**5. Discussion**

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 dynamic traits, a new analytical model for genome-wide association analysis of dynamic data, called functional GWAS (fGWAS), has been derived [65]. There are two advantages to fGWAS over GWAS: (1) fGWAS is able to identify genes that determine the final form of the trait and (2) it provides the ability to study the temporal pattern of genetic control over a time course.

The regulation network of plant height traits has been studied intensively in molecular biology. We already know that the development of plant height traits is regulated by growth hormones such as GA and IAA. Using functional mapping, we found 48 growth QTLs in *A*. *thaliana*. Through the GO annotation of QTLs, we found that there are many genes among the significant loci identified in this study that are related to the pathways for synthesis and conduction of growth hormones, such as AT4G00160.1, which encodes an F-box protein in the signal transduction pathway. It has been shown that the F-box is an auxin receptor. Thus, we can see that the QTLs identified in this study may not only be applicable to *A*. *thaliana*, but also to other plants. These results show that functional mapping can reveal more intricate details of dynamic traits such as height growth and other phenotypes.

Functional mapping is far from enough to fully study complex traits, and there are still many limitations in describing the developmental pathways leading to the final phenotype and revealing the underlying genetic mechanisms for the formation and development of these traits. It is too simple to draw a complete dynamic diagram of complex traits. Wu [66] extends functional mapping to system mapping. By identifying the dynamic formation process of complex traits as a system and decomposing it into several parts, the QTL that controls the interaction of each component during the development of complex characters is identified. From the point of view of ecology, the process of character formation is extremely complex. To draw a complete quantitative genetic structure, we need to study the characteristics of an organism affected by its own genes as well as the influence from the community partner genome. In nature, most organisms live in groups, and individuals compete with each other. Wu combined game theory with QTL mapping, which opens up new opportunities for improving the accuracy and resolution of complex phenotype QTL recognition [67].
