Functional mapping of reaction norms to multiple environmental signals.

Whether there are different genes involved in response to different environmental signals and how these genes interact to determine the final expression of the trait are of fundamental importance in agricultural and biological research. We present a statistical framework for mapping environment-induced genes (or quantitative trait loci, QTLs) of major effects on the expression of a trait that respond to changing environments. This framework is constructed with a maximum-likelihood-based mixture model, in which the mean and covariance structure of environment-induced responses is modelled. The means for responses to continuous environmental states, referred to as reaction norms, are approximated for different QTL genotypes by mathematical equations that were derived from fundamental biological principles or based on statistical goodness-of-fit to observational data. The residual covariance between different environmental states was modelled by autoregressive processes. Such an approach to studying the genetic control of reaction norms can be expected to be advantageous over traditional mapping approaches in which no biological principles and statistical structures are considered. We demonstrate the analytical procedure and power of this approach by modelling the photosynthetic rate process as a function of temperature and light irradiance. Our approach allows for testing how a QTL affects the reaction norm of photosynthetic rate to a specific environment and whether there exist different QTLs to mediate photosynthetic responses to temperature and light irradiance, respectively.