If you are a zebra hoping to avoid being eaten by lions your best bet is to live somewhere there are a lot of other zebras. A new study has found that the number of lions, and other predators, will go up in response to a larger prey population, but not as fast as the prey population itself. This pattern has been found to apply equally in environments far from Africa's grasslands, and the mathematical patterns are consistent for whales chasing fish and crustaceans consuming plankton.

When an ecosystem is rich in animals at the bottom of the food chain it naturally also tends to attract more predators. We might expect the percentage increase of predator and prey to be one to one but Dr Ian Hatton, of McGill University, Canada, told IFLScience, “This pattern has been noted qualitatively many times: the number of prey per predator is higher in productive systems than in less productive systems.”

However, it is only now, with the publication of a paper in Science based on Hatton's PhD thesis, that this pattern has been quantified, with the discovery that the rate of scaling is consistent in all sorts of environments.

Hatton and his co-authors analyzed studies of 2,260 ecosystems around the world. They examined the total biomass in each case. For species of a fairly consistent body size, biomass is closely tied to numbers of individuals, but the relationship is looser for those that vary more in weight.

They found that as the density of prey increased predator mass grew with an exponential of ¾, rather than one. If the environment supported twice as much prey, the biomass of the combined predators would 1.7 times greater. "We kept being astonished," said co-author Professor Kevin McCann, of the University of Guelph, in a statement. "This is just an amazing pattern."

“Our findings suggest this pattern is very systematic and follows a simple mathematical function, that appears to be similar across very different kinds of ecosystems,” Hatton told IFLScience. “I suspect that the quantitative nature of the pattern and its generality were not found previously because the data required is enormous. It's only in the past decade or so that the data is available for large cross-system comparisons.”

Although Hatton says, “I wouldn't be surprised if they exist,” he and his co-authors found no notable exceptions to this pattern across the extraordinary diversity of environments they considered. However, he added, “We did not study systems with complex feeding relationships. Omnivores or piscivores that feed at multiple levels in the food chain tend to obscure this pattern.”

The full explanation for the relationship remains unknown, but Hatton says it is “Underpinned by the community production-biomass power law: the number of offspring per individual declines with crowding.” This can be observed in humans – urbanization is one of the factors driving global reductions in birthrates, although the reasons may be different.

The authors conclude, “These patterns suggest a greater degree of ecosystem-level organization than previously recognized and a more predictive approach to ecological theory.”