794 



Fishery Bulletin 101(4) 



The corresponding 95% confidence interval for the pre- 

 dicted mean values (vp) was evaluated by using the width 

 1.96 a„ where <t^ is the variance of y^ given by 



ol = V(p') + V{e) 



= (log(A').VpCr,)" + p(l-p)(T- 



(5) 



of different levels of abundance into eight categories for 

 these analyses. They were <1; 1 to <2; 2 to <3; 3 to <4; 4 to 

 <5; 5 to <10; 10 to <50 and 50 or more per 10-kg subsample 

 respectively. 



The SAS procedure NLIN was used to fit the power curve 

 for catch composition, as well as the separate power curves 

 for sampling error for the different abundance classes. 



where Vp = the predicted mean proportion; 



ct2 = obtained from the mean squared residuals 

 across 20 catches by 200 analyses; and 

 a\= the estimated variance ofk across 20 catches by 

 200 analyses. 



All p and y values are presented as percentages in 

 results. 



Abundance estimates The effect of taking different size 

 subsamples, on estimating the total number of a given spe- 

 cies in a catch, was determined by using a running mean (of 

 the estimate of abundance) calculated from the equation 



s = \(n / p- TotNum)! TotNiim\ 



(6) 



where s = the absolute proportion of sampling error; 



n = the observed number of that species after p pro- 

 portion (by weight) of the catch has been sorted; 

 and 



TotNum = the total number of individuals of that species 

 in the whole catch. 



The values for s are truncated at 1 for ease of presenting 

 results. 



We used the following statistical model in which s is sub- 

 tracted from 1 in order to correspond to the equation used 

 for species composition: 



1-s 



= p* -I- f, 



(7) 



where 1-s is fixed at 1 whenp = l,and the var(c) = (1-p) a^ 

 to ensure that there is no sampling error when the entire 

 catch has been sorted. 

 To obtain estimates of c^, we fitted the following model: 



(\-s)/p-p) = p' /yj{\-p)+e/^{\-p). 



(8) 



where the errors for this model have homogeneous variance 

 structure. The variance of a predicted ( 1-s) is given by an 

 equation similar to Equation 5 (for species composition): 



(jl,=(\og{p){\-s)a^f +(\- p)a-. 



(9) 



To examine the accuracy in recording the abundance of 

 all the species in a catch, we modeled the order (200 times) 

 in which subsamples were taken (as described above for 

 catch composition estimates). For each (species by trawl) 

 case, i.e. where a species was recorded at any level of abun- 

 dance, we calculated the sampling error s for ranges of p 

 from 0.1 to 0.9. We grouped all the (species by trawl) cases 



Results 



General results 



Catches ranged in size from 71 to 445 kg, with an aver- 

 age of 117 species per trawl (84 fish and 33 invertebrate 

 species). A total of 140,253 fish and invertebrates were 

 recorded from 323 subsamples taken from the 20 prawn 

 trawl catches that were sorted entirely (Table 1). Sub- 

 samples weighed, on average, 11.2 kg and contained 434 

 individuals (or 389 individuals per standardized (std) 10- 

 kg subsample). We identified a total of 276 fish and 141 

 invertebrate species. 



A total of 69.3% (1617 out of 2333) of the (species x trawl) 

 cases of relative abundance were recorded at ratios of less 

 than one individual per std 10-kg subsample (or less than 

 one in every 389 individuals), when averaged over all 20 

 catches; they were classed as "rare" (Fig 2). A further 19% 

 (442 out of 2333) of the (species x trawl) cases of relative 

 abundance were recorded at ratios that fell between one 

 individual per std 10-kg subsample and less than five in- 

 dividuals per 10-kg subsample (or between one in 389 and 

 less than five in 389 individuals!, when averaged over all 

 20 catches; they were classed as "common." The remaining 

 11.7% (274 out of 2333) of the (species x trawl) cases of 

 relative abundance were recorded at ratios of five or more 

 individuals per std 10-kg subsample (or five or more in 

 every 389 individuals), when averaged over all 20 catches); 

 they were classed as "abundant" (Fig 2). 



Catch composition 



The number of species recorded increased as the weight of 

 sorted catch increased in 19 of the 20 catches. This rela- 

 tionship appeared to reach an asymptote in the remaining 

 large catch of 445 kg (Fig 3, A and B). 



After 10% of all 20 catches were sorted, the cumulative 

 percentage of species recorded ranged from 31% (in the 315 

 kg catch) to 78% (in the 182 kg catch) (Table 2). To detect 

 80% of the species present in a single catch, from 20% to 

 70% of the catch had to be sorted. 



Simulation modelling showed that sorting 10% of catch 

 weight detects (on average) 50% of the species present, 

 with the confidence interval ranging from 44%' to 57%' (Fig 

 4). Sorting 50% of the catch was necessary to detect 80% of 

 the species present. 



Abundance estimates The simulation model showed that 

 the mean sampling error curves (for the eight abundance 

 categories) decreased as increasing percentages of the 

 catch had been sorted (Fig 5). After 10% of the weight of 



