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Numerical experiments with least-squares catch-at-age analysis Lawson, Timothy Adair


Three methods of analyzing age composition from the catches of exploited populations are compared on the basis of their assumptions about recruitment, harvesting, and natural mortality; the manner in which data errors are treated; and how information contained in the catch data is utilized in estimating population parameters. The analysis of catch curves involves the strictest assumptions and uses the least amount of information in the data. Cohort analysis, while having the most relaxed assumptions, ignores the errors and restricts information to within cohorts. The least-squares approach of Doubleday (1S76) takes full account of data errors and information between cohorts, but assumes that the age selection characteristics of a fishery are constant over time. The least-squares technique is modified to account for changes in the relative variance of data errors with age and to prevent unreasonable estimates of population parameters. In its most general form, the method is capable of analyzing catches-at-age, estimates of catch-at-age error variances, effort data, reproduction statistics, and prior information about parameter values, all simultaneously and in a way that guarantees consistent results. The method is applied to northwestern Atlantic harp seal catch-at-age data. The results indicate that the seal population is more abundant than previous analyses have shown. However, projections with a quota of 180,000 animals predict a decline in the stock to two-thirds its present abundance over the next ten years. Monte Carlo studies were performed to investigate the general relationship between reliability of population forecasts and the information content of the data, as determined by data quantity, data errors, and the contrast in abundance and exploitation rates during the period over which the data were taken. The coefficient of variation for predictions of abundance ranged from 1% for high contrast, high quantity data sets to 91% for low quantity, low contrast data. Estimates of the natural mortality rate with the least-squares technique are precise when the data set is large, contrast is high, and errors are moderate.

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