Oct. 22, 2001 COLLEGE STATION, Texas -- What can abstract mathematical equations tell about animals and plants living in the wild? A lot, contend Texas A&M University scientists who are collaborating to better understand how wildlife animals and plants live and interact.
The project started two years ago when two Texas A&M professors, Paulo Lima-Filho of the Department of Mathematics and Thomas E. Lacher Jr. of the Department of Wildlife and Fisheries Sciences, met together at a social setting.
"Dr. Lacher was describing the problems he was encountering in modeling landscapes and ecological environments," says Lima-Filho, "and I started realizing that my expertise in topology - a branch of mathematics - could be used to provide a general framework to approach the questions he was having in modeling the environment."
The two scientists decided to work together to develop a sort of "mathematical theory of landscape" by using equations to model the environment. Their collaboration grew bigger when three other researchers from the Department of Mathematics, Peter F. Stiller, Michael S. Pilant and Jay R. Walton, joined in.
The ecologist and the four mathematicians are now trying to model Costa Rica's natural habitats - the places where animals and plants live and grow, such as forests, pastures or wetlands. The model should provide a mapping of the habitats and describe how the habitats vary with time.
"Until now, scientists have been superimposing snapshots of landscapes taken at different times in the past," says Lacher, "whereas a quantitative description of landscape patterns would give us a look at the future."
The model could be used to improve landscape development, for example by selecting appropriate agricultural areas. It could also help scientists restore previously degraded landscapes by controlling tropical deforestation or agricultural expansion.
Preliminary results show that high levels of deforestation may lead to larger than expected animal extinction rates.
"When landscape becomes too fragmented, the risk of extinction may be much higher than you would expect by counting the number of individuals or by presuming that the small habitats communicate with each other, because the smaller populations are no longer interbreeding," says Lacher.
Once the landscape habitats are modeled, the next step is to describe how animals and plants live, grow and interact with each other in each habitat. The task is particularly daunting because different animal and plant species can have very different sizes, weights, reproductive cycles, or dispersal rates, also called "allometric parameters" by biologists.
"Though biologists have models for behaviors of cells or individual organisms," says Stiller, "we need to devise larger, more integrated models, where you have many interacting species in different environments."
Species of different sizes - say an insect and an elephant - perceive environment in very different ways, says Lima-Filho. For this reason, he assigns each organism with a mathematical entity, the scaling function, which reflects the scale at which the landscape is perceived by the organism.
To describe how species interact, Lima-Filho uses the species' allometric parameters, their scaling functions, as well as information from the habitat, to determine how much energy they produce and consume, and how they compete for natural resources.
Though the project is still in its early stages, its future seems promising. It is now supported by two grants from the National Science Foundation. One of them funds hands-on research experiences for undergraduates in the wildlife and fisheries department. The other grant has been recently awarded to the department of mathematics and will fund twelve three-year post-doctoral positions, 10 summer undergraduate student stipends and eight graduate fellowships.
"What I find really exciting in this collaboration," Lacher says, "is the potential to develop predictive tools that would allow us to be proactive in developing conservation policies, instead of being reactive by simply realizing that we have lost habitats and species."
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