PULLMAN, Wash. — A research team led by a Washington State University biologist and a mathematical biologist 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), which varies depending on its age, or the size of a plant, which may vary depending on how much it is shaded during the day. 

The mathematical description of a biological trait can get very complex when it includes variables for all the factors that impact that trait. For example, the body size of a mouse depends not only on its age, but on nutrition, amount of exercise, temperature, its 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. It is useful in signal processing for filtering out the noise and creating a clean description of an electronic wave.

“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,” he said.

“Function-value methods move our analytical capabilities from a point to a curved line,” Carter said. “Instead of just 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,” Carter said. “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.”

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, Gomulkiewicz said. “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.”

In making the grant, the NSF encouraged the team’s software creation objective.  Software tools for analyzing complicated traits could be very useful to other biologists who could apply function-value-trait analysis to their own data sets.

“Having the software available will help scientists know what kind of empirical data they need to collect in order to make important predictions,” Gomulkiewicz said. “These are the kinds of predictions that could play a role in saving endangered species or in determining what environmental factors lead to extinctions.”

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. “This work would not be possible without all these kinds of people working together.  It is exciting that such an integrated yet diverse group all felt strongly that function-value-trait tools need to be developed.”

Gomulkiewicz especially values the participation of Mark Kirkpatrick, who first applied the function-value approach to evolution and genetics.  As a postdoctoral student at the University of Texas, Gomulkiewicz worked in Kirkpatrick’s lab from 1989 to 1991.

“Mark invented a general framework for studying these function-value traits, but the biologists who could potentially use this framework are not,” Gomulkiewicz said.  “What is missing are specific statistical tools and models that would be relevant to different biological systems.  What we are doing that is new is creating the specific statistics and mathematical models that are relevant for the biological systems that are under study by biologists in many fields. We are including on our team empiricists (who typically collect data sets in the field or in their labs) so that we can set up examples of how the function-value approach works for them.”

Topics of interest among the researchers include the relationship between exercise and body mass and food consumption, the effects of aging, gene expression as a function of age, the impact of crowding on plant production, and other studies relating to a spectrum of organisms from plants and insects to mammals.

Both Carter and Gomulkiewicz came to WSU in 1996. In addition to doing research, they teach a number of large undergraduate courses in their respective departments. They received a $100,000 seed grant from NSF in 2000, which was used to build their multiuniversity research team.