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



447 



where 



and 



W = Qj * exp {Q 2 * exp [ -Q 3 * t]} (4a) 



Qj = exp (a) * Pi * * b (4b) 



Q 2 = b * P 2 (4c) 



Q 3 = P 3 - ( 4d ) 



Gompertz equations were used to describe the age- 

 weight relationship for all sizes of blue marlin in this 

 study. For larvae and juveniles, we converted the 

 length parameters (P) to weight parameters (Q) directly 

 using equations 4a-d. For adults, we first converted 

 individual lengths to weights using either the equation 

 for immature fish for young adults (see Results) or the 

 sex-specific equations (see Results) for fish larger than 

 140 cm and then fit the Gompertz equation (4a) to 

 obtain a continuous young adult/adult weight-at-age 

 relationship. 



Increment counts Spearman's rank correlation (SRC; 

 Conover 1971) was used to evaluate the association of 

 total increment count with LJFL, otolith weight, and 

 round weight. Chi-square contingency table analyses 

 (Snedecor and Cochran 1980) were used to determine 

 whether the distribution of back-calculated spawning 

 dates was independent of predicted deposition rates 

 (with periodicities (P) of 0.1-0.9, 1, and 2 increments 

 per day) and days to first increment formation. Frac- 

 tional periodicity values are interpreted as the propor- 

 tion of increments actually counted; i.e., true age is 

 underestimated. Multiple increments per day would 

 correspond to overestimates of age, possibly due to 

 counting subdaily increments. To minimize the effect 

 of small sample sizes in a cell, spawning dates were 

 tallied by calendar quarters for each periodicity (P) 

 value. Because all larvae were collected within a 

 48-hour time period, only the average larval age and 

 length were used in these calculations. 



Results 



Limitation of the ageing method 



Otolith analysis Sagittae from 155 juvenile, young 

 adult, and adult blue marlin, ranging in length from 

 4.3 to 369cm LJFL, and 18 larvae, 5-10 mm NL, were 

 used to test for diel periodicity of increment deposi- 

 tion. References here to increments, primary incre- 

 ments, or daily increments generally imply daily deposi- 

 tion (see Discussion). 



The decision to analyze increment counts using the 

 whole otolith method (except for the 18 larval otoliths) 

 was based on our evaluation where both the whole and 

 sectioned otoliths were available from nine specimens. 

 Counts using the whole otolith method were higher in 

 eight out of the nine (88%) sagittae samples analyzed. 

 We felt that the differences were due to the com- 

 pressed incremental record on sectioned sagittae, and 

 as a result we concluded that section counts consistent- 

 ly underestimated the total increment count. There- 

 fore, we used whole sagittae counts in our analysis. 



The otolith microstructure method could not be ap- 

 plied with confidence to whole sagittae from fish longer 

 than 212 cm because of the limitations of light micro- 

 scopy and difficulties in discriminating finely-spaced 

 increments of less than about l^m. Discontinuities of 

 the microstructural record usually occurred at counts 

 of about 400-500 along the antirostrum dorsal lobe 

 counting path. The SEM micrograph in Figure IB and 

 the entire microstructural record from a 23-cm juvenile 

 illustrated in Figure 3 are examples of the undisrupted 

 incremental record observed on whole sagittae in 

 young fish. 



Otolith microstructural analysis was successfully ap- 

 plied to 18 larvae and 77 juvenile and young adult/adult 

 blue marlin. Forty additional blue marlin < 212 cm in 

 length (30%) could not be aged using the otolith micro- 

 structural method. These samples included otoliths 

 broken or lost during preparation and poorly section- 

 ed otoliths from another study. Therefore, the 30% re- 

 jection rate is conservative in estimating the expected 

 yield of useful counts and age data from a fresh set of 

 samples. 



Range in estimated age Estimated ages, based on 

 counts on the whole sagittae of the 18 larval blue 

 marlin, ranged from 9 to 12 days (Table 1); 66% of the 

 larvae had either 10 or 11 increments. The range in 

 estimated ages of the 77 juvenile and young adult/adult 

 blue marlin was 21-495 days (a maximum of 1.4 years, 

 Table 1). Correlations between total increment count 

 and round weight (SRC = 0.915), otolith weight (SRC 

 = 0.895), and LJFL (SRC = 0.893) for juvenile and 

 young adult/adult blue marlin were similar or the same. 



Periodicity of increment formation 



Otolith microstructure Otolith microstructure of lar- 

 val blue marlin (Fig. 4A) was indistinguishable from 

 that of frigate mackerel Auxis thazard and other 

 pelagic species of similar size (Figs. 4B-D). For some 

 species, daily increments have been validated by rear- 

 ing experiments, otolith marking, or other methods 

 (Brothers et al. 1976, Wild and Foreman 1980, 

 Brothers et al. 1983). 



