When Does Reaction Norm GWAS Discover Plasticity? The Residual Channel in Environmental Index-Based Genetic Dissection

Abstract

CERIS-JGRA replaces the environmental mean in Finlay-Wilkinson regression with a climate-derived index, so that reaction norm association mapping can dissect the genetics of phenotypic plasticity. Its defining design choice forecloses that objective. An index correlated at{rho} with the environmental means decomposes exactly into{rho} times the mean plus a residual, and its loading on informative variation orthogonal to the mean,{tau} , cannot exceed {surd}(1 -{rho} {superscript 2}). Sensitivity independent of mean performance is orthogonal to the mean by definition, reaching the slope only through{tau} , and the non-centrality of a plasticity-specific test goes as{tau} {superscript 2}. The algorithm maximizes{rho} , minimizing by construction the channel carrying the signal it is used to detect. Simulation confirms this. A parameter-free expression reproduces observed power across 189 conditions to a root mean square error of 0.030. Power to detect plasticity-specific loci falls from 0.64 at{rho} = 0 to 0.009 at{rho} = 0.99 and 0.003 at{rho} = 0.996, invariant to architecture, coupling and environment count. Holding{rho} at 0.5 while reducing{tau} from 0.87 to zero drops power from 0.576 to 0.000:{rho} governs discovery as a proxy, not a cause. Panel size compensates, scaling as 1 / (1 -{rho} {superscript 2}): 125-fold at{rho} = 0.996. Reimplemented on published sorghum data, the search returns the published index, photothermal time 18 to 43 days after planting, first of 27,144 candidates, at{tau} = 0.083. We recommend reporting{tau} beside{rho} , and reading slope loci found below{tau} {approx} 0.15 as mean-performance loci. Article summaryCrop geneticists commonly replace a field trials average yield with an index built from weather data, then map the genes controlling how a plant responds to its environment. We show by algebra that this cannot work as intended. The index is chosen to track the trial average as closely as possible, and the closer it tracks, the less room remains for the independent signal that plasticity genes need to be detected. Simulation and a reanalysis of published sorghum data agree. The search that makes an index good for predicting performance is the same search, run backwards, that makes it useless for finding genes.