293 



Abstract— Biomass indices, from com- 

 mercial catch per unit of effort (CPUE) 

 or random trawl surveys, are commonly 

 used in fisheries stock assessments. 

 Uncertainty in such indices, often ex- 

 pressed as a coefficient of variation 

 (CV), has two components: observa- 

 tion error, and annual variation in 

 catchability. Only the former can be 

 estimated directly. As a result, the CVs 

 used for these indices either ignore the 

 annual-variation component or assume 

 a value for it (often implicitly). Two 

 types of data for New Zealand stocks 

 were examined: 48 sets of residuals 

 and catchability estimates from stock 

 assessments using either CPUE or 

 trawl survey indices; and biomass esti- 

 mates from 17 time series of trawl sur- 

 veys with between 4 and 25 species per 

 time series. These data show clear evi- 

 dence of significant annual variation in 

 catchability. With the trawl survey data, 

 catchability was detectably extreme for 

 many species in about one year in six. 

 The assessment data suggest that this 

 annual variability typically has a CV of 

 about 0.2. For commercial CPUE the 

 variability is slightly less, and a typical 

 total CV (including both components) 

 of 0.15 to 0.2. This is much less than 

 the values of 0.3 to 0.35 that have com- 

 monly been assumed in New Zealand. 

 Some estimates of catchability are 

 shown to be implausible. 



Quantifying annual variation in catchability 

 for commercial and research fishing 



R.I.C. Chris Francis 

 Rosemary J. Hurst 

 James A. Renwick 



National Institute of Water and Atmospheric Research 



PO Box 14901 



Wellington, New Zealand 



E-mail address (for R I C C Francis): c frands@niwa.cri.nz 



Manuscript accepted 17 December 2002. 



Manuscript received 31 December 2002 

 at NMFS Scientific Publications Office. 



Fish. Bull. 101: 293-304 (2003i. 



Catchability is a key parameter that 

 is estimated in many fish stock assess- 

 ments (Arreguin-Sanchez, 1996). It is 

 the constant of proportionality between 

 biomass indices (either from commer- 

 cial catch per unit of effort (CPUE) or 

 random trawl surveys) and absolute 

 biomass. Despite its importance it 

 is usually thought of as a "nuisance" 

 parameter: one that is not of intrinsic 

 interest but which needs to be esti- 

 mated so that other quantities, which 

 are of interest (e.g. biomass), can be 

 estimated. For this reason estimates of 

 catchability are not often reported. 



Uncertainty in biomass indices, often 

 expressed as a coefficient of variation 

 (CV), has two components: observation 

 error and annual variation in catchabil- 

 ity. Only the former can be estimated 

 directly. As a result, the CVs used for 

 these indices either ignore the annual- 

 variation component or assume a value 

 for it (often implicitly). Our objectives in 

 this study were to estimate the extent 

 to which catchability varies from year 

 to year for New Zealand stocks. We used 

 all available data, including residuals 

 and catchability estimates from stock 

 assessments and biomass estimates 

 from time series of trawl surveys. We 

 show that standard New Zealand prac- 

 tice typically overestimates catchability 

 variation for trawl survey indices and 

 underestimates it for CPUE, and sug- 

 gest that some catchability estimates 

 are clearly implausible. More details 

 concerning the data and analyses below 

 are given by Francis et al. (2001). 



We assume throughout that catch- 

 ability does not vary systematically 

 with abundance. There is much con- 

 troversy surrounding this assumption, 

 particularly for CPUE. Since Paloheimo 



and Dickie (1964) gave theoretical rea- 

 sons to expect that catchability would 

 increase as biomass declined, many au- 

 thors have presented confirmatory data 

 (e.g. Schaaf 1975: Pope, 1980; Winters 

 and Wheeler, 1985; Quinn and Collie, 

 1990). Nevertheless, many stock assess- 

 ments are based on the assumption that 

 catchability is independent of abun- 

 dance. It is data from such assessments 

 that we examine here. We also assume, 

 of necessity, that the role of CVs in stock 

 assessments is to describe the precision 

 of biomass indices, rather than their 

 quality. This issue is discussed further 

 in the final paragraph of this paper To 

 begin with, we describe more precisely 

 what we mean by catchability. 



Definitions 



"Catchability" is used in several slightly 

 different ways in the fisheries literature. 

 The use we are concerned with is as a 

 parameter (conventionally denoted by 

 q) in a stock assessment model, defined 

 by the equations 



7, =(?B,f,orlog(/,) = log((?B,)f; (1) 



where 7, = the index in year i; 



B, = the corresponding true bio- 

 mass; and 

 the error terms, e^ and f| are ran- 

 dom variables with expectation 1 

 and CV (coefficient of variation) 



The interpretation of q in (Eq. 1) de- 

 pends on whether the 7, are from CPUE 

 or trawl surveys (other types of biomass 

 index — e.g. from acoustic surveys — are 

 possible but not considered here). In 



