Quantifying migratory delay: a new application of survival analysis methods

Statistical techniques commonly used in fish passage research fail to adequately quantify delays incurred at obstacles, or the effects of modifications to those obstacles on passage rates. Analyses of telemetry data describing these effects can be misleading, particularly when passage route of some individuals is not established (e.g., because of mortality, tag failure, passage through unmonitored or alternate routes, etc.). Here, we demonstrate how event-time analysis, better known as survival analysis, can be used to quantify passage rates for any study that allows tracking of individuals through time, even when some individuals fail to pass the route or obstacle in question. We review two of the primary methods of event-time analysis (parametric and Cox's proportional hazards regression analyses) and use them in combination with logistic regression to provide unbiased estimates of delay incurred at a hydroelectric facility, as well as insights on factors affecting both rates of passage and route selection. Passage rate increased with increased depth of a surface bypass sluice gate and, among fish that passed through the turbines, with turbine flow. The data further indicate that risk of turbine passage increased with both delay and turbine flow.