214 



FISHERY BULLETIN OF THE FISH AND WILDLIFE SERVICE 



o 



2 



THOUSANDS OF DAYS OF FISHINQ.Z 



Figure 22. — Relation of total instantaneous mortality 

 rate, i, and fishing effort, /, in the southern New Eng- 

 land stock. 



sidered to be from the third quarter of one year 

 through the second quarter of the following year. 13 



When we assume a linear relation between fish- 

 ing effort and mortality and compute the regres- 

 sion (fig. 22), we find 



^= -0.302 + 0.288/ 

 when / is the amount of fishing in thousands of 

 days. 



By definition i=p + q and, of course, when 

 p = 0, i=q, but q must be positive. Therefore, an 

 estimate of ^=-0.302 with no fishing cannot be 

 interpreted as q= -0.302. Since our estimate of i 

 was based on abundance indexes computed from 

 the fishing effort of the fleet, we immediately sus- 

 pected that the availability of the fish was not 

 constant. Not only was it not constant or even 

 random, but there must have been an average an- 

 nual increase in availability of 0.302 +q, if we 

 are to accept the relation of the apparent total 

 mortality to the amount of fishing. 



Some additional evidence of increasing avail- 

 ability may be found in the length composition 

 curve (fig. 7). Ricker (1948) and others have 

 considered that the ascending laft limb and dome 



13 We also attempted to relate the annual mortality rate for each 

 quarter to the fishing effort. The mortality, », was computed 

 from the relative apparent abundance of 3-year-old and older 

 fish In quarter N and of the 4-year-old and older fish In quarter 

 # + 4. Various combinations of fishing effort (table 38) were 

 tried to find the best correlation with mortality, and the most 

 satisfactory combination was found to be quarters N through 

 N+4 (r = 0.68). The correlation between mortality and effort 

 in quarter N was only 0.37, which is not statistically significant. 

 The best regression was i= —0.379 + 0.312/, with / expressed in 

 thousands of days. 



of age-frequency curves represent groups of fish 

 not fully available to the fishery. This applies 

 equally well to length-frequency curves when the 

 rate of growth in length is uniform (as it very 

 nearly is in yellowtail in the catch ) . If we accept 

 this interpretation, then clearly the males less 

 than 33 cm. long were not fully available nor were 

 the females less than 39 cm., although this is less 

 clear due to the spread-out curve. If we assume 

 that changing availabilty is a function of length 

 rather than age, we observe that among males 

 most 2-year-olds, about half of the 3-year-olds, and 

 some 4-year-olds, were below the 33-cm. point of 

 inflection (age and length-frequency data in ap- 

 pendix table D-2, p. 254). Even older females 

 were below the 39-cm. size, as well as most 2- and 

 3-year-olds, about half of the 4-year-olds, and some 

 5- and 6-year-olds. Such evidence suggests that 

 there was increasing availability to a large extent 

 among 2- to 4-year-olds, the most abundant age 

 groups in the fishery, and to some extent among 

 most of the other age groups. 



Not only is there evidence of increasing avail- 

 ability with age, but also of erratic changes in 

 availability due to other causes. Such is indicated 

 by the increases in catch per day of certain year 

 classes at advanced ages (table 35) . The 1940 year 

 class (age 5, fourth quarter) and the 1943 year 

 class (age 4, third quarter) are examples. The 

 great variability in the rate of decline of the year 

 classes and the erratic changes in the seasonal 

 catch (p. 197) suggest that changes in availability 

 are common occurrences. 



There is also evidence of increasing availability 

 with time, because 2-year-old yellowtail appar- 

 ently became more available to the fishery during 

 the period of study. We have previously noted 

 that the 1941 year class was probably an especially 

 good one, and this is borne out by the data in 

 table 35 which show that this year class usually 

 was the most abundant among the fish with 3 or 

 more annuli, from the second quarter through the 

 fourth. We notice, however, that it was not es- 

 pecially available as 2-year-olds, for in none 

 of the quarters did it make any particularly 

 large contribution. On the other hand, the 1943 

 and 1944 year classes were especially abundant as 

 2-year-olds during the third and fourth quarters 

 (table 35), but the 1943 year class was scarce 

 among the older age classes in subsequent years. 



