ABRAMSON and TOMLINSON: APPLICATION OF YIELD MODELS 



Table 4. — Hypothetical structure of age-structured shrimp catches and exploitation rates as arranged for analysis 



by the Murphy method. 



of the E values from the age III analysis used 

 as starting values for the year class solutions. 

 An additional problem occurred which result- 

 ed in some final changes that were arbitrary and 

 difficult to explain. For some years, especially 

 1955 through 1959, estimates of population size 

 were quite low and q very high. It was demon- 

 strated that a good transfer from age III to age 

 II across the closed season did not occur for the 

 year classes involved. Therefore, with year 

 classes 1953 through 1958, 1962, 1963, and 1966, 

 the estimation from the last catch-month at age 

 II to the first catch-month at age I disregarded 

 estimates during age III. It is hoped that the fi- 

 nal result justifies these arbitrary decisions. It 

 was also noted from the dots on Figure 3 that a 

 growth curve from the sample data (Table 2) 

 for seasons 1955 through 1959 indicates faster 

 growth during the closed season than during the 

 open season. This seems extremely doubtful in 

 light of other contrary evidence and indicates 

 that the problem was caused by inaccurate aging. 

 Since age III shrimp make up such a small frac- 

 tion of the catch and population biomass, it was 

 not considered to seriously discredit final results. 



Fishing Mortality Estimates 



Estimation of monthly instantaneous fishing 

 mortality coefficients, {F) , was accomplished for 

 each age group in each month by applying the 

 Murphy method, as described above, to catches 



in numbers (Table 2) . Since M = 0.12 was used 

 as monthly instantaneous natural mortality for 

 all months and ages, monthly exploitation rates, 

 E, and monthly survival rates, s, may be obtained 

 from 



E 



f\i — e-^f'+o-i2)1/(F + 0.12), 



and 



s = e 



-(F + 0.12) 



The estimates of F (Table 5) varied consider- 

 ably, but age I was always exploited at a rate 

 lower than ages II and III. During the 7 years, 

 1955-1961, average estimated F was 0.015 for 

 age I, 0.056 for age II, and 0.057 for age III. 

 In the 7 years, 1962-1968, F{1) = 0.023, F{ll) 

 = 0.116, and F(III) = 0.159. Averages for 

 all 14 years were F (I) = 0.019, F(II) = 0.088, 

 and F(III) = 0.089. Thus, as previously stated 

 for a condition of estimation, ages II and III 

 were exploited at about the same rates. 



Converting fishing mortality to exploitation 

 (Table 6), it was estimated that the fishery was 

 removing about 5% of ages II and III and 1% 

 of age I each month of fishing. Fishing intensity 

 increased over the years and during 1962-1968 

 exploitation was nearly double that of 1955-1961 

 for each age. During the period 1961-1967, July 

 and August were the most important months, 

 followed by May, June, and September, while 

 April and October were of little importance. 

 Average F (Table 10) during these years, for 



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