AGE AND GROWTH OF YELLOWFIN TUNA 



139 



Size of fisli in fi^curc (i was plotted in tcfnis of 

 l('i\<rlli nitlicr than wi'i^'-ht since tliis method of 

 filtin<x a fiiowth cui've is applicable to sizes above 

 the inflection point. It was obvious from a plot 

 in terms of wei<rhts ((i>r. 9) that the inflection 

 I)oint is within the ranfje of our data, whereas our 

 data in terms of length appear to be above the 

 inflection point. 



P'or the growth of a number of species of animals, 

 Walford's graphic transformation method gives a 

 straight line when the lengths at age 1, 2, H, 4, 

 . . . 7i, reiiresented on the a: axis, are plotteil 

 against the lengths at age 2, :i, 4, 5, . . . n+1, 

 on the ?/ axis. This method assumes the growth 

 during each period to be of constant ratio to that 

 of the previous period. It has already been noted 

 that the modes make all their progress during half 

 the year and none in the remainder. This should 

 and does show as a stepwise or sinuous deviation 

 from the straight line. Also, this method requires 

 length values for each consecutive unit of time, in 

 this case for each month. Within the limits of 

 our data (fig. 6) there w-ere 28 months for which no 

 modal values were evident in the plotted data. 

 To furnish estimates of the missing values, linear 

 interpolations were made between observed 

 monthly values. 



200 



ISO 





The series of actual values and interpolated 

 values was then smoothed twice by a running 

 average of three and resulting values of length at 

 age I) were [)lotted agairLst lengths at age n+1 

 where age is in months. The plotted data are 

 well fitted by the least-squares line }'=7.04 — 

 0.96.336 A^, where )' is length at age n + l, and X 

 is length at age /( (fig. 7). From this straight line 

 the upper limit of growth or the upper as\^mptote 

 can be derived according to Walford's method by 

 taking the point of intersection of the line fitted 

 to the plotted data and the line of no growth 

 represented by a line of slope 45° through the 

 zero point (fig. 7). In the case of the yellowfin tuna 

 data used herein, the value in length at the point 

 of intersection of the two lines is at 190.0 centi- 

 meters, which in terms of weight is equal to 294.9 

 pounds. A maximum weight of this magnitude 

 is within reason for this species; several specimens 

 approaching this limit have been taken in the local 

 flag-line fishery. The largest specimens included 

 in this study, however, were between 260 and 269 

 pounds. 



Because the plot of n against '(+ 1 is a constant- 

 percentage rate' and not actual-length values, it is 

 possible to choose the point through which the 

 curve should be passed. As the period from 



X 



100 



50 



10 



15 



20 



25 



30 



35 



40 



45 



50 



55 



60 



65 



70 



MONTHS 



FiGCRK 0. — Actual aiifi interpolated values in Iciintli plollcd against iiiontlis and sliowinn assisuod modal groups. Solid 

 points arc actual values and circles arc interpolated values. F'Votu coinhiricd and sniootlied 1948 and 1919 data. 



953183 O - 51 - 2 



