Reconstruction of networks with direct and indirect genetic effects

Genetic variance of a phenotypic trait can originate from direct genetic effects, or from indirect effects, i.e., through genetic effects on other traits, affecting the trait of interest. This distinction is often of great importance, for example when trying to improve crop yield and simultaneously controlling plant height. As suggested by Sewall Wright, assessing contributions of direct and indirect effects requires knowledge of (1) the presence or absence of direct genetic effects on each trait, and (2) the functional relationships between the traits. Because experimental validation of such relationships is often unfeasible, it is increasingly common to reconstruct them using causal inference methods. However, most of the current methods require all genetic variance to be explained by a small number of QTLs with fixed effects. Only few authors considered the missing heritability case, where contributions of many undetectable QTLs are modelled with random effects. Usually, these are treated as nuisance terms, that need to be eliminated by taking residuals from a multi-trait mixed model (MTM). But fitting such MTM is challenging, and it is impossible to infer the presence of direct genetic effects. Here we propose an alternative strategy, where genetic effects are formally included in the graph. This has important advantages: (1) genetic effects can be directly incorporated in causal inference, implemented via our PCgen algorithm, which can analyze many more traits and (2) we can test the existence of direct genetic effects and improve the orientation of edges between traits. Finally, we show that reconstruction is much more accurate if individual plant or plot data are used, instead of genotypic means. We have implemented the PCgen-algorithm in the R-package pcgen.