A lush savannah teeming with zebras, gazelles and buffalo may look like an all-you-can eat buffet for lions.

But a new Canadian study has revealed a surprise: When prey abound, there are relatively fewer predators. And a look at ecosystems on land and sea around the world shows that this might be a fundamental law of nature.

Intuitively, you'd expect the populations of lions, leopards and hyenas to be proportional to the quantity of zebras and antelopes around for them eat, acknowledges Ian Hatton, the McGill University researcher who led the study published this week in Science.

"If you double the prey, you should double the predators," said Hatton. "And we found that this was not the case."

Animals graze in Masai Mara game reserve. The study found predator populations grew much more slowly than prey species such as wildebeest and zebras, following a distinct mathematical pattern called a power law. (Radu Sigheti/Reuters)

Hatton conducted the study for his PhD research under Michel Loreau, who is now with the Centre national de la recherche scientifique in France. He looked at the populations of prey species such as zebras and antelopes and predator species such as lions and hyenas in different African parks with different climates and environments— some were richer and lusher than others, so some had more animals than others.

'Power law'

He found that as the number of prey animals increased, the relative number of predators declined in a very predictable way. In other words, the more prey animals (or kilograms' worth of prey animals) there were, the fewer predators (or kilograms' worth of predators) there were for each one of those prey, following a distinct mathematical pattern called a power law.

If you double the prey, you should double the predators. And we found that this was not the case. - Ian Hatton , McGill University

For example, the dry Kalahari desert has only about 200 kilograms of prey — such as buffalo, zebra and impala — combined for every square kilometre, and about 4 kilograms of predators such as lions, and hyenas combined in the same area.

The teeming Ngorongoro crater has about 20 000 kg of prey for every square kilometre or 100 times more than the Kalahari, but has only about 110 kg or 27.5 times more predators in the same area.

This pattern was independent of time and short-term fluctuations in the relative numbers of predators and prey, which would have been cancelled out by the large sample representing decades.

Ian Hatton, who led the study for his PhD research, went to high school in Zimbabwe and wanted a chance to go back to Africa to see the animals in the parks there. (Courtesy Ian Hatton)

And it didn't just apply to African ecosystems. A look at data from 1,000 studies worldwide over the past 50 years showed it also applied to predators and prey in other parts of the world, in other environments, even to animals living in lakes and oceans. In fact, it even applied to herbivores, whose populations don't keep up with the growth of plants. "You could call a herbivore a predator on plants," Hatton said.

The discovery has implications for how humans manage ecosystems for food production as well as how ecosystems store carbon, which can affect climate change, suggested University of South Alabama ecologist Just Cebrian, who was not involved in the study, in an analysis piece accompanying the paper in Science.

It's not clear exactly why predators lose out when there are plenty of prey, but both mathematics and direct studies suggest it's because prey animals (and plants) breed more slowly in denser, more crowded environments.

This could have a big impact on carnivores like lions and tigers because they tend to target very young and very old prey rather than healthy adults, Hatton said, "mainly because they tend not to be able to catch them — they're faster and fitter and all that."

Similar effects occur throughout the food chain. Young shoots tend to be more tender and nutritious and small fish tend to be easier to swallow than big fish, for example.

Excuse to visit Africa

Hatton decided to compare the populations of different animals in African parks partly out of self interest. He had gone to high school in Zimbabwe and wanted a chance to go back to see the animals there.

A lion feeds at Tanzania's Serengeti National Park. The researchers think one of the reasons predator populations don't grow as quickly as their prey is because they mainly eat young animals, and prey animals breed more slowly in more crowded conditions. (Noor Khamis/Reuters)

Unfortunately, what he needed for his research was old records on papers and punchcards that hadn't been digitized, found mostly in park and university libraries as opposed to on the savannah itself.

"I didn't spend as much time in the parks as I wanted to," he acknowledged.

One of the intriguing things about the study, the researchers note, is the power law it follows is very similar to the one that causes large animals to grow more slowly than small animals.

"The cells in an elephant grow more than 100 times more slowly than those of a mouse," said Jonathan Davies, a McGill University researcher who co-authored the paper, in a news release.

Power laws in physiology like that one are considered fundamental laws of nature, Hatton said, but he added, "Our study is too new for me to say something like that."

Still, he hopes to get a job as a postdoctoral researcher where he can look into the possible link between the similar patterns.