np QTL: networking phenotypic plasticity quantitative trait loci across heterogeneous environments.

Despite its critical importance to our understanding of plant growth and adaptation, the question of how environment-induced plastic response is affected genetically remains elusive. Previous studies have shown that the reaction norm of an organism across environmental index obeys the allometrical scaling law of part-whole relationships. The implementation of this phenomenon into functional mapping can characterize how quantitative trait loci (QTLs) modulate the phenotypic plasticity of complex traits to heterogeneous environments. Here, we assemble functional mapping and allometry theory through Lokta-Volterra ordinary differential equations (LVODE) into an R-based computing platform, np QTL, aimed to map and visualize phenotypic plasticity QTLs. Based on LVODE parameters, np QTL constructs a bidirectional, signed and weighted network of QTL-QTL epistasis, whose emergent properties reflect the ecological mechanisms for genotype-environment interactions over any range of environmental change. The utility of np QTL was validated by comprehending the genetic architecture of phenotypic plasticity via the reanalysis of published plant height data involving 3502 recombinant inbred lines of maize planted in multiple discrete environments. np QTL also provides a tool for constructing a predictive model of phenotypic responses in extreme environments relative to the median environment.