SKILLMAN and YONG: GROWTH CURVES FOR TWO MARLINS 



270 

 260 

 250 

 240 



230 

 220 

 210 

 200 

 190 

 180 

 170 

 160 

 150 

 140 

 130 



-; \ 1 1 1 1 \ 1 1 1 1 r 



MALE(«) X 



FEMALE (o) 



MALE(>) 



_i I i_ 



-I I I L. 



1.0 15 20 2.5 30 3.5 40 4.5 5.0 55 



AGE IN YEARS 



Figure 3.— Striped marlin von Bertalanffy growth curves by sex, 

 for the analysis of pooled data. Male and female growth curves 

 having the same length were obtained using 11 age-groups while 

 the longer male curve was obtained using in addition an 

 age-group 1 yr older. Observed mean lengths for male and female 

 age-groups are given. As explained in the text, the outliers at age 

 2.46 yr were not used in fitting the growth curves. 



quarter 3 yr later for females and 4 yr later for 

 males. 



Discussion 



We felt that the parameter estimates from the 

 analysis of pooled data provided better estimates 

 of population parameters than those from the 

 analysis of individual cohorts because pooling 

 smooths out variation in individual curves. In 

 addition, the less well-represented age-groups, 

 having small and large mean lengths and being 

 recruited to or escaping from the fishery, were 

 estimated more accurately given the larger sam- 

 ple size after pooling. 



Since estimates of mean lengths at age were 

 used in the fitting of the growth curves, estimates 

 of growth parameters are in terms of these aver- 

 age values. Likewise, estimates of length at age 

 derived from these models (Table 4) will actually 

 be average values and should only be calculated for 

 the range of ages used in fitting the models. In 

 fact, the greatest utility of these models will be to 

 predict length at ages within the range of the 

 observed data. The accuracy of the estimation of 

 L^ is dependent on the range of values used, and 

 it should be remembered that the data used here 

 included fish only up to the onset of sexual 

 maturity. 



Table 4.-Striped marlin von Bertalanffy growth parameters by 

 sex for analysis of pooled data. The parameter estimates, L„ 

 (asymptotic maximum fork length), K (rate of proportional 

 growth), and ^o (theoretical time at which the marlin would have 

 zero length) are given for model 1 (upper row) and model 2(lower 

 row). 



The estimation of population L^^ was complicat- 

 ed by the fact that males and females were not 

 represented in the fishery for the same length of 

 time. Obviously, the length of time (number of 

 age-groups) that the sexes were in the fishery had 

 an eff"ect on the estimation of L^o, as well as K and 

 ^0 (Table 4). We believed that the parameter 

 estimates for males using all 12 age-groups 

 provided the most accurate estimates because a 

 greater part of the growth curve was measured. 

 We must admit that the estimates may not be very 

 precise because the estimated sample size of the 

 last age-group was 14 individuals, and the stan- 

 dard error of the estimate for the growth curve 

 was larger when all age-groups were included. The 

 estimates of L^ for males using models 1 and 2 

 were 277.4 and 314.4 cm, respectively. In order to 

 obtain estimates for females that can be compared 

 to those for males, the differences found between 

 females and males using 11 age-groups, 11.3 and 

 11.8 cm for models 1 and 2, respectively, were 

 added to the estimates of L^ for males, giving 

 288.7 and 326.2 cm, respectively. These estimates 

 seemed reasonable when compared to the largest 

 striped marlin measured by personnel from the 

 Honolulu Laboratory: 296 cm for males, 305 cm for 

 females, and 310 cm for sex undetermined. 



Both the analysis of cohorts and the pooled data 

 analysis (though less so) were plagued by apparent 

 negative growth or at least by very slow growth 

 during some quarters about a year and a half after 

 recruitment. Accepting the general growth pro- 

 gression as valid, this problem probably biased the 

 estimates of L^ downward and K upward and 

 contributed to the size of the standard errors of 

 estimates. We do not believe that this period of 

 apparent negative growth resulted from some 

 physiological change in the form of growth for 

 which the von Bertalanffy model could not account 



561 



