Estimation of Recruitment and Natural Mortality Rate from Age-Composition and Catch Data in British Columbia Herring Populations

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.