l.ENARZ and ADAMS: SOME STATISTICAL CONSIDERATIONS OF TRAWL SURVEYS 



systematic sampling was more precise than sys- 

 tematic sampling when school groups were dis- 

 tributed in a highly nonrandom way. Systematic 

 sampling was more precise than stratified sys- 

 tematic sampling when sampling density was 

 high. In other cases there were no significant 

 differences between systematic and stratified sys- 

 tematic sampling. 



Fiedler based allocations of sampling effort 

 among strata on results of previous sampling. His 

 results, in conjunction with those of Abramson 

 (1968) and Venrick (1978), indicate the difficulty 

 of determining optimum allocation of sampling 

 effort among strata in the marine environment. 

 The frustration of scientists who have attempted 

 to do so is aptly stated by Venrick: "Study A 

 demonstrated the dependence of the success of a 

 sampling design upon the interaction of that 

 design with the structure of the population being 

 sampled; thus, it would seem that intelligent 

 application of knowledge about the sampled popu- 

 lation should improve the design. It was, there- 

 fore, disconcerting to find that RSS every 20 m, 

 RSS-1, consistently performed as successfully as 

 did RSS-3 which was designed by a presumably 

 experienced worker (the author) with total knowl- 

 edge about the population to be sampled." 



We hope that improved knowledge on the dis- 

 tributions of populations will eventually result in 

 more efficient allocation of effort among strata of 

 systematic or random sampling schemes in the 

 marine environment. However, we point out that 

 fishermen still have their failures in attempting 

 to restrict their sampling effort to times and areas 

 of high fish catches in spite of years of experience, 

 sophisticated fish finding equipment — presum- 

 ably flexible sampling plans — and at times recent 

 information from their colleagues. 



EXAMINATION OF TRADE OFFS 



BETWEEN TOW LENGTH AND 



NUMBER OF TOWS 



The distance trawled is an important factor to 

 consider in the design of trawl surveys. Considera- 

 tions include distance needed to obtain sufficient 

 specimens for biological samples; time required to 

 set and retrieve a trawl, to cover the distance, and 

 to move between trawl locations; and the relation- 

 ship among precision, tow length, and number 

 of tows. 



In this section we first use a negative binomial 

 model with varying element size to estimate the 



relationship among precision and tow length and 

 number of tows. We next use this relationship and 

 time factors to illustrate the relationship between 

 logistically feasible tow lengths and precision. 



Animals in nature are rarely randomly distrib- 

 uted. They usually show some degree of aggrega- 

 tion or contagion. When these populations are 

 sampled, they lead to distributions which are 

 markedly skewed and have a large proportion of 

 zero elements. The negative binomial distribution 

 is often assumed for such populations because of 

 practical performance (Laubscher 1961; Pielou 

 1969) and theoretical basis (Taylor 1953; Patil and 

 Stiteler 1974). The distribution can be used to 

 provide an estimate of the relationship between 

 sample element size and precision. 



The negative binomial distribution often is used 

 to describe observed distributions in both general 

 ecological research (Pielou 1969; Poole 1974) and 

 fisheries research (Taylor 1953; Moyle and Lound 

 1960; Lambou 1963; Roessler 1965; Clark 1974). 

 The distribution is characterized by two param- 

 eters, m the mean number of units per sampling 

 element, and k, an "index of aggregation" (Waters 

 1959). The value of k varies inversely with the 

 degree of aggregation of the population. The 

 variance of a mean drawn from a population which 

 follows a negative binomial distribution (Vnb) is 

 a function of the mean ( m ) and k , 



Xib = '^ ^ ^'Z^- 



As the degree of aggregation increases, k ap- 

 proaches and when the empty elements are 

 ignored, this distribution approaches Fisher's log- 

 arithmic series. As the degree of aggregation 

 decreases, k will approach infinity and the dis- 

 tribution converges to the Poisson. 



The negative binomial can be derived from five 

 or more different models, which may be mutually 

 contradictory (Anscombe 1950; Bliss and Fisher 

 1953). A commonly used procedure to derive the 

 distribution is to assume that it arises from a 

 cluster of objects in space where the clusters follow 

 a Poisson distribution and the number of animals 

 in a cluster are distributed according to Fisher's 

 logarithmic series. Taylor (1953) derived a form of 

 the negative binomial as a probability model 

 specifically to describe the relative abundance of 

 fish species in trawl catches. 



The data used for this analysis come from the 

 pilot survey made in Queen Charlotte Sound. 

 Since the negative binomial distribution is a 



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