Integration of Proxy Intermediate Omics traits into a Nonlinear Two-Step model for accurate phenotypic prediction

Intermediate omics traits, which mediate the effects of genetic variation on phenotypic traits, are increasingly recognised as valuable components of genetic evaluation. In particular, rhizosphere microbiota play a crucial role in plant health and productivity; however, their complex interactions with host genetics remain challenging to model. Although two-step modeling frameworks have been proposed to integrate intermediate omics traits into phenotype prediction, existing approaches do not incorporate nonlinear relationships between different omics layers. To address this, we have proposed a two-step phenotype prediction framework that integrates genomic, rhizosphere microbiome, and metabolome (meta-metabolome) data, while explicitly capturing omicsomics nonlinearities. The first step is to predict meta-metabolome traits from genetic and microbial features, thus effectively isolating them from the environmental noise. In this process, intermediate "proxy" omics traits are generated as general biological information to provide robust models. The second step utilises this "proxy" to enhance the accuracy of the phenotype prediction. We compared the linear model (Best Linear Unbiased Prediction, BLUP) and the nonlinear model (Random Forest, RF) at each step, as demonstrated through simulations and empirical analysis of a multi-omics soybean dataset in which nonlinear modeling captures intricate omics interactions. Notably, our approach enables phenotype prediction without requiring the original meta-metabolome data used in model training, thereby reducing reliance on costly omics measurements. This framework integrates intermediate omics traits into genomic prediction to improve prediction accuracy and provide solutions for deeper insights into plant-microbiome interactions.