Pray for prey
POSTED 30 NOV 2000

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photo of the measles virus
The measles virus. From Linda Stannard's Virus Ultrastructure, at the Department of Medical Microbiology, University of Cape Town.
Courtesy The Big Picture book of Viruses













Mathematical descriptions of predators and prey have failed to explain why either species survives.








An adult parasitoid wasp lays eggs under the shell of immature scale insects. The next generation of parasitoid will cut a small hole in the scale to emerge.
Copyright Max Badgley/Biological Photography, courtesy M&R Durango, Inc.

On multi-colored grass, a gray-white wolf looks backward, a small caribou dangling from its jaws.
An Alaskan wolf savors lunch -- tender tundra caribou tartare.
Copyright L.G. Adams, USGS

Ponder the paradoxical life of the polar bear, parasitic wasp, or measles virus. If they're too successful, they wipe out the seals, insects or children they prey upon -- and then starve for lack of food or a host. Even if they don't quite annihilate their victims, the predators starve when prey becomes scarce.

The peculiar finding comes from equations predicting the life and death of pathogens and hosts, parasites and hosts, and predators and prey -- anywhere a so-called "enemy-victim" relationship exists. In reality, the equations describe situations where an enemy eats only one species of victim; things rapidly get twisted if the menu gets more interesting.

The problem, however, plagues mathematical ecology -- the theoretical study of animal populations -- more than it does the real world.
With a giant rack of thick antlers hanging down in front of it, a moose grazes in a forest.
Moose and wolves live in an uneasy balance on Isle Royale. This ungulate said "cheese" in the Rocky Mountains.
Copyright Rick Cameron, courtesy Bighorn National Forest

Out in nature, of course, fox coexist with hares. The wolves of Isle Royale in Lake Superior have eaten moose for decades under the watchful eyes of scientists, and while their numbers do vary, both species survive.

And AIDS, a disease that infects our species, has yet to extinguish humanity -- or itself.

Hybrid ecology Mathematical ecology dates to the 1920s, and ever since the founders balanced their first equations, it's been clear their math did not exactly correspond to reality.

Even when describing extremely simple systems -- say a couple of microorganisms duking it out in a lab dish -- the equations have not permitted predators and prey to survive.

Where is the fly in the ointment, the error in the equations that try to describe changing populations over time?

A new study in the journal Science showed that equations for the interaction of enemies and victims are improved by accounting for the spatial location of both parties. Matthew Keeling, a zoologist at Cambridge University who published the study, emailed us to explain that, "For the first time we have been able to link three major components used in theoretical ecology (and modeling) to stabilize enemy-victim interactions. We have shown that for a wide class of spatial models, spatial heterogeneity (or patchiness), time-delays and functional forms are all representations of the same underlying processes."

Translated: data on where the animals are OR how their numbers vary over time OR how they act can all explain the spatial location of organisms.

Spaced out
While based on theory and math rather than observation, the study could help explain some of the real world, says Alan Hastings, a mathematical ecologist at the University of California at Davis.

Previous ecological equations assumed that both victims and enemies moved randomly around their environment. But predators hunt and prey flee. Including some of this complexity makes the equations a lot more plausible, Hastings says. "The enemy drives the victim to extinction over here, but the victim is also some other place, so the enemy goes over there too. Things are not distributed uniformly in space."

In the math-eco jargon, enemies and victims displayed " negative covariance." Translated: they didn't hang out much.

A golden wasp sticks its egg-laying gadget inside a scale insect's house on a green leaf.Getting under my skin
A classic enemy-victim relationship concerns parasitoids, insects that lay eggs in other insects. Over a few weeks, the developing parasitoid larva gobbles, then kills, the host.

You might dismiss parasitoids as oddities, but as Hastings notes, insects are the most common type of multi-cellular life, and 15 percent of insects dine on their victims in this grisly manner. Furthermore, since parasitoids are mainstays of biological insect controls, understanding this relationship has real-world significance.

Still, we skeptical Why Filers couldn't help wondering: Does the new understanding apply, as advertised, to all enemy-victim systems -- hosts and parasites, hosts and pathogens, hosts and parasitoids, even predators and prey? If you, like many scientists, shave with Occam's razor, Hastings says your answer is "yes."

The razor, recall, is an ingrained scientific preference for simple explanations over complicated ones. But Hastings admits that theoretical ecologists are not about to fold up shop and declare victory just yet. The Keeling equations may be an advance, but "There's no evidence that the different systems would obey these rules."

-- David Tenenbaum


•The Lion and the Lamb Find Closure, Alan Hastings, Science, 1 Dec. 2000, pp. 1712-13.

• Reinterpreting Space, Time Lags and Functional Responses in Ecological Models, Matt Keeling et al, Science, 1 Dec. 2000, pp. 1758-61.




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