Math approach may help scientists with predictions

A research team led by a biologist and a mathematical biologist from Washington State University is using special statistical methods to study how traits of biological organisms change.

Associate professors Patrick Carter, an evolutionary physiologist, and Richard Gomulkiewicz, a mathematical geneticist, won a $2.1 million, four-year grant from the National Science Foundation to fund their research on function-valued traits.

A trait that can be described as a mathematical function of some other variable is called a function-valued trait. These traits include such things as the body size of an animal — perhaps a mouse — that varies depending upon its age, or the size of a plant that may vary depending upon how much it is shaded during the day.

The mathematical description of a biological trait can get complex when it includes variables for all the factors that impact that trait. For example, the body size of the mouse depends not just upon age, but also upon nutrition, amount of exercise, temperature, genetic heredity and other factors as well.

“The function-value approach has long been used by physicists and engineers to study phenomena that are a function of time,” said Gomulkiewicz. “Such things as radio waves and pulsars.

“In the past, methods to compare biological traits with variables have been rudimentary and based on statistics. We hope to develop more sophisticated — statistical, empirical and theoretical — methods to analyze these function-value traits in natural populations.”

“Function-value methods move our analytical capabilities from a point to a curved line,” said Carter. “Instead of a single snapshot of how a trait is characterized at a single point in time, we can track it from egg to death.

“In addition, we can assess the genetic basis of that curve. A researcher might find out that genes greatly impact body mass at an early age and play less of a role at an older age. Once we understand the genetic basis of the function-value trait, we can predict how evolution will occur across generations.

“This could be useful in projecting the impact of changes in the environment, such as those caused by global warming. For example, if we know that an insect’s size depends in part on temperature, function-value trait calculations allow us to estimate the genetic basis of that trait and to predict the evolutionary impact that global warming could have on insect size over many generations.”

“These are the kinds of predictions that could play a role in saving endangered species, or in determining what environmental factors lead to extinctions,” Gomulkiewicz said.

In examples where the value of a complex trait is dependent upon many variables, the situation becomes too complex to describe with relatively simple mathematical functions, according to Gomulkiewicz. “The only way to harness this much information, in a way that is useful, is to use computers to analyze the data. The final step in our project will be to develop software to analyze and use function-value traits.”

Eight senior investigators from six other universities are also on the grant. “We have statisticians, theoreticians and empiricists working together in an integrated way,” Gomulkiewicz said.

Topics of interest among the researchers include the relationship between exercise, body mass and food consumption, the effects of aging, and the impact of crowding on plant production.

Carter and Gomulkiewicz received a $100,000 seed grant from NSF in 2000, which they used to build their multi-university research team.

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