CAE.LOUET ET AL.; TRENDS TOWARD DECREASING SIZE OF SHRIMP 



more or less constant effects on comparisons be- 

 tween Texas and Louisiana and over the period 

 from 1959 to 1976, and therefore would have only 

 minor if any effects upon our conclusions. We 

 further recognize that each size category may in- 

 clude representatives of more than one peak of 

 recruitment, since they include catches taken over 

 the period of 1 calendar year. Therefore, it is likely 

 that any differences or trends in the time phasing 

 of peak fishing activity within Texas and 

 Louisiana within a year could contribute to the 

 observed differences and trends in size composi- 

 tion of the respective catches in the two States. 



ANALYTICAL METHODS 



Percentage (by weight, heads-off) was deter- 

 mined for each size category in reported annual 

 catches of brown and white shrimp from Texas 

 coast and Mississippi River to Texas for each of 

 the years from 1959 through 1976 (see Caillouet 

 and Patella 1978). Cumulative percentage (F) for 

 each size category was then determined for 

 catches of both species, from Texas coast and Mis- 

 sissippi River to Texas, and for each year. Percen- 

 tages were summed from the smallest shrimp 

 (highest count, ^68) to the largest (lowest count, 

 <15). 



An exponential model was chosen to represent 

 the relationship between cumulative percentage, 

 F, and size category, C, for brown and white 

 shrimp, for Texas coast and Mississippi River to 

 Texas, emd for the years 1959-76 as follows: 



F, = ae>>c, 



where F, = cumulative percentage (by weight, 

 heads-off) of catch in ith size cat- 

 egory 

 C, = lower limit of ith size category (Cj 

 = 15, Ca =21,.. .,C^ =68) 

 i = 1,2,. ..,7 

 a = constant 

 b = exponent 

 e = base of natural logarithm. 



The cumulative percentages, F, were trans- 

 formed to natural logarithms, and the 

 log£irithmic form of the model was used to esti- 

 mate parameters by least squares: 



InF, = ln(a) + bC, = ( 



where e = residual (deviation from regression). 



Thus, the logEirithmic form of the model describes 

 the relationship between transformed cumulative 

 percentage and size category, and represents size 

 composition of the reported annual catches. Note 

 that this linear relationship describing size com- 

 position of the reported annual catches is 

 achieved by transforming both the cumulative 

 percentage to In F and the weight per shrimp (in 

 pound, heads-off) to count (number per pound). 



Midpoints of size categories were not used be- 

 cause the size categories have unequal intervals, 

 an unavoidable result of using data based on size 

 categories developed by the shrimping industry. 

 Upper limits of size categories were not used, be- 

 cause we could not determine the upper limit of 

 the 2=68 category, and this category represented a 

 significant proportion of the catches. Also, we did 

 not use the <15 size category because we could 

 not determine its lower limit (zero was not realis- 

 tic), and this category represented a very small 

 fraction of the catches. Apparently, total mortal- 

 ity (natural and fishing combined) is such that 

 relatively small portions of the shrimp popula- 

 tions survive to be caught at sizes as large as 

 <15/pound. Because lower limits of size 

 categories were used for regression analyses, and 

 because the < 15 size category was not used in the 

 analysis, the magnitude of the ordinate intercept, 

 ln(a), is of no particular use. It is the slope, b ( = 

 exponent of the exponential model) that is of most 

 interest and use as an index showing the rate of 

 change in InF with C. Extrapolation below 15 

 count is not advised, because the linear relation- 

 ship does not apply beyond this point. 



In order to determine whether size composition 

 of the reported annual catches changed with 

 time, the slopes, 6, of the regressions of trans- 

 formed cumulative percentage on size category 

 were plotted against years, and straight lines 

 were fitted to points b and x ( = last two digits of 

 each year) by least squares, for brown and white 

 shrimp from the Texas coast and Mississippi 

 River to Texas, 1959-76 (Figures 2, 3). 



RESULTS AND DISCUSSION 



Slopes, 6, of the regressions of transformed 

 cumulative percentage versus size category, all 

 differed significantly from zero at the 99.9% level 

 of confidence, showing that the lineeir fit was good 

 (Tables 1, 2). The slopes changed with time as 



987 



