Incorporating uncertainty into area under the curve and peak count salmon escapement estimation

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Abstract

Uncertainty can be incorporated into area-under-the-curve (AUC) and peak count estimates of salmon escapement by conducting replicate fish counts and developing independent escapement estimates over several years. We describe a bootstrap procedure that follows the trapezoidal AUC method and incorporates the uncertainty associated with fish counts, the shape of the spawner curve, observer efficiency, and residence time. However, the procedure does not incorporate all sources of uncertainty or address the problems posed by sparse surveys or nonzero first or last counts. For the peak count method, the procedure was modified to include the uncertainty from fish counts, observer efficiency, the expansion factor, and the timing of scheduled flights with respect to peak spawning activity. Data from spring-run, stream-type chinook salmon Oncorhynchus tshawytscha in the Nicola River, British Columbia, were used to demonstrate the procedures’ applications. Replicate aerial spawner counts were similar and repeatable, and annual residence times were consistent over 4 years. The AUC escapement estimates were precise, reliable, and accurate when compared with independent mark-recapture escapement estimates, whereas the peak count escapement estimates were precise but less reliable and accurate. We expect that AUC escapement estimates calculated from the mean residence time of 4 years will be less biased (28% to 15%) than peak count estimates from the mean expansion factor of 4 years (214% to 121%). The procedures that we describe for incorporating uncertainty into AUC and peak count escapement estimation should enable fisheries biologists to more adequately assess changes in abundance and stock status.