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

Abstract

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.

Keywords: association testing; functional data analysis; gene region; longitudinal traits; rare variants.

FIGURE 1

Research status on quantitative traits and genetic variants.

FIGURE 2

Power of linkage equilibrium’s case one and case two based on LFDAT for the five gene regions when c is 3, and sample size is 2000. The (A–C) denotes the power results of case one. The (D–F) denotes the power results of case two. The time effect function is $\theta \left(t\right)=2+2\sin \left(\pi t/12\right)$ for case one, and $\theta \left(t\right)=2+2\sin \left(\pi t/2\right)$ for case two. (A) Proportion of causal variants is 1% (B) Proportion of causal variants is 2% (C) Proportion of causal variants is 4%. (D) Proportion of causal variants is 1% (E) Proportion of causal variants is 2% (F) Proportion of causal variants is 4%. Note: Common region denotes gene regions only with common variants, Rare region denotes gene regions only with rare variants, Low region denotes gene regions only with low-frequency variants, Mixture region one denotes gene regions with 20% of common variants and 80% of rare variants, and the Mixture region two denotes gene regions with 80% of common variants and 20% of rare variants.

FIGURE 3

Power of linkage disequilibrium’s case one and case two based on LFDAT for the five gene regions when c is 3, and sample size is 2000. The (A–C) denotes the power results of case one. The (D–F) denotes the power results of case two. The time effect function is $\theta \left(t\right)=2+2\sin \left(\pi t/12\right)$ for case one, and $\theta \left(t\right)=2+2\sin \left(\pi t/2\right)$ for case two. Case one: (A) Proportion of causal variants is 1% (B) Proportion of causal variants is 2% (C) Proportion of causal variants is 4%. Case two: (D) Proportion of causal variants is 1% (E) Proportion of causal variants is 2% (F) Proportion of causal variants is 4%. Note: The r ² measure of linkage disequilibrium is 0.25 to 0.64; Common region denotes gene regions only with common variants, Rare region denotes gene regions only with rare variants, Low region denotes gene regions only with low-frequency variants, Mixture region one denotes gene regions with 20% of common variants and 80% of rare variants, and the Mixture region two denotes gene regions with 80% of common variants and 20% of rare variants.

FIGURE 4

The shoot biomass development trajectory of 350 samples. The solid gray line represents the trajectory curve of 350 samples, and the solid black line represents the average trajectory curve.