ANALYSIS OF DOUBLE-TAGGING EXPERIMENTS 



Jerry A. Wetherall 1 



ABSTRACT 



Statistics arising from double-tagging experiments may be applied to estimate tag-shedding prob- 

 abilities directly, to estimate parameters of underlying theoretical shedding models, or to estimate 

 mortality rates free of tag-shedding bias. 



Simple maximum likelihood estimators of tag retention rates, along with their asymptotic vari- 

 ances, may be derived assuming conditional multinomial sampling models. If specific models of 

 shedding are of interest, limitations of existing theory may be reduced by assuming the Type II 

 shedding rate is time-dependent. In the more realistic models and their simpler precursors, parame- 

 ters may be estimated by least squares or by maximum likelihood methods. Complications arising in 

 the direct maximization of the conditional likelihood may be circumvented by use of iteratively 

 reweighted Gauss-Newton algorithms available in standard statistical software packages. Simple 

 diagnostic plots may be helpful in model selection. 



When a sequence of double-tagged cohorts is released, recapture statistics may be treated sepa- 

 rately or combined to estimate common shedding rates, but a more general linear model may be used 

 to fully exploit the structure of the experiment and to estimate both common parameters and those 

 unique to each cohort. 



When recapture times are unknown but the experiment spans a sufficiently long period, the ratio 

 of constant Type II tag-shedding rate to constant Type II total mortality rate may be estimated. 

 Under similar circumstances, but with exact recapture times known for each fish, maximum like- 

 lihood estimates of both parameters may be computed. 



If only the Type II mortality rate is of interest, it may be estimated free of tag-shedding bias by 

 simple linear regression of appropriate double-tagging statistics, if Type II shedding and Type II 

 mortality are constant during the experiment. 



The estimation of fishing mortality rate, exploi- 

 tation rate, and population size through mark 

 and recapture experiments is often complicated 

 by the incidental shedding or loss of marks. Fail- 

 ure to account for tag shedding may lead to biased 

 parameter estimates. Thus a well-designed tag- 

 ging experiment will incorporate some provision 

 for estimating shedding rates and computing 

 correction factors. 



The approach usually taken is to release a 

 group, or perhaps several groups of double- 

 tagged fish, and then to estimate shedding rates 

 using information on the number of fish returned 

 in a sequence of recapture samples still bearing 

 both tags and on the number of returns with only 

 one tag remaining. A variety of statistical meth- 

 ods and estimation procedures have been devel- 

 oped. Papers by Beverton and Holt (1957), Gul- 

 land (1963), Chapman et al. (1965), Robson and 

 Regier (1966), Chapman (1969), Bayliff and Mo- 

 brand (1972), Seber (1973), Laurs et al. (1976), 



Arnason and Mills (1981), Kirkwood (1981), and 

 Seber and Felton (1981) are particularly note- 

 worthy. In recent years attention has focused pri- 

 marily on the regression methods developed by 

 Chapman et al. (1965) and extended first by Bay- 

 liff and Mobrand (1972) and most recently by 

 Kirkwood (1981). 



Despite the extensive literature on double-tag- 

 ging there is need for an integration of existing 

 thought and for development of new ideas and 

 statistical methods. Accordingly, this paper sur- 

 veys basic tag-shedding theory and the most 

 widely used analytical techniques, and describes 

 a variety of new models and estimation proce- 

 dures. Left unaddressed are several important 

 aspects of planning double-tagging experiments. 

 These are the subject of a companion paper by 

 Wetherall and Yong (1981). 



TAG LOSS IN 

 SINGLE-TAGGING EXPERIMENTS 



'Southwest Fisheries Center Honolulu Laboratory, National 

 Marine Fisheries Service, NOAA, P.O. Box 3830, Honolulu, HI 

 96812. 



To establish a context for later derivations we 

 begin by reviewing the process of tag loss in a 

 population of single-tagged fish. In such a popu- 



Manuscript accepted April 1982. 



FISHERY BULLETIN: VOL. 80. NO. 4. 1982. 



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