Using Structural Equation Models to Interpret Genome-Wide Association Studies for Morphological and Productive Traits in Soybean [Glycine max (L.) Merr.]

Understanding trait relationships is fundamental in soybean breeding because the goal is to maximize simultaneous gains. Standard multi-trait genome-wide association studies (MT-GWAS) identify variants linked to multiple traits but fail to capture phenotypic structures or interrelations. Structural Equation Models (SEM) account for covariances and recursion, enabling the decomposition of single nucleotide polymorphism (SNP) effects into direct or indirect components and identifying pleiotropic regions. We applied SEM to analyze morphology (pod thickness, PT) and yield traits (number of pods, NP; number of grains, NG; hundred-grain weight, HGW). The dataset comprised 96 soybean individuals genotyped with 4070 SNP markers. The phenotypic network was constructed using the hill-climbing algorithm, a class of score-based methods commonly applied to learn the structure of Bayesian networks, and structural coefficients were estimated with SEM. According to coefficient signs, we identified negative interrelationships between NG and HGW, and positive ones between NP and NG, and HGW and PT. NG, HGW, and PT showed indirect SNP effects. We also found loci jointly controlling traits. In total, 46 candidate genes were identified: 7 associated exclusively with NP and 4 associated with NG. An additional 15 genes were common to NP and NG, 3 were common to NP and HGW, 6 were common to NG and HGW, and 11 were common to NP, NG, and HGW. In summary, SEM-GWAS revealed novel relationships among soybean traits, including PT, supporting breeding programs.