When The Best-Fit Model Is Not The Best: Selecting a Model From a Biological Point Of View

The Alaska Department of Fish and Game use sonar to monitor Sockeye salmon return in the Kenai River, Alaska. Due to timing of fish arrivals and limitation of budgets, the sonar monitoring may not start at the beginning of return, and often ends before the end of return. In order to estimate arrivals of salmon missed by the sonar at the start and end of return, we used three probability models to fit the sonar counts data. We applied a model selection criterion AIC, Akaike Information Criterion, to select the best model.  However, the best model by AIC is the worst one to estimate the tails of daily arrivals. In the end we chose a model from a biological point of view, not from a statistical criterion.