Bayesian networks and structural equation models reveal genetic causal relationships between productivity, defense, and climate-adaptability traits in interior lodgepole pine

Abstract

This study investigates the integration of Bayesian networks (BN) and structural equation models (SEM) to explore genomic relationships among nine traits related to productivity, defense, and climate-adaptability in an interior lodgepole pine breeding program. Data from 392 open-pollinated trees, genotyped with 25,099 SNP markers, were analyzed. The traditional multi-trait model (MTM) served as a benchmark for comparing SEM in estimating genetic (co)variance components, genetic correlations, breeding value (BV) predictions, and predictive ability, using both pedigree- (ABLUP) and genomic-based (GBLUP) individual-tree mixed models. The Hill-Climbing algorithm identified 12 significant causal structures (λ) among traits. Strong positive causal effects included tree height (HT) on wood density (WD) (λHT→WD = 0.413) and on stable carbon isotope ratio (C13) (λHT→C13 = 0.565), and limonene (LIMO) on carbon assimilation rate (CAR) (λLIMO→CAR = 0.368). The most influential causal relationship was HT → C13, followed by resistance to western gall rust (WGR) → CAR, CAR → LIMO, and WGR → C13. SEM incorporated these relationships, capturing both direct and indirect effects. Compared with MTM, SEM yielded lower residual variances, higher additive variances, and higher heritability estimates for all traits. The λ values from SEM correlated strongly with genetic correlations (0.932), with similarly high correlations between models (0.929), though SEM produced lower posterior mean correlations. BV correlations between models were high (ABLUP > 0.82, GBLUP > 0.84), but some reranking occurred among the top 39-trees (ABLUP > 0.71, GBLUP > 0.42). ABLUP and GBLUP-SEM models outperformed MTM in predictive ability, with mean gains of 6.62% and 6.03%, mainly for conditioned traits. BN-SEM enhances understanding of trait networks, improving genomic evaluations and breeding strategies in forest trees.