Genomic selection, which predicts phenotypes such as yield and drought resistance in crops from high-density markers positioned throughout the genome of the varieties, is moving towards machine learning techniques to make predictions on complex traits that are controlled by several genes. In this paper, we consider sparse Bayesian learning and ensemble learning as a technique for genomic selection and ranking markers based on their relevance to a trait. We define and explore two different forms of the sparse Bayesian learning for predicting phenotypes and identifying the most influential markers of a trait, respectively. We apply our methods on a Saccharomyces cerevisiae dataset, and analyse our results with respect to existing related works, trait heritability, as well as the accuracies obtained from linear and Gaussian kernel functions. We find that sparse Bayesian methods are not only competitive with other machine learning methods in predicting yeast growth in different environments, but are also capable of identifying the most important markers, including both positive and negative effects on the growth, from which biologists can get insight. This attribute can make our proposed ensemble of sparse Bayesian learners favourable in ranking markers based on their relevance to a trait.