Abstract
If absolute recruitment (R) and natural mortality rate (q) are both presumed constant in each of two or more periods of stabilized fishing, it is shown that i = q + (1/R)iC, where i is instantaneous total mortality rate and C is catch in numbers. The relationship yields approximate estimates of R and q under semi-stable conditions if "average referable C" is related to apparent i, the former derived from catch data and the latter from age-composition data for post-recruited age-groups. In the herring population, in which recruitment takes place mostly at age III but is spread from ages I to IV, the average of the catch of years x and x + 1 is referable to apparent i at ages IV to V in year x + 2, at ages V to VI in year x + 3, etc. When q increases with advancing age, it is shown that R is most accurately estimated from data for ages IV to V; q is slightly overestimated at ages IV to V and underestimated at ages VI to VII and VII to VIII. From data for periods of approximate stability in the lower east coast of Vancouver Island population, average R is estimated at about 500 million fish per year; average q appears to increase with age, ranging from about 0.4 at ages IV to V to about 0.85 at ages VII to VIII. For a recent period of stabilized intensive fishing, a rough estimate of the average initial size of the fishable stock, based on age-composition and catch data, agrees well with that estimated by another method. For populations along the west coast of Vancouver Island, q also appears to increase with advancing age; R is estimated at about 400 million fish. In an appendix it is shown that a method of estimating q from age-composition and effort data gives unsatisfactory results because effort expended in herring fishing is not proportional to rate of fishing of the stock.
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