Simple rules predict the outcome of predator-prey struggles

December 05, 2000

ITHACA, N.Y. -- Whether the battlefield was pond water filled with algae-eating zooplankton or London during a measles epidemic, life's struggles for survival once seemed so complex that only a highly sophisticated model running on a supercomputer could predict the outcome.

Not necessarily so, say ecologists at Cornell University and North Carolina State University who have developed a new mathematical model: If just a few factors are sufficient to capture the essentials of predator-prey battles, many seemingly complex problems in population dynamics can be understood using only a desktop computer.

"Ever since ecologists in the 1920s began to model interacting populations, they have been struggling with the observation that very simple theoretical models predict very complicated dynamics like population cycles," said Gregor F. Fussmann, a postdoctoral associate in ecology and evolutionary biology at Cornell and lead author of an article in the Nov. 17 issue of the journal Science (Vol. 290, No. 5495, pp. 1358-60).

But do these predictions hold when real, live organisms are the players?

"It is a problem of counting trees and missing the forest," said Nelson G. Hairston Jr., another article author and the Rhodes Professor of Environmental Science at Cornell whose laboratory performed a key test of the new model. "It has become popular recently to model populations using an equation for each individual as a way to try to understand complicated patterns of increases and decreases in numbers. It turns out for our system that a few simple and general equations can explain the complex switch from constant population sizes to extreme cycles." The test was simple enough: Day after day for more than 14 weeks, single-celled green algae (Chlorella vulgaris ) and the microscopic animals that eat them (planktonic rotifers, Brachinus calyciflorus ) faced off in vessels called chemostats. Chemostats are glass tubes that can be filled with water and stocked with predator and prey species, allowing researchers to control the supply of an essential nutrient -- in this case, nitrogen. At high nitrogen supply, the algae can be expected to reproduce quickly; farther up in the food chain, the rotifer population also should thrive. At low nitrogen supply, however, both algae and rotifers might struggle to survive.

In a series of chemostat trials, the researchers varied the rate at which fresh water or nitrogen entered to the system. Then they sat back to watch and found these results:

• When nitrogen concentrations or supply rates were relatively low, the system remained at equilibrium with just enough algae for the rotifers to eat and enough rotifers to prevent overpopulation of the algae.

• But lower nitrogen supply rates were detrimental for predator populations for another reason: rotifer individuals usually remained longer in the chemostat vessels before they were washed out, and this shifted the population toward older, less reproductive predators.

• And when large amounts of nitrogen entered the system, numbers of both the predators and prey oscillated wildly, resulting in the extinction of both.

The predators and prey in the laboratory microcosm had responded just the way the model predicted, given the cards that "life," in the form of pumps and chemostat valves, had dealt them.

"Similarly simple models have been successful in a variety of circumstances, including measles 'preying on' people in large cities like London, on commercially important crab populations in the Pacific and on forest insect pests, despite the fact that the patterns of population variation look quite complicated," said Stephen P. Ellner, the Cornell professor of ecology and evolutionary biology who was a professor of biomathematics at North Carolina State when the study began.

"More complicated systems can be broken down to examine and model individually," added Kyle W. Shertzer, a graduate student of biomathematics at North Carolina State.

The chemostat model, although verifiedin vitro , will get one of its first real-world tests when Cornell ecologists begin a five-year, $3 million "biocomplexity" study for the National Science Foundation in the freshwater bays and lagoons of Lake Ontario. Scientists are intrigued by the analogy between the chemostat set experiment and tributaries and runoff from the surrounding land carrying nutrients to the plankton, fish and other inhabitants in the bay ecosystems. Judicious application of the model should make the bio-complex a little less so.
Related World Wide Web sites: The following sites provide additional information on this news release. Some might not be part of the Cornell University community, and Cornell has no control over their content or availability. • News release from NC State:

• Cornell Ecology and Evolutionary Biology:

• NSF biocomplexity study:

Cornell University

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