Young pianists broaden their experience at Summer School
Become a Living BookUNE mathematician crunches numbers on species extinction
January 18, 2008
Like the heroes of the TV program "Numb3rs", mathematicians at the University of New England are attempting to use maths to model real-world situations and make predictions about their outcomes – most recently, to model the struggle between two competing species fighting to occupy the same territory.
The research has a number of potential applications, including fisheries management and the protection of endangered species.
Yihong Du, a professor in the School of Science and Technology at UNE, has been using differential equations to model animal populations and predator-prey interactions for the past 10 years. His latest research, about to be published in the Journal of Differential Equations, looks at how the survival of species is affected by the shape and size of their habitat.
Prof Du collaborated on the research with colleagues from China, Taiwan, the US, as well as Australia.
He said that while theoretical results generally matched well with real situations, there were very few models that could be used to make accurate predictions about life in the animal world.
"The models I am working on will hopefully reveal new phenomena," he said.
According to Prof Du's theory, where two species are fiercely competing for resources in a round or spherical shaped habitat, the stronger species will inevitably prevail, while the weaker species will die out. In a dumbbell or hourglass shaped habitat, however, the two species will be able to co-exist, with a mathematically predictable "border" arising between their respective territories.
"Mathematically, this division will occur at the place with the shortest border," Prof Du said.
Prof Du has also used maths to predict how big a protective reserve needs to be to protect a weaker species from a stronger one.
"If we want to create a protective zone for a weaker species, there is a critical size," Prof Du said. "If the protective zone is smaller than that size, it will have no effect, and the weaker species will be wiped out regardless of our efforts."
The critical size of the habitat was mathematically determined by the birth-rate of the weaker species, Prof Du said.
While he hastened to point out that his model was merely a theoretical representation of what might happen in the real world, Prof Du said that he hoped by publishing his research in prestigious international journals, others might pick up where he left off.
"If a biologist or someone reads about this model and is able to apply it to his own populations research, then that would be great," Prof Du said.
Posted by Leon Braun at January 18, 2008 03:19 PM