Calculation of Catch Rate and Total Catch in Roving Surveys of Anglers

To estimate the total catch in a sport fishery sampled by a roving creel survey, we multiply an estimate of the total fishing effort by the estimated catch rate (i.e., catch per unit of fishing effort). While the statistical theory for estimating the fishing effort from instantaneous or progressive counts is well established, there is much confusion about the appropriate way to estimate the catch rate. Most studies have used the ratio of means or the mean of the ratios of individual catches and efforts. We analyzed the properties of these estimators of catch rate under the assumption that fishing is a stationary Poisson process. The ratio of means estimator has a finite second moment, while the mean ratio estimator has infinite variance. Simulation studies showed that the mean of ratios estimator tends to have high and unstable mean squared error relative to the ratio of means estimator and this is in accordance with empirical observations. We also studied the properties of the mean of ratios estimator when all interviews with people fishing for less than ε minutes duration were disregarded for values of ε up to 60 minutes. There was typically a marked reduction in mean squared error when the shorter trips were not included. We recommend that the mean of ratios estimator, with all trips less than 30 minutes disregarded, be used to estimate catch rate and hence total catch under the roving creel survey design. It has the correct expectation (at least approximately after the truncation) and almost always had smaller mean squared error than the ratio of means estimates in our simulations.