DEVELOPING FOUR PLAUSIBLE PARAMETERISATIONS OF FOOSA (A SO-CALLED REFERENCE SET OF PARAMETERISATIONS) BY CONDITIONING THE MODEL ON A CALENDAR OF EVENTS THAT DESCRIBES CHANGES IN THE ABUNDANCES OF KRILL AND THEIR PREDATORS IN THE SCOTIA SEA

We tuned four parameterizations of Foosa to provide predictions that are consistent with the agreed calendar, as specified by the WG-SAM, that describes changes in the abundances of krill and their predators in the Scotia Sea. First, we compiled a set of base parameterizations from information in the literature and following specifications laid out by the WG-SAM. These base parameterizations cover a combinatorial framework that considers krill movement (or lack thereof) and the shape of a relationship determining how the effective abundance of breeding predators depends on foraging success during the breeding season. We also added a new functional relationship to Foosa: a relationship that determines the degrees to which the survival of juvenile predators depends on foraging success in their first winter of life. The dynamics predicted by our base parameterizations were loosely consistent with the direction and timing of changes in predator abundance specified by the numerical calendar from Hill et al. (2008). This indicated that our base parameterizations were reasonable and that tuning to the numerical calendar would be feasible. Second, we tuned, via sums of squares, one stock-recruitment parameter for each predator population in each parameterization to the “empirical abundance estimates” for predators reported by Hill et al. (2008). Tuning the peak recruitment by all 19 predator populations was sufficient to predict the empirical abundance estimates almost exactly for all predators by all parameterizations. The dynamics predicted by these tuned parameterizations often had trends and changes in magnitude that were roughly consistent with those in the numerical calendar, lending additional support to the validity of the initial conditions, un-tuned parameters, and functional forms used in this application of Foosa. Finally, we tuned, via an objective function that minimizes the sum of absolute proportional differences in abundance, one or two stock-recruitment parameters for each predator population to the numerical calendar itself. Parameterizations tuned in this last step constitute our reference set and predict plausible dynamics by reasonably matching the timing of events and magnitude of changes that are specified in numerical calendar. This reference set encapsulates hypotheses that go beyond the basic contrasts between krill movement and predator response to foraging success in the breeding season, implying a diverse set of hypotheses that includes SSMU-specific views about the productivities of individual predator populations and the effects of winter foraging conditions on juvenile survival. All four parameterizations in our reference set imply ongoing trends in predator populations, and, in forward simulations, changes in abundance predicted from these ongoing trends will likely need to be separated from changes caused by krill fishing. Although we believe that all four parameterizations in our reference set are plausible to some degree, we do not think that they are equally plausible. We suggest plausibility ranks for these four parameterizations that might be useful for synthesizing the output of future modeling efforts and simplifying communications with decision makers. After completing our analytical work and writing most of this paper, we found a small error in the initial conditions used in one of our four parameterizations. We discuss why this error does not affect the conclusions presented here or in our follow-on effort to conduct a risk assessment using the reference set.