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

## TL;DR

This study uses Bayesian networks and structural equation models to uncover genetic relationships among traits in lodgepole pine trees, improving breeding strategies.

## Contribution

The novel integration of Bayesian networks and structural equation models reveals causal genetic relationships among productivity, defense, and climate-adaptability traits in lodgepole pine.

## Key findings

- Tree height has strong positive causal effects on wood density and stable carbon isotope ratio.
- SEM models outperformed traditional multitrait models in capturing genetic relationships and predictive ability.
- SEM produced higher heritability estimates and lower residual variances compared to traditional models.

## 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 multitrait 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.