Reconstruction of Networks with Direct and Indirect Genetic Effects

Abstract

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 control 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 current methods require all genetic variance to be explained by a small number of quantitative trait loci (QTL) with fixed effects. Only a few authors have considered the “missing heritability” case, where contributions of many undetectable QTL are modeled 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 an 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.

Improving Genomic Prediction Using High-Dimensional Secondary Phenotypes

“…The arrow Y s → Y f represents a causal effect from at least one of the secondary traits on the target trait. (Left) Some of the genetic correlations between Y s and Y f are the result of the causal effect Y s → Y f ; to some extent they may also be a consequence from correlation between the direct genetic effects G → Y f and G → Y s (see Kruijer et al, 2020 for more mathematical details). (Right) There is no causal effect Y s → Y f , and genetic correlations between them may be induced by genetic effects on a latent trait L that is affecting both Y s and Y f .…”

“…The ( k, l )th entry of Λ contains the effect of trait k on trait l , and the vectors g i and r i have zero mean Gaussian distributions with covariance matrices Σ g and Σ r , respectively. The joint distribution of all n ( p + 1) trait values is then as in (1), with Σ u = Γ t Σ g Γ and Σ e = Γ t Σ r Γ, where Γ = ( I − Λ) −1 (Gianola and Sorensen, 2004 ; Töpner et al, 2017 ; Kruijer et al, 2020 ).…”

Machine learning in plant science and plant breeding

“…For examples, see e.g. ( Kruijer et al, 2020 ) (crop species) and ( Meinshausen et al, 2016 ; Peters et al., 2017 ) (yeast). The advantage of these approaches is that the effect of interventions can be predicted, for example, what will happen in case of different conditions or management or upon silencing a gene.…”

Perspectives on Applications of Hierarchical Gene-To-Phenotype (G2P) Maps to Capture Non-stationary Effects of Alleles in Genomic Prediction

“…However, hierarchical G2P maps with partial knowledge of intermediate processes offer promise for predicting long-term response to selection, given their success in improved short-term predictions of non-stationary effects of alleles. An obstacle in the practical applications of such hierarchical G2P modeling approaches is non-identifiability, also referred to as equifinality or the many-to-one property (Lamsal et al, 2018;Barghi et al, 2020;Henshaw et al, 2020;Kruijer et al, 2020;Tsutsumi-Morita et al, 2021). Effects can be non-identifiable due to unmeasured confounders that generate correlated errors between effects, which results in multiple, equally likely hierarchical G2P maps for experimental data sets.…”