Investigation of density dependence in salmon spawner–egg relationships using queueing theory

A model based on queueing theory is presented to explain salmonid spawner–egg relationships caused by redd superimposition. The model incorporates carrying capacity, spawner arrival times, egg protection, preference of potential redd sites and accumulation of waiting spawners. Results show that the relationship described by the Beverton–Holt stock recruitment model produces a greater density dependent effect than just redd superimposition from random spawning, whereas, the Ricker stock recruitment model produces similar results as the random spawning model at low spawner levels. A queueing model of waiting spawners explains reduced recruitment at high spawner levels similar to the Ricker model, but results are dependent on the assumptions made about the reduction in egg viability as spawning is delayed in waiting spawners. These results show that when the carrying capacity and maximum rate of recruitment are fixed, the Ricker and Beverton–Holt models differ at both low and high spawner stock size. Therefore, the choice between Ricker and Beverton–Holt models should not depend only on the comparison of recruitment at high spawning stock sizes. The model presented here is a good initial building block for a full life history model for salmonids or other species and similar techniques could be used for the other life history stages.