**Acknowledgements**

antibiotics, one-carbon pool by folate, starch, and sucrose metabolism, glycerolipid metabolism (synthase), glycerolipid metabolism (lipase), polyketide sugar unit biosynthesis, streptomycin biosynthesis, and pentose and glucuronate interconversions. We found that these nine pathways are mostly associated with carbohydrate, energy, and amino acid metabolism. These biological processes play an important role in the development of height in *Arabidopsis*.

We also found that AT4G00160.1 encodes an F-box protein in the signal transduction pathway. It has been shown that F-box is an auxin receptor [54]. Plant height development is regulated by gibberellin (GA) and auxin (indole-3-acetic acid [IAA]) [55], and GA20ox and GA30ox are encoded by multiple genes, and mutations in these loci can result in dwarfing of the plant in the later stage of GA biosynthesis [56]. The most significant site, AT4G01150.1, is related to protein curvature thylakoid chloroplastic. Protein curvature thylakoid chloroplastic tends to be located in leaves and stems, and plays an important role in plant photosynthesis, which affects plant growth [57].

Gene mapping has been shown to be a powerful approach for the study of the genetic architecture of complex traits. It has been instrumental for the characterization of QTLs that control quantitative traits of interest to agriculture, biology, and human disease [58, 59]. However, traditional mapping strategies do not provide much insight into the genetic control mechanisms for phenotypic variations if some statistical and biological issues related to the approach are not resolved. Ma et al. (2002) integrated some fundamental biological principles into the mapping framework, aimed at generating more biologically meaningful discoveries related to trait formation and development, further proposing so-called functional mapping [13]. Functional mapping attempts to combine strong statistical and molecular genetics with the developmental mechanisms of biological features, and to elucidate the genetic mechanisms of complex traits. Since functional mapping combines different mathematical functions with biological significance, it possesses three advantages over traditional mapping methods in QTL mapping: (1) because the underlying biological mechanism is considered, the results of functional mapping are closer to biological reality; (2) a smaller sample size can be used to achieve sufficient accuracy for QTL detection because multiple measurements of the same individual improve mapping accuracy; and (3) by treating the growth process as a smooth curve, a large number of variables can be analyzed simultaneously, and the estimation of a small number of parameters can improve the accuracy of the parameter estimation and flexibility of the model.

With the development of high-throughput sequencing technology and the reduction of sequencing cost, GWAS have become an important tool for studying complex traits and have been widely used in genetic studies of complex traits in humans, animals, and plants [60]. Most GWAS only use single phenotypic data to perform regression analysis with each SNP such as with Plink software [61]. In addition, some GWAS have been developed to solve the false positive loci of population structure and genetic relationship [62–64]. The successes and potential of GWAS have not been explored when complex phenotypes arise as a curve. In any regard, a curve is more informative than a point in describing the biological features of a trait. To apply functional mapping to GWAS by integrating GWAS and functional aspects of

**5. Discussion**

86 Next Generation Plant Breeding

This work is supported by National Natural Science Foundation of China (grant 31700576) and grant 201404102 from the State Administration of Forestry of China.
