NELSON and AHRENHOLZ: CHARACTERISTICS OF GULF MENHADEN 



SUSTAINABLE YIELD AND 

 POPULATION SIMULATION 



Production functions were developed from the 

 1946-79 catch and effort data to provide an estimate 

 of maximum sustainable yield (MSY) for gulf men- 

 haden. Application of a standard parabolic surplus 

 production model (Schaefer 1954, 1957) yields an 

 MSY estimate of 553,000 t at 555,000 vessel-ton- 

 weeks. Past updates of MSY for the Gulf fishery have 

 shown continual increases as additional years are 

 added. Chapoton (1972) estimated an MSY of 

 430,000 t for the 1946-70 period, and Schaafs 

 (1975a) estimate of 478,000 t included the 1971 and 

 1972 catch and effort. 



For the years in which estimates of catchability 

 coefficient (q) were calculated (1964-77) nominal ef- 

 fort was adjusted to the mean population q of that 

 period. For that time period, mean catchability coef- 

 ficient was divided by the estimate of population F 

 each year, to provide an estimate of effort adjusted 

 for "average" conditions from 1964 to 1977. 



A parabolic surplus production function was ap- 

 plied to the 1946-79 data set, with adjusted effort 

 used instead of nominal effort for 1964-77. The 

 results were similar to model results using nominal 

 effort with an estimated MSY of 541,904 t at an ef- 

 fort of 505,483 vessel-ton-weeks (Fig. 8). A general- 

 ized stock production model (PRODFIT) which 

 allows the shape of the curve to vary based on a least 

 squares fit to the data (Fox 1975) was also applied, 

 yielding an estimate of MSY of 636,886 t at an ef- 

 fort of 531,201 vessel-ton-weeks (Fig. 8). 



The two curves provide estimates that vary by 

 about 95,000 1 with the PRODFIT model indicating 

 a sharp drop in yield after MSY is exceeded. 



An estimate of MSY based on biological charac- 

 teristics should be more reliable than one based on 

 yield and nominal effort, particularly when there is 

 not a clear nominal effort-effective effort relation- 

 ship. Accordingly, we applied a population simula- 

 tion model (Walters 1969) for the 1964-77 period 

 which incorporated our estimates of growth, 

 spawner-recruit relationship, fishing mortality, and 

 natural mortality. This estimated the impact of fish- 

 ing mortality on stock and yield at an array of fish- 

 ing mortality rates. The model can also iterate to 

 MSY. Underlying assumptions of the Walters' 

 model are that the 1) spawner-recruit relationship 

 incorporated is realistic, 2) array of F's accurately 

 reflect the distribution of fishing effort and avail- 

 ability at age, and 3) time increment estimates of 

 weight are sufficiently brief to realistically estimate 

 both population and catch biomass during the 



fishing periods. The model calculates population 

 biomass, yield, residual spawners of age 2 and 

 greater, and incoming recruitment. We used weight- 

 at-age data described in the section on average size 

 and growth (Equations (1) and (2)), and used the 

 spawner-recruit relationship developed for the 

 number of spawners and recruits (Equation (7)). The 

 instantaneous natural mortality rate was 1.1 as 

 discussed earlier. Fishing mortality could not 

 precisely mimic that for the fishery, because the 

 program requires either zero fishing mortality or a 

 constant fishing mortality for any within-year incre- 

 ment. However, it does allow for an array of multi- 

 pliers at a given fishing mortality, providing dif- 

 ferent F's for each age, if desired. Therefore, we 

 were able to vary fishing mortality by age, but used 

 either zero or a constant fishing mortality for 

 quarterly increments within each year. Since fishing 

 mortality was essentially zero on age-0 fish and was 

 inconsistent between years, a fishing mortality rate 

 of zero was applied to that age group. For age 

 groups 1-4, all of the fishing mortality was by defini- 

 tion imposed equally in quarters 2 and 3 (April- June, 

 July-September), and no fishing mortality was ap- 

 plied in quarters 1 and 4, even though we knew that 

 fishing mortality during the July- September period 

 was consistently higher than that observed for the 



900 r 



800- 



700- 



200 



100- 



100 200 300 400 500 600 700 800 

 EFFORT (Thousands of Vessel Ton Weeks) 



Figure 8.— Parabolic (dashed line) and prodfit (solid line) surplus 

 production function models fitted to catch and effort data for the 

 gulf menhaden fishery from 1946 to 1979, with 1964-77 data being 

 estimates of effective effort, based on adjustments from calculated 

 catchability coefficients for those years. 



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