Estimating spawning escapements from periodic counts: a comparison of methods

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The escapement of Pacific salmon is often estimated by periodic counts of spawners, calculating the number of fish-days present and dividing by the average number of days a fish spends in the survey area. We present a maximum likelihood method to calculate the number of spawning fish and compare this approach with the most commonly used method, which relies on linear interpolation between observations. The maximum likelihood method is computationally more demanding; however, it does provide a statistical basis for describing uncertainty and can also be used to deal with data sets where the first or last counts are nonzero or where there are few observations. We compared escapement estimation methods using data from 18 experimental streams where the number of fish in the stream was evaluated by weir and carcass counts. In this comparison, the method of linear interpolation deviated from the weir count by an average of 19%, whereas the maximum likelihood method deviated by 23, 24, 30, or 40% depending upon which likelihood and arrival time model was used. We conclude that for most data sets where measures of uncertainty are not required, the linear interpolation method is adequate but recommend an examination of maximum likelihood methods when an estimate of uncertainty is required.