and 



VAR B Tk = £ VAR B, k 



(=1 •- 



'&)' 



• VAR CPUE 



,1 



■* 



(14) 



where a, indicates the number of stations in subarea i with length- 

 frequency data available for species k. 



Method 2. Where length-frequency data and/or length- 

 weight relationships were not available, the overall mean weight 

 per individual within each subarea was calculated from stations at 

 which the number of individuals had been reliably determined: 



Population numbers. — Because the numbers of fish caught 

 during each trawl were not always recorded, estimates of the 

 number of individuals within each subarea were usually obtained 

 by dividing the estimated popuation weight by the mean weight 

 per individual: 



w ik = 



y=i 





m 



uk 



(19) 



N, 



ijk 



A 



= k 



ik —, 



(15) 



where P ik is the estimated number of individuals of species k in 

 subarea i available to the sampling gear. Depending on the avail- 

 ability of data for each species and subarea, the mean weight per 

 individual (w ik ) was computed by either of two methods. 



Method 1 . Where length-frequency data were available from 

 most stations ( >50% of total) and the relationship between the 

 length and weight of individuals (w = a • 1*) within each subarea 

 had been determined, then mean weight at each station with 

 length-frequency data was computed: 



L ijk 



1=1 



syki . w ik i 



w Uk = 



hjk 



(16) 



Li s ijkl 

 / = ! 



where s ilkl is the number of individuals of species k of length / 



"tiki 

 within each length-frequency subsample, w lkl is the calculated 



weight (from the length-weight relationship) of individuals of 



length /, and L is the number of size categories recorded. The 



number of individuals caught per standard sampling unit (1 .0 km) 



at each station with length-frequency data was then estimated as 



Sijk ~ 



CPUE 



ijk 



(17) 



where W indicates observed catch weight, N is the number of 

 individuals within each catch, and « ; is the number of stations 

 with determinations of numbers of individuals. 



With both methods, estimates of population numbers for the 

 entire survey area were the sum of the population estimates for 

 the individual subareas. 



Population size composition.— For species for which length- 

 frequency data had been collected, estimates of the numbers of 

 individuals (available to the trawl) of each sex within 1 cm size 

 classes were made by proportioning the total population estimate 

 for each subarea by the overall fraction of each size class within all 

 length-frequency observations. 



At each station with accompanying length-frequency data, the 

 number of individuals (samples) within each sex and centimeter 

 size class was estimated by expanding the length-frequency sub- 

 sample to the total catch (per standard sampling unit): 



*ijk 



ijklm s ijklm 



2 J2 s ' jkin 



m=\ 1=1 



(20) 



where s rklm is the number of individuals within the length- 

 frequency subsample of species k at theyth station of subarea /' for 

 length / and sex m, and L is the number of size classes 

 represented. 



The number of individuals (population) within sex and cen- 

 timeter size classes for each statistical subarea was then estimated: 



»» 



The overall mean weight per indhidual within each subarea was 

 then calculated: 



CPUE 



J=\ 



Uk 



j=\ 



ijk 



(18) 



Mm ~ r ik 



L * 



tjkim 



J2 ]C s 'j kim 

 j=\ i=i 



(21) 



l k was determined from Equation (15), and «, indicates 



where P lt 



the number of length-frequency samples 



The overall size composition of populations within the total 

 survey area was determined by summing the estimated numbers 



10 



