McConnaughey and Conquest Comparative trawl-survey estimation based on lognormal theory 



1 15 



tion over using any single estimator alone. For the 

 Estuary data, trends in abundance routinely paral- 

 leled one another, differing only by their relative mag- 

 nitude (Fig. 7a). Characteristically, estimates of u from 

 the survey data obtained with the FM method exceeded 

 those of the AM, which, in turn, exceeded estimates of 

 the GM parameter (e MLN ). In some cases, trends in the 

 Coast estimates were diametrically opposed (Fig. 7b). 

 As expected, the GM estimate was consistently lower 

 than both AM and FM, reflecting the difference in the 

 population parameter being estimated. Noteworthy was 

 the reversal in the relative magnitudes of the AM and 

 FM estimates during the interval between Cruise 2 

 and Cruise 4. 



Discussion 



Conventional analysis of catch data and 

 alternatives 



Population estimates are routinely generated using 

 untransformed catch data and arithmetic mean calcu- 



1,400 



1,200 



"a 



& 1 ,000 

 800 



v> 



UJ 



D 



3 600 



O 



400 

 200 



12 



13 



14 



15 



14,000 

 12,000 

 10,000 



t 8,000 

 (0 



z 



w 6,000 



CD 



< 4,000 



O 



2,000 



12 3 4 5 



CRUISE 



Figure 7 



Comparison of three measures of central tendency calculated 

 for Cancer magister using monthly cruise data for (a) the 

 estuarine area (year 3) and (b) the coastal area (year 1). 

 (The order of the coast/estuary figures is deliberately reversed 

 here to illustrate certain results; see text.) 



lations (e.g., BIOMASS procedure of the U.S. NMFS, 

 Gunderson et al. 1978; STRAP procedure of Can. Dep. 

 Fish. & Oceans, Smith & Somerton 1981). Several 

 methods for reducing the variance associated with these 

 estimates of abundance have been used, often despite 

 recognizable limitations. These fall broadly into two 

 categories: (1) model-based approaches, which model 

 the underlying distribution of the data, and (2) design- 

 based approaches, which rely upon probability sam- 

 pling and large sample results. Smith (1990) compared 

 the two approaches for estimating resource abundance 

 with trawl surveys and concluded with an example of 

 a model-based predictive estimate using additional in- 

 formation (salinity, temperature, depth). Other ex- 

 amples of model-based estimation in fisheries applica- 

 tions include use of a weighted negative binomial 

 distribution (Zweifel & Smith 1981), the delta distri- 

 bution (Pennington 1983), and the geostatistical tech- 

 nique of kriging (Conan 1985). Stratification of the 

 sampling frame is a common example of a design-based 

 approach. Although this is theoretically appealing, 

 Gavaris & Smith ( 1987) have demonstrated that strati- 

 fied random sampling may be inferior to a simple ran- 

 dom design, because of suboptimal allocation of sta- 

 tions to strata. They suggest that a decrease in the 

 number of strata used in the eastern Scotian Shelf 

 groundfish survey would provide for more flexible allo- 

 cation of total sampling effort in the future. Unfortu- 

 nately, many of the problems attendant with specify- 

 ing stratum boundaries will persist; these include 

 interannual variability in distribution and abundance 

 of stocks related to environmental factors and the typi- 

 cal multi-species scope of most research trawl surveys. 

 Because of these difficulties, catch data are commonly 

 stratified after sampling is completed (Picquelle & 

 Stauffer 1985, Otto 1986). However, post-stratification 

 (i.e., a priori examination of catch data for the purpose 

 of assigning strata) is not a valid approach and is not 

 recommended (Cochran 1977). 



Other methods for estimation of abundance are ex- 

 pedient, yet may be based on the specious assumption 

 that extreme values are "outliers" and are therefore 

 not integral to the data set. Included is the practice of 

 eliminating extreme values or the use of trimmed (or 

 Winsorized) means (Halliday & Koeller 1981, Bates 

 1987, Harding et al. 1987, Smith 1981). Ignoring in- 

 stances where human error is involved, these ad hoc 

 procedures may introduce substantial negative bias to 

 estimates of the true population mean (compare u and 

 the trimmed means in Table 2), thereby contributing 

 to misleading conclusions about trends in the data. 



Design-based and model-based approaches 



A strict probability sampling approach (i.e., design- 

 based and without any underlying models) requires 



