On Making Statistical Inferences Regarding the Relationship between Spawners and Recruits and the Irresolute Case of Western Atlantic Bluefin Tuna (Thunnus thynnus)

Forecasts of the future abundance of western Atlantic bluefin tuna (Thunnus thynnus) have, for nearly two decades, been based on two competing views of future recruitment potential: (1) a "low" recruitment scenario based on hockey-stick (two-line) curve where the expected level of recruitment is set equal to the geometric mean of the recruitment estimates for the years after a supposed regime-shift in 1975, and (2) a "high" recruitment scenario based on a Beverton-Holt curve fit to the time series of spawner-recruit pairs beginning in 1970. Several investigators inferred the relative plausibility of these two scenarios based on measures of their ability to fit estimates of spawning biomass and recruitment derived from stock assessment outputs. Typically, these comparisons have assumed the assessment estimates of spawning biomass are known without error. It is shown here that ignoring error in the spawning biomass estimates can predispose model-choice approaches to favor the regime-shift hypothesis over the Beverton-Holt curve with higher recruitment potential. When the variance of the observation error approaches that which is typically estimated for assessment outputs, the same model-choice approaches tend to favor the single Beverton-Holt curve. For this and other reasons, it is argued that standard model-choice approaches are insufficient to make the case for a regime shift in the recruitment dynamics of western Atlantic bluefin tuna. A more fruitful course of action may be to move away from the current high/low recruitment dichotomy and focus instead on adopting biological reference points and management procedures that are robust to these and other sources of uncertainty.