Reply to Szuwalski: Policies robust to uncertainty in causes of productivity changes are needed

Szuwalski (1) has greatly misinterpreted the principal message of our report (2). We did not claim you could reliably estimate regime shifts for individual stocks. Table 2 in our report (2) clearly shows that the chance of improper assignment of the hypothesis is very high, even when you have a long time-series of data in hand. At any point in time, managers will rarely know if observed changes in productivity are a result of regime changes, changes in biomass, or random.

What is needed is to find harvest policies that are robust to all of the alternatives, recognizing that we will be uncertain at any given time. This uncertainty is a problem in risk analysis: evaluating the risks of assuming it is a regime shift when it is really biomass driven, and the risks of assuming changes in productivity are because of changes in biomass when it is in reality a change in regime. Our report (2) simply illustrated the importance of considering both hypotheses and provided guidance on how frequently different hypotheses are likely to be true. In the Bayesian statistical, world our analysis provided a prior.

Szuwalski’s figure is highly misleading (1). When the simulations in his figure (see figure 1 of ref. 1) are replotted (Fig. 1) with zero as the origin on the x and y axes, it is obvious that the changes observed in surplus production are very small, and the differences because of age structure are miniscule compared with the jumps in productivity, averaging 100% we identified from the real data [see figure 2 in our report (2)]. Furthermore, although Szuwalski claims his simulation has an almost ideal contrast in the data, the range of depletion levels explored (Fig. 1A) is very narrow compared with that observed in actual exploited fish stock.

Fig. 1.

Replication of Szuwalski’s (1) deterministic simulation of a stock with dynamics driven by spawning biomass, with the life-history characteristics and F trajectory used by the Szuwalski. purple boxes (B) denote regime shifts identified by STARS (see description of Szuwalski’s methods in ref. 1). Red lines are the fits of the respective models, A and C.

The probability of errors in identifying hypotheses depends greatly on the history of fishing mortality rates and productivity of the stock. The simulations reported in our study (2) used the actual values for the datasets we were evaluating, whereas Szuwalski (1) uses values for both that are not from the actual data; therefore, we believe our estimates of the frequency of misclassification are much more reliable. To assess the performance of Szuwalski’s simulations under more realistic fishing patterns, we reproduced his analysis using 116 fishing mortality time-series extracted from the Ram II Legacy database (3) (data were rescaled to fall in the range 0.2–0.4, similar to Szuwalski’s). Using a deterministic recruitment, the Fox model was selected 94% of the time, but the mixed model was selected only 6% of the time.

Age-structured models do behave slightly differently from biomass dynamics models, but the differences are commonly in the order of 10–20% (as seen in our plotting of Szuwalski’s data in Fig. 1), whereas we found the regime shifts in both the regime and mixed models were much larger.