210 



FISHERY BULLETIN OF THE FISH AND WILDLIFE SERVICE 



SURVIVAL, MORTALITY, AND AVAILABILITY 



Three methods were used to estimate survival 

 and mortality rates, no one of which is completely 

 satisfactory but each of which contributes some- 

 thing to the sum of the information. These meth- 

 ods are as follows: (1) Immediate fishing 

 mortality determined from the ratio of early re- 

 turns of tagged fish to total number released ; (2) 

 total mortality determined from the ratios of the 

 numbers of tag returns in successive years; and 

 (3) total mortality determined from the ratios of 

 the apparent abundance of certain age groups to 

 comparable groups in successive years. 



Immediate Fishing Mortality 



The recaptures of tagged yellowtail during the 

 first 10 days after release on the principal fishing 

 areas usually show a high mortality rate (table 

 32). The recapture rate may be converted to the 

 annual fishing rate, to, 9 if we assume that the 10- 

 day mortality is equal to the instantaneous fishing 

 mortality rate/?, where m= l — e' p . 



The calculations (table 32) yield estimates of 

 to ranging from 0.43 to 0.97 and averaging 0.86 

 from the sum of returns and releases. These values 

 can be considered minimal estimates of the annual 

 total mortality rate a of the group tagged because 

 natural mortality is not included. They will, of 

 course, have been reduced by deaths due to tagging 

 during the 10-day period, but because only lively 

 fish were released such deaths should not have been 

 immediate. 



Table 32. — Early recaptures of tagged yellowtail released on 

 the principal Ashing grounds off Nantucket Shoals and No 

 Mans Land 



Such a high rate of exploitation for a small 

 group of fish is subject to criticism as not being 

 representative of the rates experienced by the 

 population, unless availability is not uniform 

 among all parts of the population. However, 



' This and other symbols for mortality rates are used as defined 

 by Rieker (1948) and Widrlg (1954). 



rates calculated in this way are probably indica- 

 tive of the mortalities experienced by groups of 

 fish while completely available to the fishery. All 

 of the lots except No. 10 were released from com- 

 mercial fishing vessels, and in such an operation 

 the tagged fish probably were released over a sub- 

 stantial part of the area that the fleet was fishing 

 at the time. One characteristic of the yellowtail 

 fishery has been the appearance of concentrations 

 of yellowtail at various places with a subsequent 

 shift of the fleet to those areas. We have actually 

 observed a group of about 50 vessels fishing at one 

 time in an area of not more than 300 square miles. 

 At the mean rate of fishing found from the tag 

 returns, the "half life" (the period required to 

 catch half of the fish exclusive of any natural mor- 

 tality) would be 123 days. 10 At the maximum 

 rate of fishing (lot No. 11), the half life would be 

 only 72 days — a period similar to the length of 

 time fishing was frequently pursued intensively 

 in a small area. 



Mortality from Tag Returns in Successive Years 



Estimates of the rate of fishing, to, derived from 

 the early recaptures are not greatly different from 

 estimates of the total annual mortality rate, a, de- 

 rived from the tag returns in successive years. 11 

 If we consider the same four experiments (lot 

 Nos. 4, 5, 10, and 11) used to estimate immediate 

 mortality, we note that 103 yellowtail were recap- 

 tured during the first year, 11 during the next 

 year, and 1 in the third year (table 33). Rieker 

 ( 1948) has pointed out that such a series of recap- 

 tures provides direct estimates of the survival 



f? R 



rate, 8=1 — a, simply by taking -^- , -^-, etcet- 

 era. If we do this, we find s= :™ =0.11, 

 a=0.89. Between the second and third years, 

 a=l— rpr =0.91, but this estimate, of course, is 



much less reliable because of the small numbers. 

 Similar computations for the total returns in 

 successive years from all the lots released in the 



25 

 southern New England stock show s= -~?~ , a=0.88 



between the first year and the second after tagging. 



10 The half life was computed by substituting the observed 

 recapture rate p and 0.5 for m in the "compound Interest" 

 formula m = l — (l-"p") n and solving for n. Then, n times the 

 period in days gives the half life. 



"These years start with each release date and are different 

 for each lot released. 



