Modeling temporal phenomena in variable environments with parametric models: An application to migrating salmon

Timing phenomena are integral to many ecological processes but are difficult to analyze due to the unique nature of timing data and because environmental conditions and behavior can vary during the observation period. We demonstrated methods, based on parametric hazard-rate modeling, to analyze “time-to-event” data under time-varying conditions. We developed routines in R to apply parametric models, based on the exponential, Weibull, and modified Weibull distributions, to time-to-event data. We applied the models to data on the time for migrating adult salmonids to successfully pass a hydroelectric dam. The model captured pronounced diel behavior and the effects of time-varying covariates river flow, spill, and water temperature on passage times. The methods we demonstrated have potential application to a broad range of ecological questions.