The Harvest Rate Model for Klamath River Fall Chinook Salmon, with Management Applications and Comments on Model Development and Documentation

The fall run of chinook salmon Oncorhynchus tshawytscha in the California portion of the Klamath River supports important ocean and river fisheries. At the start of each annual management season, the Klamath Harvest Rate Model (KHRM) is used to propose preliminary harvest levels that are subsequently used as the basis of negotiations on harvest allocation and fishing season structure. Until recently, the KHRM existed only as a computer spreadsheet file without written documentation, from which optimal harvest levels (the highest levels attainable within current management policy) were found by repeated manual adjustment of trial values, a tedious and error‐prone procedure. We provide formal treatment of the KHRM by setting forth the equations that define it and providing the analytical solution to its optimization. We then give three examples of its use in managing the stock, ranging from routine use to incorporation into simulation studies. Introduction of spreadsheets and similar simplified programming tools has encouraged the implementation of computer models that are not clearly defined mathematically. That approach forces users to decipher programming code to grasp model structure and raises the question whether model structure was carefully thought out. Written development of theory properly precedes and provides a foundation for any implementation. Explicit development of theory is critical to foster mathematical insight and consequent progress in model development. Documentation of theory is particularly important for models that are used in setting public policy since it allows them to undergo peer and stakeholder review, which increases accountability and public trust.