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In the process of growth and development in life, gene expressions that control quantitative traits will turn on or off with time. Studies of longitudinal traits are of great significance in revealing the genetic mechanism of biological development. With the development of ultra-high-density sequencing technology, the associated analysis has tremendous challenges to statistical methods. In this paper, a longitudinal functional data association test (LFDAT) method is proposed based on the function-on-function regression model. LFDAT can simultaneously treat phenotypic traits and marker information as continuum variables and analyze the association of longitudinal quantitative traits and gene regions. Simulation studies showed that: 1) LFDAT performs well for both linkage equilibrium simulation and linkage disequilibrium simulation, 2) LFDAT has better performance for gene regions (include common variants, low-frequency variants, rare variants and mixture), and 3) LFDAT can accurately identify gene switching in the growth and development stage. The longitudinal data of the Oryza sativa projected shoot area is analyzed by LFDAT. It showed that there is the advantage of quick calculations. Further, an association analysis was conducted between longitudinal traits and gene regions by integrating the micro effects of multiple related variants and using the information of the entire gene region. LFDAT provides a feasible method for studying the formation and expression of longitudinal traits.

Gene Region Association Analysis of Longitudinal Quantitative Traits Based on a Function-On-Function Regression Model