Infinite-Dimensional Traits: Estimation of Mean, Covariance, and Selection Gradient of Tribolium Castaneum Growth Curves

Abstract

In evolutionary biology, traits like growth curves, reaction norms or morphological shapes cannot be described by a finite vector of components alone. Instead, continuous functions represent a more useful structure. Such traits are called function-valued or infinite-dimensional traits. Kirkpatrick and Heckmann outlined the first quantitative genetic model for these traits. Beder and Gomulkiewicz extended the theory on the selection gradient and the evolutionary response from finite- to infinite-dimensional traits. Rigorous methods for the estimation of these quantities were developed throughout the years. In his dissertation, Baur defines estimators for the mean and covariance function, as well as for the selection gradient based on two different assumptions. First, it is assumed that all individuals are independent. The second case considers a sample of independent families of equally related individuals. In this thesis, results of the estimations based on data on Tribolium Castaneum larvae will be stated. Estimations of the pre-selection mean, the evolutionary response to selection, and the phe- notypic covariance function were run for five consecutive generations - once assuming that all larvae are independent and once for independent families of full-siblings. Using the pre-selection mean and the evolutionary response to selection, the mean function among newborns of the successive generation is computed. The selection gradient is not explicitly estimated as it is contained in the computation of the evolutionary response to selection. The differences in results from using Ornstein-Uhlenbeck and Wiener covariance functions are examined. It becomes evident that the choice of the candidate covariance function heavily impacts the results of the estimation. With respect to this observation, alternative ways to find a suitable candidate covariance function, based on the provided data, are discussed.