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October 25, 2013

Can the 'butterfly effect' inform fisheries management?

by Dr. Heather Deese

Dr. Les Kaufman, a marine ecologist at Boston University, has been deploying his considerable talents in the service of fisheries science and management for over three decades, but it is in the last year that he has developed an approach that very well may elevate our ability to manage fisheries onto a new level.

This approach uses a set of mathematical tools developed a century ago by Edward Lorenz to capture the behavior of weather data, and made famous through a movie on the "butterfly effect." The butterfly effect describes high sensitivity to initial conditions within a complex, non-linear system like our planet's weather patterns—captured for the movies in the idea that a butterfly flapping its wings in Chile could set up a small disturbance in local air movement that ultimately leads to a typhoon in Tokyo.

By investigating the patterns of fish population sizes (stock size) using a dynamical systems approach, Kaufman and his colleagues are diagnosing the ways in which the population sizes of multiple fish species co-vary with each other and in relation to environmental factors. Their results provide new insights into the ways in which populations of species that previously weren't thought to have much to do with each other may in fact co-vary in time.

In the immediate, the results from their work could provide much-needed contextual understanding for those charged with decisions necessary to rebuild our fisheries.

At a recent presentation Kaufman emphasized: "When you grasp what this dynamical systems analysis allows us to do, it blows your socks off. The implications are tremendous. And we don't need a change in Magnuson," the law that controls federal fisheries management. "We can start using these results right away."

Why are the implications of a new analysis approach potentially so important? In fisheries stock assessment science, as in most sciences, the Holy Grail is prediction. Federal fisheries law currently requires the regional councils and NOAA to look out ten or more years to decide how many fish can be caught this year, and stock assessment scientists have built their predictive models to try to serve this requirement.

Traditional stock assessment models attempt to capture the key factors we think influence the size of a specific animal population, such as growth, natural mortality and mortality due to fishing, and then plug in data from shipboard fish surveys and run computer models to predict how many fish will be in the sea next year, the year after that, and the year after that.

But there are problems with the traditional population modeling approach. One is that the factors that affect the size of an animal population are not constant in time. Natural mortality, for example, can swing wildly from one year to the next due to a disease outbreak or a new predator in the region. Growth rates could vacillate due to environmental conditions, like temperature, or the availability of prey of different nutritional value. (A herring is a much more nutritious meal for a cod than a sand lance).

Kaufman's work with a small group of colleagues takes an entirely different tack. The dynamical systems approach investigates temporal changes in multiple fish species populations and environmental factors to look for patterns, rather than trying to model each population’s behavior mechanistically. The results provide insight into which external factors (prey species numbers, water temperature, competing populations) most strongly affect the population size of a specific species.

The picture that emerges provides a few new pieces of information that could be used to make better management decisions right away. One critical piece of information is the extent to which a species displays a close relationship with another time series—are the number of cod in the sea more closely related to the number of herring, or the water temperature? In combination with the history of stock size changes for each animal, this information can provide probabilities on whether the population is likely to increase or decrease in the following year, or the year after that. In short, this new approach may take us one giant step closer to that holy grail of prediction.

Fathoming is supported by a grant from the Maine Sea Grant program.

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