A QTL model to map the common genetic basis for correlative phenotypic plasticity

As an important mechanism for adaptation to heterogeneous environment, plastic responses of correlated traits to environmental alteration may also be genetically correlated, but less is known about the underlying genetic basis. We describe a statistical model for mapping specific quantitative trait loci (QTLs) that control the interrelationship of phenotypic plasticity between different traits. The model is constructed by a bivariate mixture setting, implemented with the EM algorithm to estimate the genetic effects of QTLs on correlative plastic response. We provide a series of procedure that test (1) how a QTL controls the phenotypic plasticity of a single trait; and (2) how the QTL determines the correlation of environment-induced changes of different traits. The model is readily extended to test how epistatic interactions among QTLs play a part in the correlations of different plastic traits. The model was validated through computer simulation and used to analyse multi-environment data of genetic mapping in winter wheat, showing its utilization in practice.