| Abstract: | This paper develops the equilibrium solutions for an age-structured life cycle model where spawning stock is split between natural and hatchery spawners. Mixing is allowed between the stocks through natural stock take by the hatchery and release of eggs or fry by the hatchery when its capacity is exceeded. The natural stock is assumed to have density-dependent egg-smolt survival while the hatchery stock has linear survival. The model can be applied to any hatchery reared fish stock but is most appropriate for salmon, where hatchery and naturally spawned fish mix completely later in life. Questions about the mix between the hatchery and natural stocks can be addressed by computing the fraction of naturally and hatchery derived stock among the natural and hatchery spawners as well as among the total adult run. Columbia River chinook stock are used as an example for which equilibria and mixing fractions are computed. A Monte Carlo sensitivity study on model parameters showed that the natural stock survival from smoltification to age 1 and the natural basin smolt carrying capacity are most important in controlling the equilibrium age-1 naturally spawned stock. Changing hatchery capacity over two orders of magnitude showed a 50 percent change in the fraction of naturally derived fish in the natural spawning stock, while the relative size of natural and hatchery stocks changed over two orders of magnitude. The model can serve as a tool for quickly assessing the effects of spawning habitat modification and hatchery supplementation practices on long-term stock mixing and stock abundance. |
