Heales et al : Effect of size of subsamples on estimates of catcfi composition and abundance. 



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occurred at many different levels of relative abundance. To 

 obtain an overview of how rarely, or how frequently, differ- 

 ent species occurred in catches, we reduced each occurrence 

 of a species in a catch to an index of relative abundance. We 

 concentrated solely on determining the accuracy of taking 

 different size subsamples in representing the range of rela- 

 tive abundances (from very low to very high) of the species 

 in these catches. 



The relative abundance indices were based on the av- 

 erage number of individuals of a given species that were 

 recorded in a standardized 10-kg subsaniple taken from 

 that catch. To generate this index, we used the following 

 equation; 



n = 10 X (TotNum I Weight). 



(1) 



where n = the mean number of individuals of a given spe- 

 cies per 10-kg subsample; 



TotNum = the total number of individuals of that species 

 in the whole catch; and 

 Weight = the total weight of the catch in kg. 



We derived a separate index of abundance for each species 

 in every catch where it was recorded. Thus, a species that 

 occurred in all 20 catches would have 20 different abun- 

 dance indices in the analysis. 



To highlight the differences in distribution between 

 the two extremes of the "rare" species and the "abundant" 

 species when estimating catch composition, we grouped 

 the indices of abundance into 11 categories, ranging from 

 less than one individual per 10-kg subsample, up to 10 or 

 more individuals per subsample. Species with abundance 

 indices of less than one individual per 10-kg subsample 

 were classed as "rare"; those with one to less than five 

 individuals were classed as "common"; and those with five 

 or more individuals per 10-kg subsample were classed as 

 "abundant." 



For example, the common ponyfish (Leiognathus moreto- 

 niensi), was classed as "abundant" in 11 of the 20 catches, as 

 "common" in eight catches, and "rare" in one catch. Because 

 a species could have different abundance indices in each 

 catch, individual species are not referred to by name in the 

 results. Instead, we refer to the occurrence of each species in 

 a catch, as one case of some relative abundance index that 

 was recorded in that catch (i.e. one "case" of species by trawl 

 abundance). The relativefrequency of all the cases (i.e. abun- 

 dance indices) in each of the three abundance categories 

 (throughout the combined 20 catches) was then calculated. 



To calculate the average number of bycatch individuals 

 per 10-kg subsample (over all the catches), the following 

 equation was used: 



X = 10 X (Total number /Total weight) 



(2) 



where 



X = the mean number of bycatch individuals 

 (per 10-kg subsample); 

 Total number = the total number of all bycatch individu- 

 als (summed over all 20 catches); and 

 Total weight = the total weight (kg) of all bycatch indi- 

 viduals (summed over all 20 catches). 



We then examined the average occurrence ratios within 

 10-kg subsamples for the "rare," "common ," and "abundant" 

 species. 



Catch composition To examine the relationship between 

 the number of recorded species and the weight of sorted 

 catch, the subsamples were first analyzed in the order 

 that they were collected. The cumulative number of spe- 

 cies (both fish and invertebrates) was plotted against 

 the cumulative weight of sorted catch, for each of the 20 

 catches. Each catch was also summarized in terms of the 

 percentage of species recorded for each 10% increment of 

 weight of sorted catch. 



The order (position on the sorting tray) where the sub- 

 samples were collected on both the research and commercial 

 vessels was just one of the many possible ways that a catch 

 can be divided into 10-kg subsamples. To determine the level 

 of accuracy in recording the number of species in a catch, 

 we examined 200 combinations of subsample selection (with 

 no replacement), by randomly reordering the subsamples 

 using Monte Carlo simulations for each catch. We also cal- 

 culated the cumulative number and percentage of species 

 recorded, as well as the cumulative weight and percentage 

 of the sorted catch, for each catch. The proportion of species 

 recorded was fitted as a power function of the proportion 

 of the weight of sorted catch, as described by the following 

 asymptotic equation (Snedecor and Cochran, 1980): 



y=p'' + e. 



(3) 



where y = the proportion of species recorded; 



p = the proportion of the weight of catch sorted; 

 k = the mean exponential parameter; and 

 e = the random normal error term, with unequal 

 variance. 



The variance of £ is assumed to be p (1-p) a^ to ensure 

 that the variance of y is fixed at zero when p = and 1. 

 This formulation has the property that, when none of the 

 catch has been sorted, no species will have been recorded. 

 It also ensures thaty = 1 whenp =1, i.e. when all the catch 

 has been sorted, all of the species have been recorded. The 

 estimate of ct- was obtained by fitting the following model 

 according to the SAS procedure NLIN (version 7, SAS Inst., 

 Cary NC): 



y 



* = p' I ^{pO-p)) + £' 



(4) 



where y* = y H(p(l-p)) and £* = E/^(p(l-p)); and 



£* now has homogeneous variance structure. 



Different k values were estimated for each catch to re- 

 flect the variation in the relationship. The mean ki value for 

 a given catch (! = l-20) was obtained from 200 analyses for 

 that catch. The predicted y values i.e. y^ (atp=0.1, 0.2 etc. 

 to 1.0) were obtained by averaging p*' values across_the 20 

 catches (note that this is different from p'- where k is the 

 mean k value for the 20 catches). We defined the y^ values 

 as the predicted expected proportion of species recorded 

 after p proportion of catches had been sorted. 



