Studies on Estimation of Mortalities: I. Comparison of a Method Described by Beverton and Holt and a New Linear Formula

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Abstract
A method, described by Beverton (1954) and Beverton and Holt (1956 and 1957), giving estimates of the natural mortality rate, M, and the catchability coefficient, q, from catch at age and effort data, is examined. This method requires 4 to 5 iterations to arrive at the estimates. We have derived approximate solutions for q and M in a closed form. This makes the laborious iterations unnecessary, and gives virtually the same values as arrived at by iterations.The effectiveness of the iterative Beverton and Holt method is evaluated by calculating q and M in 30 hypothetical examples. A new and simple (linear formula) method for estimating q and M is derived. Application of the new method to these 30 examples resulted in a 48% reduction in the standard deviation of q and a 45% reduction in that of M. The new method is in part the same as one suggested by Gulland, Beverton, and Holt (Beverton et al., MS, 1958; Holt, MS, 1959) to arrive at initial values in their short-cut (iterative) method of estimating the mortality rates. Thus we show that these initial values are actually better estimates than the final values arrived at by the iteration.Neither the Beverton and Holt method nor the linear formula give necessarily unbiased estimates; the bias depends on the types of variability in the data.To arrive at non-biased, least squares estimates would require ancillary information not usually available on the distributions of the three variates: catch at age, effort, and catchability coefficient.

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