192 



FISHERY BULLETIN OF THE FISH AND WILDLIFE SERVICE 



This matter will be discussed further after data 

 on abundance, age, and rate of growth have been 

 presented. 



LENGTH-WEIGHT RELATION 



The regression of weight on length of the yel- 

 lowtail flounder was determined (1) to provide 

 data to convert the landings from pounds to 

 numbers of fish, and (2) to provide data on fat- 

 ness of the yellowtail which may furnish clues 

 to changing ecological conditions. Information 

 obtained during each quarter of 1943 provided a 

 good basis for estimating weight from length 

 during the several years of our study, assuming 

 that the relation did not change from year to year. 

 In addition, it provided a critical comparison of 

 the differences in the length-weight relation be- 

 tween the sexes and among the seasons. The re- 

 duced statistical data are presented to permit fur- 

 ther comparison with data which may be collected 

 later. 



Samples were obtained near the middle of each 

 calendar quarter of 1943 (table 14). The fish to 

 be weighed and measured were taken at random 

 from the landings in the same manner as those 

 measured for length (p. 186). Usually a sample 

 of 50 fish was weighed and measured from a 

 vessel that had fished in a single statistical sub- 

 area. No attempt was made to equalize the num- 

 bers of each sex. 



Table 14. — Numbers of yellowtail from the southern New 

 England stock, by subarea and by sex, weighed and meas- 

 ured during 1943 



The lengths were obtained on a measuring board 

 and the weights on balances provided with special 



scales graduated in 2-place logarithms to simplify 

 the computation. The balances were of the spring 

 type, one with a capacity of 5 pounds, the other 

 of 1 pound. Since the weighing was done in the 

 field it was necessary to set up the balances for 

 each sample. Check weights were used prior to, 

 midway through, and at the end of the weighing 

 of a sample. The scales were adjusted at the be- 

 ginning of the weighing and subsequent checks 

 revealed no error of more than 1 percent in the 

 weighing. 



The regression of weight on length was com- 

 puted with the assumption that the relation is of 

 the form 



W=aL\ 

 Changing this to logarithms, of course, reduces 

 it to 



Log W= Log a+b Log Z, 

 which is a straight-line relation easy and con- 

 venient to compute by the standard method of 

 minimizing the squared deviations. (The reduced 

 logarithmic data from the observations are pre- 

 sented in table 15.) Plots of all the data in log- 

 arithms were made to test the assumption of linear- 

 ity and as a final check on the computations. These 

 plots showed no deviation from linearity, but they 

 did identify two aberrant observations, which were 

 located away from the regression line by several 

 times the standard error of estimate. These two 

 observations — one male and one female from the 

 sample of August 9, 1943 — were omitted from the 

 analysis. 



The several regression formulas (table 16) have 

 been computed to permit estimating the weight 

 from the length of the yellowtail for each sex in 

 each quarter and for combinations of the sexes 

 and quarters. When these formulas are used to 

 estimate the -weight of each sex at the mean length 

 of 35.869 cm. (table 17), the females are consist- 

 ently heavier than the males. The difference 

 varies from 0.041 pound in the first quarter to 

 0.119 pound in the second quarter — amounts 

 which are 4.5 percent and 14.4 percent of the aver- 

 age weight of the males. The greater difference 

 (in the second quarter) reflects the greater weight 

 of the females laden with ova. However, the 

 samples were taken slightly after the middle of 

 the spawning season when 67 percent of the ma- 

 ture females in the samples were spent (see 

 Spawning Season, p. 216). Therefore, the differ- 



