Solved! Mystery That Stumped Ecosystem Modelers

As scientists warn that the Earth is on the brink of a period of mass extinctions, they are struggling to identify ecosystem responses to environmental change. But to truly understand these responses, more information is needed about how the Earth's staggering diversity of species originated.

Curiously, a vexing modeling mystery has stymied research on this topic: mathematical models have told us that complex ecosystems, such as jungles, deserts and coral reefs, in which species coexist and interact with another, cannot persist--even though they obviously do.

But now, Stefano Allesina and Si Tang, both of the University of Chicago, have solved that vexing modeling mystery, and have thereby laid the groundwork for improvements in the modeling of complex ecosystems to environmental change.

The researchers' work, which was funded by the National Science Foundation (NSF), is published in this week's issue of Nature.

The tension between mathematical models of ecosystems and the existence of the Earth's rich biodiversity was first exposed about 40 years ago by the development of a ground-breaking mathematical model that represented the relationship between ecosystem stability and diversity; the model was developed by Robert M. May of Oxford University.

According to May's model, ecosystems that harbor large numbers of interacting species would necessarily be extremely unstable--so unstable that even slight perturbations, such as variable weather and environmental conditions, would be enough to trigger massive extinctions within them. Therein lies a paradox: According to May's modeling, the persistence in nature of the complex ecosystems we observe should be exceedingly improbable.

Ever since May released his modeling results, scientists have been attempting to identify factors that enable species to persist despite the general tendency towards instability and extinctions highlighted by May's results. Now, in their Nature paper, Allesina and Tang explain why May's results do not accurately describe ecosystems in which "Eat or be eaten", relationships (predator/prey relationships) are prevalent. Allesina explains: "May's model assumes that any two species in a large ecological network interact with one another at random, and without any consideration of the specific type of interaction between them, whether it is a predator-prey relationship, a mutualistic relationship or a competitive relationship."

But in their recent research, Allesina and Tang modeled ecosystems in which species consume each other in addition to interacting with one another as competitors or mutualists. Their results explain why large numbers of species do, in fact, thrive instead of necessarily going extinct as predicted by May's model. This advance provides the foundation for the development of increasingly sophisticated analyses of ecosystem responses to environmental change.

Allesina believes that it is predator/prey relationships (not competitor or mutualistic relationships) that provide the necessary stability for almost infinite numbers of species to exist in ecosystems. They do so by keeping the size of species populations in check at supportable levels. Allesina explains, "When prey are high, predators increase and reduce the number of prey by predation. When predators are low, prey decrease and thus reduce the number of predators by starvation. These predator/prey relationships thereby promote stability in ecosystems and enable them to maintain large numbers of species."

By contrast, mutualistic relationships may reinforce the growth of large populations and competitive relationships may depress population numbers to the point of ecological instability. Allesina says that May's model mixed various types of species interactions but could not represent these relationships accurately because of technical modeling constraints that he and Tang overcame.

"The results of Allesina and Tang's network analyses are important," says David Spiller, an NSF program director, "because they show that the stability properties of complex ecological systems are determined by the type of interaction among species (predation, competition, mutualism) and the strength of those interactions."

Allesina says that he and Tang intend to further improve their ecosystem model by embedding into it well-known interactions that exist between particular species. He also says that the insights gleaned through this study may be used to improve models of other types of networks that are unrelated to ecology, such as various types of gene regulatory networks and chemical reactions.

Remarkably, Allesina says that he and Tang cracked the biodiversity mystery without supercomputers or other high-tech instruments that are so frequently at the core of current biological discoveries: "We did the necessary calculations with just a pen and paper after finding a 1988 article on quantum physics that gave us the key to crack the problem."

-NSF-

Puzzle Play Improves Math Skills

An important context for figuring out problems through reasoning is puzzle play, say researchers at University of Chicago.

Psychologist Susan Levine and colleagues recently conducted a study that found 2-4 year-old children, who play with puzzles, have better spatial skills when assessed at 4 1/2 years of age.

After controlling for differences in parents' income, education and overall amount of parent language input, researchers say puzzle play proved to be a significant predictor of spatial skills--skills important in mathematics, science and technology and a key aspect of cognition.

"As early as the preschool years and persisting into adulthood, there are individual and gender differences on certain spatial tasks, notably those involving mental rotation [of objects]," the researchers write in their report, published in Developmental Science. "These variations are of considerable interest because of their reported relation to mathematics achievement."

Improvements in math education are a point of emphasis for the National Science Foundation, which partly funded the study. "This study brings greater awareness of the learning opportunities for children in everyday activities," said Soo-Siang Lim, program director for the NSF's Science of Learning Centers Program. "It is important because this and follow-up studies could potentially lead to relatively easy and inexpensive interventions to improve spatial skills important for STEM education."

STEM education involves science, technology, engineering and mathematics. Activities such as early puzzle play may lay the groundwork for development in these areas. In particular, the ability to mentally transform shapes is an important predictor of STEM course taking, degrees and careers, say researchers.

"The children who played with puzzles performed better than those who did not on tasks that assessed their ability to rotate and translate shapes," said Levine, a leading expert on mathematics development in young children.

The study was the first to look at puzzle play in a naturalistic setting. The researchers followed 53 child-parent pairs from diverse socioeconomic backgrounds for a two-year period. Researchers recorded parent-child interactions on video during 90-minute sessions that occurred every four months between 26 and 46 months of age.

The researchers asked the parents to interact with their children as they normally would and about half of the children in the sample played with puzzles at least one time. Higher income parents tended to engage children with puzzles more frequently. Both boys and girls who played with puzzles had better spatial skills, but boys played with more complicated puzzles than girls, and the parents of boys provided more spatial language during puzzle play and were more engaged in the play than the parents of girls.

The boys also performed better than the girls on a mental transformation task given at 54 months of age.

"Further study is needed to determine if the puzzle play and the language children hear about spatial concepts actually causes the development of spatial skills and to examine why there is a sex difference in the difficulty of the puzzles played with and in the parents' interactions with boys and girls," said Levine. "We are currently conducting a laboratory study in which parents are asked to play with puzzles with their preschool sons and daughters, and the same puzzles are provided to all participants.

"We want to see whether parents provide the same input to boys and girls when the puzzles are of the same difficulty," Levine said. "In the naturalistic study, parents of boys may have used more spatial language in order to scaffold their ability to put more difficult puzzles together."

Alternatively, the difference in parent spatial language and engagement may be related to a societal stereotype that males have better spatial skills. "Our findings suggest that engaging both boys and girls in puzzle play can support the development of an aspect of cognition that has been implicated in success in the STEM disciplines," Levine said.

Joining Levine in writing the paper are Kristin R. Ratliff and Janellen Huttenlocher of the University of Chicago and Joanna Cannon of the New York City Department of Education.

In addition to NSF, the National Institutes of Health/National Institute of Child Health and Human Development provided funding for the study.

-NSF-