The primary goal of common wheat (T. aestivum) breeding is increasing yield without negatively impacting the agronomic traits or product quality. Genetic approaches to improve the yield increasingly target genes that impact the grain weight and number. An energetic trade-off exists between the grain weight and grain number, the result of which is that most genes that increase the grain weight also decrease the grain number. QTL associated with grain weight and number have been identified throughout the hexaploid wheat genome, leading to the discovery of numerous genes that impact these traits. Genes that have been shown to impact these traits will be discussed in this review, including TaGNI, TaGW2, TaCKX6, TaGS5, TaDA1, WAPO1, and TaRht1. As more genes impacting the grain weight and number are characterized, the opportunity is increasingly available to improve common wheat agronomic yield by stacking the beneficial alleles. This review provides a synopsis of the genes that impact grain weight and number, and the most beneficial alleles of those genes with respect to increasing the yield in dryland and irrigated conditions. It also provides insight into some of the genetic mechanisms underpinning the trade-off between grain weight and number and their relationship to the source-to-sink pathway. These mechanisms include the plant size, the water soluble carbohydrate levels in plant tissue, the size and number of pericarp cells, the cytokinin and expansin levels in developing reproductive tissue, floral architecture and floral fertility.
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