Molecular Plant Breeding 2024, Vol.15, No.5, 247-258 http://genbreedpublisher.com/index.php/mpb 253 Bayesian methods provide a probabilistic framework for QTL mapping and GS, integrating prior knowledge about the distribution of QTL effects. Bayesian LASSO, for instance, extends the LASSO method by employing a Bayesian approach to estimate shrinkage parameters, thereby enhancing the accuracy of QTL detection and breeding value prediction. Other Bayesian methods, such as BayesA, BayesB, and BayesCπ, have been developed to address different genetic architectures and marker densities. These methods have demonstrated strong performance under various conditions, with BayesCπ being particularly recommended when a small number of loci have large effects on the trait (Clark et al., 2011; Wang et al., 2015). 6.2 Model validation and accuracy Validating GS models is crucial to ensure their predictive accuracy and reliability. Common validation methods include cross-validation, which involves dividing the data into multiple training and testing sets to evaluate the model's performance, and independent testing, where the model is validated using a completely separate dataset. These methods help evaluate the model’s ability to generalize to new data and avoid overfitting (Goddard and Hayes, 2007; Li et al., 2017). Cross-validation and independent testing are essential for evaluating the robustness and accuracy of GS models. Cross-validation estimates the model's performance by repeatedly splitting the data into training and testing sets, which helps identify potential overfitting. Independent testing, on the other hand, validates the model on a separate dataset not used during training, providing a more stringent assessment of the model’s predictive power. Both methods are critical for ensuring that GS models are reliable and applicable to diverse populations (Goddard and Hayes, 2007; Li et al., 2017). 6.3 Software and computational tools Several software tools are available for QTL mapping and GS, each with its own strengths and limitations. Some of the widely used software includes the following: R/qtl is a comprehensive tool for QTL mapping that supports various types of genetic crosses and provides a range of statistical methods for QTL analysis. GEMMA is a software for genome-wide association studies (GWAS) and GS that implements linear mixed models to account for population structure and relatedness. BGLR is a Bayesian generalized linear regression package in R that supports various Bayesian methods for genomic prediction, including Bayesian LASSO, BayesA, BayesB, and BayesCπ (Li and Sillanpää, 2012; Wimmer et al., 2013; Wang et al., 2015). The increasing availability of high-density marker data presents significant computational challenges for QTL mapping and GS. These challenges include managing large datasets, ensuring computational efficiency, and developing robust statistical methods. Addressing these issues requires the development of more efficient algorithms, the use of parallel computing, and leveraging high-performance computing resources. For instance, the Stepwise Linear Mixed Model (StepLMM) has been proposed to integrate GWAS and GS into a single statistical model, improving computational efficiency and accuracy (Eeuwijk et al., 2009; Li et al., 2017). Additionally, Bayesian methods and penalized regression techniques like LASSO can help manage the complexity of the data and improve the robustness of the models (Li and Sillanpää, 2012; Wimmer et al., 2013; Wang et al., 2015). 7 Case Studies inEucommia ulmoides 7.1 Growth traits QTL mapping has been extensively used to identify genetic regions associated with growth traits in E. ulmoides. Jin et al. (2020) constructed a comprehensive genetic linkage map using 452 polymorphic markers, covering 94.10% of the estimated genome (Figure 2). This study identified 25 QTLs for tree height, 32 QTLs for ground diameter, and 15 QTLs for crown diameter, distributed across various linkage groups. Li et al. (2014) mapped 706 markers across 25 linkage groups, covering approximately 89% of the genome, and identified 18 QTLs explaining 12.4% to 33.3% of the phenotypic variance in growth traits. Additionally, Liu et al. (2022) used GBS to construct a high-density genetic map and identified 44 QTLs associated with growth traits, with phenotypic variance ranging from 10.0% to 14.2%.
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