PERRIN ET AL.: GROWTH AND REPRODUCTION OF SPOTTED PORPOISE 



Figure lO. — Relationship of difference between fetal growth 

 rate during linear phase and average growth rate during post- 

 natal period equal to gestation period to length at birth in five 

 odontocete cetaceans. Line is linear regression line of log 

 difference on log length. Data from Figure 11. Y is predicted 

 difference for Stenella attenuata from the offshore eastern 

 tropical Pacific. 



4.5 for Globicephala, and 4. 5 for P. phocoe?ia)^; and 

 yields a predicted length at 1 yr of 138 cm. 



Length Relative to Tooth Layers 



Total length was plotted on number of postnatal 

 layers for 115 males and 306 females (Figure 11). 

 The teeth of five males and three females had 

 completely filled pulp cavities. These are included 

 in the plots in a separate category "occluded." 



The plots of means for 2-layer intervals (the 

 points in Figure 12; the curves were fitted as ex- 

 plained below) very closely resemble the growth 

 curve obtained by Sergeant (1962) for 

 Globicephala. Asymptotic length (L ^) for females 

 is approximately 190 cm and for males approxi- 

 mately 200 cm. There appears to be a secondary 

 surge in growth at about 6 layers. With the restric- 

 tion that the curves must pass through birth 

 length of 82.5 cm and asymptotic lengths of 190 

 and 200 cm, it is not possible to fit any continuous 

 equation to the data satisfactorily. Continuous 

 curves that fit well at the upper and lower ranges 

 of layer count seriously underestimate length at 5 



*Fisher and Harrison (1970) stated that their data suggest 

 that Phocoena in Canadian waters grows approximately 30 cm 

 during the first year of life, or at an average rate of about 2.5 

 cm/mo, as opposed to the 4.5 cm/mo hypothesized by M0hl- 

 Hansen (1954). However, they also suggested, and their figure 2 

 showed, an average rate of at least 5 cm/mo during the first 

 4 mo. It seems unlikely that the rate would drop to an average 

 of — 1.25 cm/mo in the remaining 8 mo of the first year. 



to 7 layers. Kasuya (1972) also encountered 

 difficulty in attempting to fit a continuous model 

 to growth of a delphinid, S. coeruleoalba . Good fits 

 can be obtained, however, by assuming a dynamic 

 growth function. A two-phase version of Laird's 

 (1969) growth model was fitted to the 2-cm means 

 for all males and females, using an iterative 

 least-squares method. The occluded specimens 

 were assigned to the 16+ interval. 

 Laird's model is 



Lit) 



exp 



exp (- at) 



where 



L(t) = length at time t 



Lq = length at birth ( 82. 5 cm in this case) 



t = time (layers in this case) 



a = specific rate of exponential growth 



a = rate ofdecay of exponential growth. 



This model assumes that an organism's growth 

 pattern is determined at conception. The fitted 

 parameters a and a express the premise that 

 "growth is fundamentally exponential (implied by 

 the normal binary fission of cells), and it also un- 

 dergoes exponential retardation by some as yet 

 unknown physiological mechanism" (Laird 1969). 



In the two-phase approach, separate equations 

 were simultaneously fitted to the upper and lower 

 range of means. The assumptions were made that 

 juvenile growth is the same for males and females 

 (supported by the data) and that the growth dis- 

 continuity comes at about the same age for males 

 and females. The only fixed point was 82.5 cm at 

 layers (birth). The convergence point (inflection in 

 the growth curve) was allowed to float to the posi- 

 tion that gave the best fit, with males and females 

 considered jointly for lesser ages. The equations 

 converged at 5.59 layers (rounded off to 6 below) at 

 which predicted length is 159.9 cm. The fit is excel- 

 lent for females (Figures 11, 12). Asymptotic 

 length is 190 cm at predicted age of 18 layers. 

 Average length of adult females (those with ovar- 

 ian scars) is 187.3 cm, based on a sample of 555 

 (Perrin 1975). The largest female of 2,138 mea- 

 sured was 220 cm long. The equation for juvenile 

 growth to less than 6 layers is 



L = 82.5 exp 



0.4817 

 0.7172 



[l - exp (-0.7172^], 



where L = length, in centimeters 

 t = age in layers. 



239 



