GITLF OF MEXICO COMMERCIAL SHRIMP POPULATION'S 



359 



neous observations (e.g., Springer and Bullis, 1956). 

 To simplify calculations, three suhsubareas or 

 depth zones were designated for eacii coastal sub- 

 area, viz., 0-10, 1 1-20, and 21-45 fathoms. Catch 

 and effort totals for each were obtained by com- 

 bining data from included 5-fathoni depth zones. 

 In a few instances where no effort was expended 

 in a particular depth zone, information derived by 

 consolidating data from ailjacent zones was 

 assumed indicative of population status in that 

 zone. 



To illustrate the mechanics of inde.x computa- 

 tion, let us select for treatment some statistics 

 typical of the Gulf coast shrimp fishery. Table 5 

 gives published commercial effort and brown 

 shrimp catch figures (June 195S) for each of 12 

 unequal subsubareas comprising the Te.xas Coast 

 offshore trawling grounds. If it is assumed that 

 these statistics are reasonably accurate and that 

 the biomass as manifested by the ratio of catch to 

 effort {di) was constant within each of the i sub- 

 subareas throughout the period indicated, then, 

 from the theory outlined above, the best index of 

 overall population biomass is the weighted mean 

 catch-effort ratio for each subsubarea. Hence 



^!rirfj = 0.68 = Fishable Biomass Index 



where ?/•,, the areal weighting factor, is the pro- 

 portion of the total occupied area represented by 

 the ?*" subsubarea. The following identity re- 

 lates, in terms of their notation, the corresponding 

 concepts of GuUand (1955, 1956) and Beverton 

 and Holt (1957): 



Table 5. — Commercial slatislics from the of shore (brown) 

 shrimp fishery in Ike Texas Coast area, June 1958 



S!-, j:y 



Si", 



^■'•(t;) ?'■ 



' J< 







12 ai So, 



--^w,d, 



where fi=gi/at is the fishing intensity in the 7'" 

 subsubarea; J'.Y, is the index of fishable biomass 

 in the i'" subsubarea; and the remaining notation 

 is as given in the heading of table 5. 



The value obtained, 0.68, may also be referred 

 to as the "catch per unit effective fishing intensity" 

 to distinguish it from the "simple catch per unit 

 fishing effort", 0.84, the value obtained and 

 employed as a population index if, as would have 

 been necessarj- had effort and catch stiitistics not 

 been available on a subsubarea basis, the biomass 

 were assumed uniformly distributed throughout 

 the coastal area being studied. Had the latter 

 situation prevailed, an overall population level too 

 high by about 24 percent would have been 

 indicated. 



Since commercial fishing effort tends to con- 

 centrate in areas of greatest density, the simple 

 catch-effort ratio usually "overestimates" overall 

 population density. Actually, this ratio would 

 constitute as good an index of population size as 

 that between catch and intensity if the effort 

 distribution bias remained constant. This not 

 being the rule, the catch-intensity ratio thereby 

 establishes itself as the more efficient and consist- 

 ent of the two possible estimators. In cases 

 where there is no alternative but to use the simple 

 catch-effort ratio as a biomass index, a high pro- 

 portion of its differential between successive time 

 intervals could just as easily be attributed to 

 changes in effort distribution as to real changes in 

 population biomass. 



Crutle monthly indices of biomass during those 

 stages of population development occurring in 

 inshore waters were secured by calculating the 

 ratio between total commercial catch and total 

 unweiglited effort as recorded for such watei-s. 

 These totals were ol)tained for each coastal area by 

 summing montiily catcli and effort data over 

 specific inshore waters included therein. Such 



