584 



Fishery Bulletin 98(3) 



Procedure for estimating bycatch with the 

 general linear model 



In the bycatch estimation procedure with CPUE, it is 

 assumed that the estimated annual shrimping effort is 

 known and no variance is associated with this value. 

 Therefore, we restricted our evaluation to the general 

 linear model method to estimate the bycatch rates (CPUE) 

 within each stratum. The general linear model is defined 

 for each bycatch species by Nichols et al. ( 19872) as 



Logjf, (CPUE + 1 ),,<.,„, = r7iean + dataset, + 

 year + season/. + area/ + depth^^^ + f, ^^^^ , 



(1) 



vhere 



CPUE = the catch in numbers per trawl for 



each hour of shrimp fishing; 

 mean = the overall mean; 

 dataset HI = a fixed effect term differentiating 

 commercial shrimp fishing from 

 research trawls; and 

 the terms year (j). 

 season (k), 

 area (I), and 



depth (ml = also fixed-effect terms characteriz- 

 ing the spatiotemporal variability of 

 shrimp bycatch. 



This model assumes that the error terms are random, 

 independent, and normally distributed, with equal vari- 

 ance throughout. Predicted catch per trawl net for each 

 hour of shrimp fishing is then estimated for each stratum 

 for the commercial shrimp fishery as 



CPUE = 10 



1»1 1S1,).«.WSI 



(2) 



where 



Y = the general linear model predicted logj^ 

 (CPUE+\);anA 

 RMS = the residual mean square from the general 

 linear model. 



The RMS term is required to estimate the arithmetic mean 

 from the geometric mean of the assumed lognormal distri- 

 bution. The constant 1.1513 is a correction factor for esti- 

 mations derived with log base 10 instead of the natural 

 log. 



The predicted CPUE in each stratum is then multiplied 

 by the estimated shrimping effort in the corresponding 

 stratum. CPUEs are estimated for each trawl net. An aver- 

 age of two trawl nets per commercial shrimp vessel for 

 the 1972-95 time series is assumed owing to the lack of 

 information on number of nets per boat for each stratum 

 (cell in the matrix configuration) or other grouping cate- 

 egory. Total annual bycatch estimates for a given species 

 are then simply the sum of the commercial bycatch (;=1) 

 in all strata for that year (,/) as 



where /^^.,^, = the estimated total shrimping effort (hours 

 of fishing) for yearj, area k, season /, and 

 depth zone m. 



The general linear model estimates an approximate vari- 

 ance for the arithmetic mean CPUE for each cell as 



where Y and i?MS = the predicted log^, (CPUE+1) and 

 the residual mean square respec- 

 tively; 

 S~ = the estimate of variance of the pre- 

 dicted logio (CPUE+1> for the cell; 

 and 

 rdf = the residual degrees of freedom. 



No variance estimates for the estimated shrimping effort 

 are included in this model; thus effort is considered as if it 

 were known exactly (Nichols et al.^). 



The database for estimating shrimp bycatch CPUEs was 

 derived from information collected in several projects. The 

 current database comprises two types of data sources: 1) 

 direct measurements of finfish catch by observers onboard 

 of commercial shrimp vessels, and 2) catch rates from 

 research surveys. Direct observations came from four main 

 programs: the Sea Turtle Incidental Catch and Mortality 

 Project (Henwood and Stuntz, 1987), the Excluder Trawl 

 Device Evaluation Project (Henwood and Stuntz, 1987), 

 the Shrimp Fleet Discards Project (Pellegrin, 1982), and 

 the Cooperative Shrimp Bycatch Characterization Project 

 (NOAAM. Direct observations were discontinuous in time 

 and space; in particular, no onboard commercial vessels 

 observations occurred between 1982 and 1991. Research 

 observations came primarily from two annual trawling 

 projects: the Fall Groundfish Surveys and the Summer 

 SEAMAP Program. With over 22,000 tows documented from 

 1972 through 1995, research observations were the main 

 source of the bycatch database. Research obsei-vations were 

 restricted to tow surveys with the RV Oregon II equipped 

 with a standard 40-ft shrimp trawl (Nichols et al.-*). 



For estimating bycatch, the U.S. Gulf of Mexico was divided 

 into four geographic areas, two depth zones, and three sea- 

 sons. Aj-ea 1 covered the Texas coastline, area 2 covered the 

 Louisiana coast, area 3 covered the Alabama and Missis- 

 sippi coasts, and area 4 covered to the Florida West Coast 

 and the Lower Florida Keys. Two depth strata were defined 

 by using the 10-fathom depth as the divider of inshore and 

 offshore regions. Temporal variability of shrimp bycatch was 

 taken into account by including three seasons: 1) January- 

 April, 2) May-August, and 3) September-December 



Annual estimates of bycatch for the finfish category (i.e. 

 all fish species, in weight units instead of numbers offish), 

 and for three fish species (Atlantic croaker, Spanish mack- 



Byeatch^=2x'^CPUE,,„„xf^, 



(3) 



■■* Nichols S.,A. Shah. G.J. Pellegrin and K.Mullin. 1990. Updated 

 estimates of shrimp fleet bycatch in the offshore waters of the US 

 Gulf of Mexico 1972^1989. Report to the Gulf of Mexico Fish- 

 ery Management Council. The Commons at Rivergate 3018 U.S. 

 Highway 301 N., Tampa, FL 33619. 



