercept line was 

 y = 0.18L - L5L Final equation is S = 0.18L - L51 - 4.777. 



vals except for the yolk-sac larvae (3.7 mm) which 

 were all about the same length. For larvae 10.0 mm 

 or larger, we calculated sinking speeds from the 

 mean swim bladder volume given in Figure 4 

 using the equation given in the preceding 

 paragraph. 



Sinking speed increased exponentially with 

 length, when larvae sampled at night are excluded 

 (Figure 6). The increase is roughly proportional to 

 the cube of the length (curved line in Figure 6). 

 This might be expected since sinking speed is 

 dependent upon buoyancy which varies with the 

 volume (L^) and the difference in specific gravity 

 between the fish and its medium. For estimating 

 mean sinking speed for larvae with swim bladders 

 in the day, or for those without swim bladders the 

 equation S = 0.094 -i- 0.000264^^ where L is 

 length in millimeters and S is sinking speed in 

 centimeters per second, gives a good fit to the data. 



The length threshold for filling the swim bladder 

 (about 10 mm) coincides with a rapid acceleration 



851 



