Prince et al.: Otolith analysis of Makaira nigricans age and growth 



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Figure 2 



(A) Photomicrograph and (B) SEM micrograph of the video image of primary (between large arrows) and subdaily (small arrows) 

 increments in a whole sagitta from a 178cm LJFL Atlantic blue marlin Makaira nigricans. Black bar = lOfim. 



Computations of APE were not made for the 18 

 larval blue marlin because only one count was made 

 for each of these samples. 



Statistical procedures 



Length-at-age The growth trajectory for the age 

 range in our sample, as summarized in Table 1, is asym- 

 metric and S-shaped, with growth rates increasing up 

 to about 40-50 cm and declining thereafter. Richards 

 (1959) described the relationship between this inflec- 

 tion point (relative to the maximum or asymptotic size) 

 and the most common growth equations. The von Ber- 

 talanffy equation has no inflection point and those for 

 the Gompertz and logistic equations are at 3/8 and 1/2 

 of the maximum size, respectively. In addition, the 

 logistic equation is symmetric around the point of 

 inflection. 



The Gompertz equation was appropriate for model- 

 ing growth of younger fish (i.e., it had an inflection 

 point and was asymmetric). Assuming an inflection 

 point of 40cm and dividing by 3/8, we estimated a max- 

 imum size of 107cm for this growth phase. In order 

 to obtain a better estimate of limiting size for this 

 growth stanza, we included data up to 113cm (111 days) 

 and fit the Gompertz equation 



L = Pj * exp { -P 2 * exp [ -P 3 * t]} 



(3a) 



tion (i.e., above and below 110cm). 

 We used the von Bertalanffy equation 



L = Pi * {1 - exp[P 2 *(t - P s )]} 



(3b) 



to data for young fish. This procedure allowed us to 

 assess the upper and lower limits of each growth equa- 



for older fish, including data down to 95 cm (96 days), 

 since no inflection point was evident in this range. 

 Results using the two equations differed by less than 

 2cm at 110cm body length, and growth rates were 

 nearly the same at this length. Therefore, data were 

 separated at 110 cm for subsequent analyses. Combin- 

 ing these two equations provides continuous estimates 

 of size-at-age and daily growth rates for the age range 

 in our data. 



Generic parameter labels (P for length, Q for weight) 

 are used in growth equations to indicate that no 

 physical or biological meaning should be ascribed. In 

 general, growth equation parameters are highly inter- 

 correlated and, in addition, are highly correlated with 

 the size range of the data. Our data covers only the 

 initial phase of adult growth, so the usual biological and 

 temporal interpretations are unwarranted. For the 

 same reason, the use of generalized or multicycle equa- 

 tions did not seem appropriate. 



Least-squares estimates of the parameters of the von 

 Bertalanffy and Gompertz equations were obtained us- 

 ing Marquardt's (1963) algorithm and the methods of 

 Conway et al. (1970). Because the size range in our data 

 covers fish from 5mm to over 212cm, the natural log 

 transformation was used to minimize proportional 

 rather than absolute differences. 



