Abstract. -The spatial distribu- 

 tions of marine biota are frequently 

 patchy. Samples taken from these 

 populations are characterized by val- 

 ues which are mostly small, relative 

 to the population mean, and a few 

 that are very large. It is therefore 

 difficult to estimate stock size using 

 conventional methods. We performed 

 Monte Carlo simulations based on 

 trawl data for Dungeness crab Can- 

 cer magister and compared the be- 

 havior of three estimators of central 

 tendency: sample mean, geometric 

 mean, and a lognormal estimate. Al- 

 though the sample mean is unbi- 

 ased, results indicate that single es- 

 timates of the population mean (and 

 thus population estimates obtained 

 using area-swept) may be overly sen- 

 sitive to extreme values; confidence 

 intervals are large and capture the 

 true value at a level well below that 

 prescribed. Estimates of the geomet- 

 ric mean exhibit more stable behav- 

 ior about its parameter, with mixed 

 results for the lognormal estimate. 

 We propose a conservative approach 

 based on comparison of trends found 

 in each of the three estimators. 

 Moreover, we suggest that abun- 

 dance of aggregated stocks should 

 be indexed with an estimator that 

 has more desirable statistical prop- 

 erties, such as the geometric mean. 

 This may reduce error associated 

 with conventional fisheries stock- 

 assessment practices and thus pro- 

 vide for more effective management 

 of overdispersed stocks. 



Trawl survey estimation using a 

 comparative approach based on 

 lognormal theory* 



Robert A. McConnaughey 



School of Fisheries. WH-10 



University of Washington, Seattle, Washington 98 1 95 



Present address. Alaska Fisheries Science Center, National Marine Fisheries Service. 



NOAA. 7600 Sand Point Way NE, Seattle, Washington 981 1 5-0070 



Loveday L. Conquest 



Center for Quantitative Science, University of Washington 

 Seattle. Washington 98195 



Effective scientific management of 

 fishery resources is dependent upon 

 reliable measures of stock abundance. 

 To this end, research trawl surveys 

 are routinely used in concert with 

 fishery catch statistics to provide es- 

 timates of population parameters. 

 The analytical procedures used often 

 rely on the assumption that statisti- 

 cal methods based on normal prob- 

 ability theory are appropriate and, 

 as such, that the individuals compris- 

 ing the population are not aggregated 

 in space (Elliott 1977). However, ma- 

 rine biota are commonly overdis- 

 persed, and frequently it is the loga- 

 rithms of abundance (or biomass) 

 which conform to the normal or 

 Gaussian distribution (reviewed by 

 McConnaughey 1991). Rather than 

 an artifact of sampling, in many cases 

 this spatial attribute is the product 

 of behavioral responses and/or physi- 

 cal processes affecting dispersal (e.g., 

 Epifanio 1987, Dew 1990). Samples 

 taken from these populations are 

 characterized by mostly small values 

 relative to the population mean, and 

 a few very large ones. Under these 

 circumstances, single estimates of the 

 population mean from the arithmetic 

 mean (sample average) may be too 

 low because very large values are of- 



Manuscript accepted 28 October 1992. 

 Fishery Bulletin, U.S. 91:107-118 ( 1993) 



■"Contribution 853 of the School of Fisheries, 

 University of Washington. 



ten underrepresented at the levels of 

 sampling effort common to research 

 trawl surveys. When large catches 

 are present in a sample, variance es- 

 timates may become excessively high 

 (e.g., Otto 1986). This may introduce 

 a high degree of uncertainty into the 

 resource management process which, 

 if ignored, can have potentially seri- 

 ous repercussions (Ludwig & Walters 

 1981). 



We investigated two alternative 

 measures of central tendency and 

 compared their statistical behavior 

 with that of the arithmetic mean. 

 These alternatives are the geometric 

 mean and a model-based estimate of 

 the arithmetic mean based on log- 

 normal theory. An evaluation of 

 trends based on a comparison of the 

 three estimators is proposed. This 

 approach may identify error associ- 

 ated with the conventional index of 

 abundance, thereby reducing the like- 

 lihood of false conclusions concern- 

 ing trends in stock abundance. 



Data and methods 



Monthly trawl surveys of Dungeness 

 crab Cancer magister abundance 

 along the southern Washington coast 

 provided representative values of 

 density (rc/ha) for analysis with 

 Monte Carlo techniques. Density data 



107 



