To survive, a successful predator needs to be good at catching its prey, but if it becomes too efficient, will it eat itself out of prey and starve? Since the 1920s, scientists have developed mathematical models of predator and prey relationships. The models tend to be unstable, with wild swings in population size, while the natural world is full of examples of stable relationships, according to mathematical ecologist Alan Hastings of the University of California, Davis. Scientists have looked hard for stabilizing factors to add to the models. Now, a team led by Matt Keeling of Cambridge University, England, has resolved some of these problems. In the current issue of the journal Science, Keeling and colleagues show that stability can be explained by a single finding. Enemies and victims tend not to be in the same place at the same time. This is not due to active avoidance by victims, said Hastings, who wrote a commentary on the paper for the same issue of Science. It arises purely from the dynamics of the model -- in very simple terms, predators have eaten all the prey in the immediate area and need to move to feed again. The new model could explain stability previously attributed to other factors, such as changes in predator behavior, said Hastings. The original paper by Keeling and others and the commentary by Hastings were published in the Dec. 1 issue of Science.