SKILLMAN and YONG: GROWTH CURVES FOR TWO MARLINS 



In order to efficiently separate age-groups from 

 the frequency distributions, the data were 

 grouped and length intervals set up (Simpson et al. 

 1960). Lengths for striped marlin were grouped by 

 sex, year, quarter, and 3-cm interval, and these 

 groupings resulted in a maximum of 96-length 

 intervals per quarter. Blue marlin lengths were 

 grouped by sex, quarter, year, and 5-cm interval, 

 and these groupings resulted in a maximum of 

 73-size intervals per quarter. 



Separation of Age- Groups 



The computer program ENORMSEP (Yong and 

 Skillman 1975) was used to separate the grouped, 

 length-frequency data into constituent age- 

 groups and to calculate estimates of the mean 

 length, variance, percent representation, and 

 numerical size of the age-groups. Essentially this 

 computer program automates the Cassie-Harding 

 probability paper method (Harding 1949; Cassie 

 1954) and enters intermediate results into 

 NORMSEP which performs the actual separation 

 of age-groups. 



Progression of Age-Groups 



The estimates of mean lengths for age-groups 

 were plotted by quarter in order to check for 

 reasonable progression and to assign age. Ages 

 were assigned by determining the time of peak 

 spawning, estimating the age at recruitment, and 

 then merely assigning ages progressively as the 

 age-groups passed through the fishery. 



The time of spawning is not well established for 



either striped or blue marlin. For striped marlin, 



Nakamura (1949) stated that the time of peak 



spawning seemed to be from April to May in the 



South China Sea near the Republic of China and 



from May to June near the Bonin Islands. Royce 



(1957) stated that testes with free flowing milt 



were collected in the equatorial central Pacific in 



March. Kume and Joseph (1969) estimated, on the 



basis of gonad index of females taken in the 



eastern tropical North Pacific, that peak spawning 



occurs in May and June. From specimens landed in 



southern California and northern Mexico, El- 



dridge and Wares (1974) indicated that gonad 



index was highest in June and July, but they did 



not have samples for August or September. Hence, 



we took June 1st as the time of peak spawning and 



assigned an age of 1.46 yr to the 151-cm male and 



152-cm female age-groups recruited in the fourth 



quarter. 



For blue marlin, Royce (1957) stated that males 

 with free flowing milt were collected from Feb- 

 ruary through October in the equatorial Pacific, 

 and cited Nakamura (1942) as indicating that 

 spawning occurs east of Luzon (Philippines) from 

 May to July. Kume and Joseph (1969), on the basis 

 of gonad index of females taken in the eastern 

 tropical Pacific, concluded that spawning occurs in 

 December and January; however, most of their 

 samples were collected from south of the equator. 

 We arbitrarily took June 1st as the time of peak 

 spawning and assigned an age of 0.71 yr to the 

 55.5-cm female age-group recruited in the first 

 quarter. 



Von Bertalanffy Growth Model 



Two computer programs, BGC3 and BGC4, 

 assembled by Abramson (1971) and written by 

 Patrick Tomlinson were used in this paper to 

 obtain estimates of von Bertalanffy growth pa- 

 rameters. The computer program for model 1, 

 BGC3, fits the von Bertalanffy model by the least 

 squares method to lengths from fish of known or, 

 in this case, assumed age. The basic model is the 

 familiar equation 



A = L^a-e 



KU - („) 



o)) 



(1) 



where L , = length at age f 



Loo = a parameter depicting asymptotic 



maximum length 

 K = a. parameter indicating the rate of pro- 

 portional growth 

 f^^ = a parameter depicting the theoretical 

 age at which the fish has zero length 

 given the adult growth form. 



The computer program for model 2, BGC4, a 

 version of the size-increment method proposed by 

 Fabens (1965), fits the von Bertalanffy model by the 

 least squares method to observed lengths, using 

 data on growth increment in known time intervals 

 but making no assumptions about absolute age. 

 Parameter estimates using this method are in- 

 cluded in the tables so that any future estimates of 

 striped or blue marlin growth from tagging data 

 can be compared directly to our results. For model 

 2, the von Bertalanffy model is written as 



L, =L„(l-6e-'^') 



(2a) 

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