A multistage Gompertz life‐cycle model applied to threatened Chinook salmon

Abstract Because the Gompertz model has a long history of use as a population model, we analyzed its properties as a multistage stock‐recruitment model. We found that if a life‐cycle model is a sequence of linked Gompertz stock‐recruitment models at each life stage, then it is also a Gompertz stock‐recruitment model. This is similar to the well‐known result for the Beverton–Holt stock‐recruitment model. The Gompertz model is guaranteed to yield least squares estimates and therefore, can offer a distinct advantage over the Beverton–Holt model, which cannot be fit using linear regression and may not yield valid maximum likelihood estimates. We illustrate the use of this multistage modelling framework by applying it to Snake River spring/summer Chinook salmon (Oncorhynchus tshawytscha). We found that the Gompertz model fit the data better than the Beverton–Holt Model, and yielded similar carrying capacity estimates for both juveniles and adults. Past work by others on these populations has usually assumed that parr‐to‐adult survival is density independent. However, we found that this assumption may be incorrect: when we applied two‐stage models to these populations, we found density dependence at the juvenile‐to‐adult stage. This suggests that life‐cycle modelling to date has been overly optimistic about the benefits of survival rate increases in the hydro‐system and elsewhere to improve the viability of salmon populations threatened with high extinction risk.