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



as applied in biomass computations, examine 

 the particular problem of bias in mortality 

 estimates, and introduce another model to 

 extend the indirect approach developed by 

 Parker (1962), Ricker (1962), Fredin (1964), 

 and Cleaver (1969). Bias in estimated maturity 

 and abundance schedules is examined also. 



METHODS AND LIMITATIONS 



The indirect approach is applicable to species 

 in which maturing adults from the seaward 

 migrants in a given year (or smolt class) 

 return to their natal area in 2 or more years: 

 single-return pink salmon are excluded. The 

 following minimum data are required for 

 multireturn species: 1) origin-specific number 

 of seaward migrants or smolts in a given year, 

 2) number of survivors returning from the 

 ocean each year until the smolt class is extinct, 

 and 3) intervals between times of seaward 

 migration and of each return or spawning 

 escapement. An offshore fishery may or may 

 not exist; origin-specific catch data for the 

 inshore fishery or an offshore fishery may or 

 may not be available. No unique solution exists 

 for the mortality, maturity, and abundance 

 schedules from the foregoing data base: dif- 

 ferent combinations of mortality and maturity 

 schedules can generate the same set of observed 

 data. 



I consider only the bias due to the absence 

 of unique solutions in estimating models. Data 

 on the numbers of smolts and returning adults 

 may be biased additionally in practice; in 

 fact, the very existence of basic data is un- 

 fortunately the exception in wild stocks (e.g., 

 Gilbert, 1963). Data as ob'served in practice 

 are assumed here to be accurate in order to 

 emphasize the methodological problem. 



The number of mortality, maturity, and 

 abundance parameters increases formidably 

 with the number of returns and with the 

 possible regimes of offshore-inshore exploitation. 

 The case of only two returns, typical of hatchery 

 and most wild stocks of coho salmon south of 

 British Columbia (Shapovalov and Taft, 1954; 

 Godfrey, 1965; Drucker, 1972), is emphasized 

 throughout. 



Finally, the study is heuristic. Explicit 



equations for bias are available for only two 

 of the four models as treated here. The equation 

 for one of the two is tedious to write for just 

 one parameter — say the monthly coefficient 

 of total mortality between times of outmigration 

 and of the last return— and descriptive equa- 

 tions for bias are very cumbersome when 

 estimates for all mortality, maturity, and 

 abundance parameters are considered. Relations 

 among all parameters are evident from initial 

 description of the actual situation, however, and 

 are utilized for some numerical comparisons 

 from a set of hypothetical data. These numerical 

 comparisons of bias are selective also with 

 respect to the two general cases considered: 

 1) catch data unknown and 2) catch data known 

 from marking (or otherwise identifying) smolts 

 and from sampling the catch for recoveries. I 

 try to avoid unfair comparisons between models, 

 to compare them where justified, and to demon- 

 strate how small bias in one parameter estimate 

 may translate to large bias in another estimate 

 from the same model. 



ACTUAL SITUATION 



Pertinent events of the life history (Shapo- 

 valov and Taft, 1954; Godfrey, 1965; Johnson, 

 1970; Drucker. 1972), observational data, and 

 parameters are related below for coho salmon 

 in the southern part of their freshwater range 

 in North America. 



Spawning occurs during November-January 

 and typically the surviving fry are free-swim- 

 ming during the next February-April. The 

 cohort stays in fresh water until downstream 

 migration of survivors begins about a year 

 later at time t = /(»; the actual time of entry 

 to the ocean, some weeks later, depends on 

 physiological condition, stream flow and tem- 

 perature, and distance from spawning areas. 

 Our mortality schedule starts at time t — to 

 and includes downstream mortality of smolts 

 unless their number is known when they enter 

 the sea. 



The first return from the sea is in the year 

 of outmigration (6-9 mo later) and occurs at 

 time t = fi, usually during October-December 

 or about 2 years after eggs are spawned. This 

 first return is all or nearly all males or "jacks." 



514 



