A Bayesian Analysis of Biological Uncertainty for a Whole-Lake Fertilization Experiment for Sockeye Salmon in Chilko Lake, British Columbia, and Implications for the Benefit–Cost Ratio

Abstract

Chilko Lake in British Columbia, Canada, was fertilized with nitrogen and phosphorus in the late 1980s and early 1990s to increase abundance and harvests of adult sockeye salmon Oncorhynchus nerka. Because of the short, 5-year duration of this program and the large inherent natural variation in adult recruits produced per spawner both before and during lake fertilization, there is considerable uncertainty about the efficacy of that fertilization. Recent analyses suggest a high probability that more adult sockeye salmon were produced per spawner from fertilization than would have been produced without fertilization, but the confidence interval on that increase is large. Furthermore, no economic analysis has been done to determine the effect of the large biological uncertainties on the benefit–cost (BC) ratio of the project. We filled this need by using Bayesian statistical analysis to estimate uncertainty in the parameters of four models that reflected different hypotheses about the biological effects of fertilization on sockeye salmon. We then used those estimated posterior probability distributions for (1) additional sockeye salmon recruits that were attributable to fertilization and (2) the resulting economic BC ratio. This ratio took into account costs of fertilization as well as costs and benefits of harvesting additional fish. We found evidence of biological and net economic benefits for the Chilko Lake fertilization project. Depending on the model, the posterior probability was at least 81% that the abundance of adult sockeye salmon increased owing to fertilization and at least 84% that the BC ratio was greater than 1.0 (mean BC ratio = 27). Nevertheless, considerable uncertainty remains because the 95% probability interval was large for the BC ratio. The breadth of the distribution for the BC ratio was probably underestimated because of uncertainties (omitted here) concerning various economic components of our analysis as well as the costs and benefits of the indirect effects of fertilization.