PROBLEM OF BIAS IN MODELS TO APPROXIMATE 



OCEAN MORTALITY, MATURITY, AND ABUNDANCE SCHEDULES 



OF SALMON FROM KNOWN SMOLTS AND RETURNS 



Robert H. Lander' 



ABSTRACT 



The problem of methodological bias in estimating ocean mortality or survival, maturity, 

 and abundance of multireturn species of Pacific salmon (Oncorhynchus spp.) is examined 

 heuristically with a data base for which no unbiased estimators exist. The case of hatchery 

 coho salmon (O. kisuich) is emphasized to treat the problem in its simplest form (two 

 returns). Models previously reported by Ricker. Fredin, and Cleaver are considered in the 

 context of their application in biomass computations and the particular problem of bias 

 in approximating average and interval-specific mortality coefficients during ocean life. A 

 new scheme is introduced as the limit-mean model, and the assumptions in all four 

 models are contrasted. Numerical examples for a hypothetical cohort demonstrate a wide 

 range of bias in estimates of different parameters from the same model and also in 

 estimates of the same parameter from different models applied in different situations. For 

 the hypothetical data, overall performance is best for the limit-mean model with the 

 offshore catch known; this model also provides estimates of natural and fishing mortality 

 rates offshore during the last year at sea. For coho and chinook salmon, (O. ishawytscha) 

 caught off western North America, it is recommended that 1) maturity be directly sampled 

 to help provide nominally unbiased estimates for certain of the parameters and 2) research 

 be intensified on determining offshore catch by origin independently of marking smolls. 



Three oceanic fisheries have motivated research 

 on the geographic origins, distribution patterns, 

 and changes in biomass during the marine life 

 of salmon. One is the Japanese mothership 

 fishery, since 1952 by drift gill nets west of 

 long 175 °W in the North Pacific Ocean — mainly 

 for pink {OiicorJtyucJiMs gorbuscha), chum (O. 

 keta), and sockeye (O. iierka) salmon (Fukuhara, 

 1953). Another is the offshore troll and sport 

 fishery from California to Alaska for chinook 

 (O. tshairytscJia) and coho (0. kit.sutch) salmon 

 (Godfrey, 1965; Mason, 1965). Third is the 

 drift net fishery for Atlantic salmon (Salnio 

 sola)-), since 1964 off southeast Greenland and 

 northern Norway (Horsted, 1971). 



The results of biomass computations based on 

 growth and natural mortality estimates must 

 be combined with catches (real or assumed) by 

 natal origin in order to assess the impact of 

 offshore vis-a-vis inshore fishing (Taguchi, 



' Northwest Fisheries Center, National Marine Fisheries 

 Service, NOAA, 2725 Montlake Boulevard East, Seattle, 

 WA 98112. 



1961a, 1961b; Doi, 1962; Ricker. 1962, 1964; 

 Parker. 1963; Fredin. 1964; Hirschhorn, 1966; 

 Cleaver. 1969; Henry. 1971. 1972). Investiga- 

 tors have recognized the scarcity of e.xisting field 

 data, the high cost of direct marking/recovery 

 at sea, and the technical difficulties of obtaining 

 unbiased data and constructing realistic models 

 to approximate the time distribution of mortality 

 (Ricker, 1962; Parker. 1960. 1962. 1963. 1968; 

 Fredin. 1964; Lander et al.. 1967; Cleaver. 

 1969). 



Biased estimates can distort the interpreta- 

 tion of actual time changes in biomass of a 

 cohort and impede the application of rational 

 conservation measures. On the other hand, 

 reasonably accurate approximations to interval- 

 specific mortality can be useful not only in 

 biomass computations: they may help also to 

 ):)redict returns from the sea and thereby to 

 improve management of inshore salmon fisheries 

 (e.g., Gilbert. 1963). 



In this report I review three published models 

 for approximating ocean mortality schedules 



Manuscript accepted October 1972. 



FISHERY BULLETIN: VOL. 71, NO. 2, 1973. 



513 



