Errors in Estimates of Mortality Obtained from Virtual Populations

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Abstract
The bias in individual estimates of the natural mortality coefficient derived from the ratio of successive virtual populations is defined algebraically and is shown to be unchanged whether one or more year-classes is considered, if the mortality coefficients are assumed to be constant for all exploitable fish. Limiting and probable values of this bias are shown graphically for a coefficient of fishing mortality ranging from 0 to −2.0 in the year for which the estimate is obtained. These values are drawn for a true natural mortality of −0.2 and −0.4 and for both an increasing and a decreasing fishing effort. Bias in individual estimates of natural mortality is greatest when there are large fluctuations in fishing effort, particularly when fishing mortality is low relative to natural mortality, and it increases with increased natural mortality.A linear regression of a series of virtual population ratios would in general give an intercept value which underestimated the coefficient of natural mortality, and a slope which overestimated the coefficient of fishing mortality, in situations where F has tended to increase and also where it has had no trend (the "steady state" of Table I). Both these errors would be in the opposite direction during a period when there was a decline in fishing effort.

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