Equation-free mechanistic ecosystem forecasting using empirical dynamic modeling.

It is well known that current equilibrium-based models fall short as predictive descriptions of natural ecosystems, and particularly of fisheries systems that exhibit nonlinear dynamics. For example, model parameters assumed to be fixed constants may actually vary in time, models may fit well to existing data but lack out-of-sample predictive skill, and key driving variables may be misidentified due to transient (mirage) correlations that are common in nonlinear systems. With these frailties, it is somewhat surprising that static equilibrium models continue to be widely used. Here, we examine empirical dynamic modeling (EDM) as an alternative to imposed model equations and that accommodates both nonequilibrium dynamics and nonlinearity. Using time series from nine stocks of sockeye salmon (Oncorhynchus nerka) from the Fraser River system in British Columbia, Canada, we perform, for the the first time to our knowledge, real-data comparison of contemporary fisheries models with equivalent EDM formulations that explicitly use spawning stock and environmental variables to forecast recruitment. We find that EDM models produce more accurate and precise forecasts, and unlike extensions of the classic Ricker spawner-recruit equation, they show significant improvements when environmental factors are included. Our analysis demonstrates the strategic utility of EDM for incorporating environmental influences into fisheries forecasts and, more generally, for providing insight into how environmental factors can operate in forecast models, thus paving the way for equation-free mechanistic forecasting to be applied in management contexts.

Prey selection by an intertidal beetle: field test of an optimal diet model.

Adult beetles Thinopinus pictus LeConte (Staphlyinidae) live on sand beaches in temporary burrows from which they emerge at night to prey on amphipods Orchestoidea calforniana (Brandt). I constructed models of amphipod size selection by beetles, using the size distributions of amphipods measured on the beach, and the results of laboratory experiments on capture success, reaction distance and feeding rates. Capture success decreased and the probability that an amphipod was detected increased with increasing amphipod size. Beetles observed during beach searches selected larger sizes of amphipods than predicted from availability and vulnerability of different sizes. To apply an optimal foraging model, I estimated the profitability of different sizes of amphipods from the number of amphipods of a given size required to satiate a beetle in the laboratory. Profitability was highest for large amphipods and lowest for small amphipods and isopods. However, amphipod abundance on the beach was always below the threshold at which specialization on larger sizes was predicted to occur.

Comment on "Declining wild salmon populations in relation to parasites from farm salmon".

Krkosek et al. (Reports, 14 December 2007, p. 1772) claimed that sea lice spread from salmon farms placed wild pink salmon populations "on a trajectory toward rapid local extinction." Their prediction is inconsistent with observed pink salmon returns and overstates the risks from sea lice and salmon farming.