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Fishery Bulletin 101 (2) 



the former case, q may be interpreted as the proportion 

 of the population biomass that is caught by one unit of 

 effort. Often the CPUE is standardized (using methods 

 akin to those of Punt et al., 2000), so that the unit of effort 

 is a standard one (e.g. if nationahty and area are factors 

 in the CPUE standardization, then the standard unit of 

 effort will be that for a vessel from the reference nation in 

 the reference area). However, the unit of effort is changed 

 when, as is common in New Zealand, CPUE indices are 

 standardized to have value 1 in a reference year. If the /, 

 are from a trawl survey series, the interpretation of q is 

 slightly different. Here, it is the product of the survey area 

 and the proportion of the biomass that is caught per unit 

 of area swept (because trawl survey indices are usually 

 scaled up by the survey area, whereas no such scaling is 

 done for CPUE indices). 



Trawl survey catchability may also be interpreted as 

 the product of three components: vulnerability, v, vertical 

 availability, u^,, and areal availability, u^ (Francis^). These 

 components are defined in the framework of a conceptual 

 model in which the trawl gear is thought of as sweeping a 

 volume of water in the shape of a cuboid of width equal to 

 the distance between the trawl doors, height equal to the 

 headline height, and length equal to the distance trawled. 

 Vulnerability is the average proportion offish in the swept 

 volume that are caught. Vertical availability is the propor- 

 tion of fish in the survey area that could be encountered 

 by the trawl gear (i.e. that are close enough to the bottom 

 to be below the trawl headline but not so close as to pass 

 under the footrope). Areal availability is the proportion of 

 fish in the population being surveyed that are in the survey 

 area at the time of the survey (this is important in stock 

 assessment when the full range of the stock being assessed 

 is not covered by a survey). 



These three components are usually of more theoretical 

 than practical use. That is, they help us to think about the 

 relationship between a trawl survey biomass index and the 

 actual biomass. In New Zealand the common practice is to 

 calculate survey biomass indices as if all three constants 

 had value 1. This means that the catchability associated 

 with these indices is the product of the three components, 

 i.e. q = vu^M„- This interpretation restricts the range of 

 plausible values for a trawl survey q. Because all three 

 catchability components are defined as proportions their 

 product should be less than (or equal to) 1. (It is techni- 

 cally possible for u to exceed 1 |if, for instance, fish that are 

 initially above the headline, and thus unavailable to the 

 net. are herded downwards] but it is most unlikely that cw, 

 would be greater than 1; «,, cannot exceed 1.) Thus, if the 

 default values of the catchability components have been 

 used, we would expect q to be less than 1. Also, very small 

 values off/ are implausible for any species that is assessed 

 by using trawl survey biomasses. Although there are spe- 

 cies that are not well caught by trawls (e.g. because they 



' Francis, R. I. C. C. 1989. A standard approach to biomass 

 estimation from bottom trawl surveys. N.Z. Fish. Assess. Ros. 

 Doc. 89/rj, 4 p. Nation.-d Institute of Water and Atmospheric 

 Research, P.O. Box 14901. VVelluiKton. New Zealand. 



are fast-swimming, high above the bottom, or because they 

 burrow in the substrate) and thus have very low values of 

 V or u^. (or both), such species are not, for that reason, as- 

 sessed with trawl survey indices. Similarly, a very low areal 

 availability (implying that most of a fish stock is outside 

 the survey area) would rule out the use of trawl surveys in 

 assessing a stock. 



There is also a limit to how much we would expect values 

 of q for the same species to vary between surveys. For a 

 given fishing vessel and trawl net, the components v and 

 r/j, are determined by fish behavior (e.g. swimming speed, 

 typical height above the bottom, reaction to an approaching 

 net). This means that if the same vessel and gear are used 

 in surveys in different areas we would expect the product 

 CM, not to vary very much for the same species (except, 

 perhaps, between spawning and nonspawning periods, 

 when there may be substantial behavioral differences). If 

 different vessels, or gear, are used, we might obtain larger 

 differences in vu,.. 



Materials and methods 



Data 



Two types of New Zealand data were examined: those from 

 stock assessments and those from random trawl surveys. 



Assessment data We gathered data from all recent stock 

 assessments that used biomass indices from either trawl 

 sui^eys or CPUE. One data set was constructed for each 

 separate series of biomass indices (so that an assessment 

 using two different series provided two data sets). Each 

 data set consisted of the following variables: 



• the biomass indices input to the assessment; 



• the years associated with these indices; 



• the CV(s) assumed for these indices; 



• a description of the assumed error distribution type; 



• the model estimates of (absolute) biomass that cor- 

 respond to each biomass index; and 



• the model estimate of catchability, q. for the indices. 



For each stock the latest available assessment (usually car- 

 ried out in 2000) was used. Data sets with fewer than four 

 annual indices were discarded. 



A total of 48 such data sets was constructed (30 with 

 CPUE indices and 18 with trawl survey indices), ranging 

 in length from 4 to 40 indices, with CVs between 0.02 and 

 0.61 (Fig. lA) (details of the individual assessments are 

 given in Francis et al., 2001). In most data sets (43 of 48) 

 a single CV was assumed for all indices. Two rock lobster 

 assessments used a time step of six months; all other as- 

 sessments used a one-year time step. Amongst these data 

 sets there were three different error-distribution assump- 

 tions; these deterniiiie how standardized residuals are 

 calculated (Table 1). 



We refer to the CVs for the assessment data sets as "as- 

 sumed," rather than "estimated," because we can estimate 

 only one component of these CVs, that due to observation 



