ABRAMSON and TOMLINSON: APPLICATION OF YIELD MODFXS 



the annual yield could theoretically be increased 

 to about 2.8 million pounds by shifting fishing 

 mortality so that I's and II's suffered equal rates. 

 This would involve a 75% reduction in fishing 

 mortality at ages II and III and assumes that 

 the population with the new age structure would 

 continue to produce 1.155 billion recruits. Such 

 a change would also produce a reduction of 26% 

 in the average size of shrimp in the catch and 

 pose the problem of how the mortality pattern 

 could be so altered. 



INTER-MODEL COMPARISONS 



Because we were unable to determine a spawn- 

 er-recruit relationship and produce a self-gen- 

 erating form of the dynamic pool model, a 

 realistic comparison of the results from the two 

 types of models is not possible. In addition, the 

 yield-per-recruit model treats natural mortality 

 and growth parameters as constant while in the 

 Schaefer model they are components of density 

 dependent terms. 



It is of interest to note that the biomass esti- 

 mates obtained from the age-structured catch 

 data by the Murphy method are in general agree- 

 ment with the corresponding estimates of the 

 Schaefer model. Although this does not compare 

 the yield-per-recruit and Schaefer models, we 

 feel it indicates some support of the Schaefer 

 model from a semi-independent source. Another 

 point of agreement between the yield-per-recruit 

 and Schaefer models was that, given the average 

 recruitment over the 1961-67 period, the former 

 required a 75% increase in fishing mortality to 

 produce the Schaefer model's maximum sustain- 

 able yield while the average annual effort ex- 

 pended during that period would require a 68% 

 increase to reach the optimum effort level of the 

 Schaefer model. However, as can be seen from 

 Figure 9, maximum yield-per-recruit is predict- 

 ed to occur at a much higher effort level under 

 the previously mentioned assumption of constant 

 parameters. 



It seems clear from the foregoing discussion 

 of results relative to the two models that man- 

 agement procedures should be based on the 

 Schaefer model at the present time. 



PROPOSED MANAGEMENT STRATEGY 



Fitting an equation such as the Schaefer model 

 to a set of actual catch and effort data may be 

 viewed as merely an interesting exercise unless 

 one has to make actual management recommen- 

 dations based upon the results. Then the situ- 

 ation becomes somewhat sticky. It is obvious 

 that a simple deterministic model such as Schaef- 

 er's will not precisely describe the dynamics of 

 a fish population. At best, thei'e will be fluctu- 

 ations in recruitment, growth, and catchability 

 which will cause some consternation to the man- 

 ager attempting to use such a model. 



In the case of the shrimp fishery, the manage- 

 ment strategy we propose treats the Schaefer 

 model estimates as exactly correct, responds to 

 indicated deviations from the optimum popula- 

 tion size in a relatively arbitrary but conserva- 

 tive manner, and integrates the Oregon and 

 California fishing. This conservative strategy- 

 attempts a gradual reduction in the biomass 

 when the model estimates it to be above Popt and 

 a rapid increase in the stock size when it is es- 

 timated to be below Po„t. To formulate this pro- 

 cedure, let Q be the catch quota (California + 

 Oregon) and CeiP) = HP- — KP be the equi- 

 librium yield obtainable from a population of 

 size P. With P{t) the population when the next 

 fishing season commences. 



Q 



Pit) - P 



opt 



+ Ce 



( 



Pit) + Popt 



)■■ 



Pit) > Popt, 



= Pit) — Popt + CelPit)]] 

 Pit) < Popt. 



When the model predicts the stock is in the sur- 

 plus condition we are, then, proposing to harvest 

 one-half of this surplus plus the predicted sus- 

 tainable yield at the point midway between 

 Pit) and Popt. A predicted stock deficit evokes 

 a procedure which harvests the sustainable yield 

 at Pit) minus the amount by which the stock 

 falls short of Popt. For example, the 1970 Cal- 

 ifornia shrimp quota of 3.4 million pounds was 

 set by the above method with Pit) — Popt = 



1039 



