A Computational Approach for Functional Mapping of Quantitative Trait Loci That Regulate Thermal Performance Curves

Whether and how thermal reaction norm is under genetic control is fundamental to understand the mechanistic basis of adaptation to novel thermal environments. However, the genetic study of thermal reaction norm is difficult because it is often expressed as a continuous function or curve. Here we derive a statistical model for dissecting thermal performance curves into individual quantitative trait loci (QTL) with the aid of a genetic linkage map. The model is constructed within the maximum likelihood context and implemented with the EM algorithm. It integrates the biological principle of responses to temperature into a framework for genetic mapping through rigorous mathematical functions established to describe the pattern and shape of thermal reaction norms. The biological advantages of the model lie in the decomposition of the genetic causes for thermal reaction norm into its biologically interpretable modes, such as hotter-colder, faster-slower and generalist-specialist, as well as the formulation of a series of hypotheses at the interface between genetic actions/interactions and temperature-dependent sensitivity. The model is also meritorious in statistics because the precision of parameter estimation and power of QTLdetection can be increased by modeling the mean-covariance structure with a small set of parameters. The results from simulation studies suggest that the model displays favorable statistical properties and can be robust in practical genetic applications. The model provides a conceptual platform for testing many ecologically relevant hypotheses regarding organismic adaptation within the Eco-Devo paradigm.