The evolution of function-valued traits. As part of the study of the evolution of the integrated phenotype, we measured salamander body size as a function of age (Ragland and Carter 2004), and mouse body mass, activity behavior, and food consumption as a function of age in the model system of aging mice (Morgan, Garland and Carter 2003; Morgan and Carter, in prep). A trait that can be described as a mathematical function of some other variable (e.g., body size as a function of age) is called a function-valued (or infinite-dimensional) trait, and can be analyzed using special statistical methods. These function-valued methods are more powerful than conventional statistical methods, and when applied to a trait measured in a population of organisms in which family relationships are known, can estimate the genetic structure and the evolutionary potential of the trait across all values of the independent variable.
I am collaborating with Dr. Richard Gomulkiewicz , a biological mathematician at WSU who helped develop function-valued methods, to improve and extend the methods (Kingsolver, Gomulkiewicz and Carter 2001). Dr. Gomulkiewicz and I received an incubation grant from the Biocomplexity Program at NSF in 2000 to develop a research group to tackle this problem. We were successful in this endeavor and currently we are funded by NSF to work with 8 other senior investigators (Jay Beder, George Gilchrist, Nancy Heckman, Joel Kingsolver, Mark Kirpatrick, Steve Marron, Scott Pletcher, and Annie Schmidt) to further develop function-valued methods and apply them to multiple empirical systems.