A Time Density Model to Estimate Run Size and Entry Timing in a Salmon Fishery

Abstract

Managers need improved estimates of run size and entry timing for salmon migrating to their natal spawning grounds if they are to improve the biological and economic management of salmon fisheries. A time density model was derived from the inverted exponential model of Mathisen and Berg. During a fishery, this model provides three estimates of run size that are more accurate than the preseason forecast. The result is used to manage fisheries for chum salmon Oncorhynchus keta in the entire Hood Canal area and the Skokomish River of western Washington state. The model uses both daily catches per unit effort (CPUE) by drift gill nets and peak purse-seine catches from a northern Hood Canal fishery to estimate run size and entry timing. Run size and entry timing estimates are derived from a fitted cumulative time density of daily CPUE; historical data are used to correct for missing daily gill-net CPUE values. The result is estimates of run size with increased precision and decreased bias. A linear regression model, in which a peak 1-d purse-seine catch is an independent variable, is used to correct the time density run size estimate. This correction decreased the run size mean percent error from 18% to 5% and from 27% to 4% on two successive updates. The assumptions are that: (1) the timing and progression of a salmon migration are consistent; (2) there is continuous fish passage in one direction; (3) the gill nets sample passively; (4) estimates of daily CPUE from the fishery can be used to construct the time density; and (5) the cumulative daily CPUE for the season is directly proportional to run size. The accuracy of run size and entry timing estimates obtained during the fishery are likely to be affected by gear competition between the purse-seine fleet and the drift gill-net fleet, as well as by data misreporting and time delays in reporting daily drift gill-net CPUE. This model could be applied to most exploited animal populations where the abundance of individuals over time at a fixed geographic reference frame is approximately normally distributed.

Notes

² A Treaty Indian is an enrolled member of any tribe recognized by the U.S. Bureau of Indian Affairs in western Washington as having descended from any tribe or band that signed any one of the Stevens Treaties of 1854 and 1855. A Treaty Indian fisher is a person who is directly authorized under tribal law of his or her tribe to excercise reserved fishing rights ofthat tribe. A nontreaty fisher is a person who is not a member of a Treaty Indian tribe or a tribal member not authorized to exercise treaty fishing rights.

³ North of Cape Falcon meetings are preseason fishery planning sessions involving the management agencies of Northwest Treaty Indian tribes and the states of Oregon and Washington, which coordinate management in U.S. salmon fisheries north of the latitude of Cape Falcon, Oregon (approximately 45°45′N) and south of the Canadian border. This coordination is mandated by two United States Court orders (Order Adopting Puget Sound Salmon Management Plan, United States of America vs. The State of Washington, Civil 9213, Proc 85-2; and Order Regarding Hood Canal Management Plan, United States of America vs. The State of Washington, Civil 9213, Proc 83-8). A run is an anadromous salmonid population of a single species migrating during a particular season to a specific fish production facility or to any freshwater subregion of Puget Sound.

⁴ A fish management period is defined as “The time interval during which regulatory actions are taken to meet the escapement requirements for a stock or group of salmonid stocks which are aggregated for the purpose of achieving a desired spawning escapement objective, taking into account actual or expected catches outside its management period” (Order Adopting Puget Sound Salmon Management Plan, United States of America vs. The State of Washington, Civil 9213, Proc 85-2).

⁵ Harvestable surplus is the portion of the stock remaining after spawning escapement requirements are subtracted. Actual harvest depends on fishing regulations, size of the fishing fleet, and weather conditions.

⁶ A management week starts on Sunday and ends on Saturday. In 1995, management week 44 was October 29–November 4, management week 45 was November 5–11, and management week 46 was November 12–18.