Researchers establish formula for predicting predator-prey populations

November 15, 2000

The complicated population interactions of predator and prey species have long intrigued scientists, who have developed mathematical models that predict how those populations interact. They've had difficulty, however, demonstrating that such predictions reflect reality for species more complex than single-celled organisms.

Now, a team of scientists from Cornell University and North Carolina State University has done exactly that. Their laboratory research - on the population interactions of tiny multicellular planktonic rotifers and the single-celled green algae on which they feed - is highlighted in the Nov. 16 issue of the journal Science.

Their research is the first to use long-duration experiments of multiple interacting species to verify a mathematical population model. Their conclusion: a few straightforward rules can govern predator-prey population dynamics for species more complex than single-celled bacteria and protists.

"We combine theoretical and empirical approaches to demonstrate that a few simple mechanistic processes underlie complex multispecies dynamics and that a correspondingly simple model is a sound tool for investigating community properties," the researchers write in the Science article.

The co-authors on the Science paper are Dr. Gregor F. Fussmann, a post-doctoral associate at Cornell University; Dr. Stephen P. Ellner, formerly a professor of biomathematics at NC State and now at Cornell; Kyle W. Shertzer, a biomathematics doctoral candidate at NC State; and Dr. Nelson G. Hairston Jr., Frank H.T. Rhodes Professor of Environmental Science at Cornell.

Their research indicates that simple mathematical models may be useful in helping to predict the population dynamics of a variety of multicellular organisms in the natural world, such as during outbreaks of agricultural pest species. And it could serve as a launching point for studies on the possible co-evolution of predator and prey species, and on the possibility that some organisms have evolved in a way that reduces the likelihood of complex population dynamics.

The model developed by the researchers is a set of four equations designed to describe the dynamics of the system. They tested the model by running experiments using a water-containing apparatus, in which they placed the predator rotifers - Brachionus calyciflorus - and the prey algae - Chlorella vulgaris.

During 18 experimental trials, they varied the concentration of nitrogen pumped into the system and the dilution rate of the water in the system. The nitrogen concentration determined the birth rate of the algae, which, in turn, determined the rotifers' birth rate.

Those trials yielded results expected by the model, varying according to the nitrogen concentration input and the rate at which the water was diluted. At low nitrogen levels, the two species coexisted at an equilibrium or in cycles. At intermediate dilution rates, the populations oscillated, while they remained at equilibrium at high and low dilution levels.

Shertzer, the NC State biomathematics doctoral candidate, said the research indicates that internal population limitations - such as predator-prey interactions - can drive population cycles without any forcing from external limitations such as environmental conditions. And, he explains, the research team has demonstrated that researchers don't need to know everything about an environmental system to predict its population dynamics.

"It is a really simple model that's able to catch the important mechanisms of the system necessary to describe the system," he said. "This shows that you don't necessarily need to track every detail to make accurate predictions." Shertzer continues to work with Dr. Stephen Ellner to refine the model.
"Crossing the Hopf Bifurcation in a Live Predator-Prey System" Published: Nov. 16, 2000, in Science.


Gregor F. Fussmann, Cornell University; Stephen P. Ellner, Cornell University and North Carolina State University; Kyle W. Shertzer, North Carolina State University; Nelson G. Hairston Jr., Cornell University.


Population biologists have long been interested in the oscillations in population size displayed by many organisms in the field and laboratory. A wide range of deterministic mathematical models predict that these fluctuations can be generated internally by nonlinear interactions among species and, if correct, would provide important insights for understanding and predicting the dynamics of interacting populations.

We studied the dynamical behavior of a two-species aquatic laboratory community encompassing the interactions between a demographically structured herbivore population, a primary producer, and a mineral resource, yet still amenable to description and parameterization using a mathematical model. The qualitative dynamical behavior of our experimental system, that is, cycles, equilibria, and extinction, is highly predictable by a simple nonlinear model.NC State University News Services
Campus Box 7504
Raleigh, NC 27695-7504


Media Contacts:

Dr. Stephen Ellner, Cornell University, 607-254-4221 or

Kevin Potter, NC State News Services, 919-515-3470 or

North Carolina State University is a participant in the Amazon Services LLC Associates Program, an affiliate advertising program designed to provide a means for sites to earn advertising fees by advertising and linking to