A functional mixed-effects model for the joint analysis of amplitude and phase variations in function-valued traits
Abstract
Quantitative genetics is the study of continuous traits and the statistical analysis of phenotypic variation, that is, the observable differences in physical traits among individuals within a population. If family relationships between individuals are known, phenotypic variation can be partitioned into genetic and environmental components. Some traits, such as growth trajectories, can be described as a function of a continuous index and are known as function-valued traits. However, function-valued traits from different individuals often vary not only in their shape (amplitude) but also in the speed at which the biological process develops (phase). In this work, we present and compare two approaches to account for amplitude and phase variations in estimating the additive genetic and environmental components. The first one follows from a conventional framework where warping functions remove phase variations, and then the aligned curves are analysed. The second approach adopts the perspective of looking at the aligned curve and the warping function as a joint functional object. In both cases, we propose a functional mixed-effects framework that uses functional principal components as the data-driven basis for genetically correlated data. The proposed procedure is applied to simulations and a real-case study of Tribolium castaneum growth trajectories.
Related
- Vector valued continuous function spaces as C∗-algebras
- Function-Valued Causal Influence in Nonlinear Time Series
- Functional Autoencoders for Amplitude-Phase Representation Learning
- A Hilbert-Valued Functional Decomposition Framework for Explaining Time-Dependent Outputs
- Geometric Feature Learning for Functional Data Valued on the Symmetric Positive Definite Manifold
BibTeX
@misc{chen2026functional,
title = {{A functional mixed-effects model for the joint analysis of amplitude and phase variations in function-valued traits}},
author = {Yilin Chen and Davide Pigoli and John A. D. Aston and Patrick A. Carter},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.13459},
eprint = {2610.13459},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.13459},
}
RIS
TY - UNPB
TI - A functional mixed-effects model for the joint analysis of amplitude and phase variations in function-valued traits
AU - Yilin Chen
AU - Davide Pigoli
AU - John A. D. Aston
AU - Patrick A. Carter
PY - 2026
DA - 2026/10/09
PB - arXiv
DO - 10.48550/arxiv.2610.13459
UR - https://arxiv.org/abs/2610.13459
AB - Quantitative genetics is the study of continuous traits and the statistical analysis of phenotypic variation, that is, the observable differences in physical traits among individuals within a population. If family relationships between individuals are known, phenotypic variation can be partitioned into genetic and environmental components. Some traits, such as growth trajectories, can be described as a function of a continuous index and are known as function-valued traits. However, function-valued traits from different individuals often vary not only in their shape (amplitude) but also in the speed at which the biological process develops (phase). In this work, we present and compare two approaches to account for amplitude and phase variations in estimating the additive genetic and environmental components. The first one follows from a conventional framework where warping functions remove phase variations, and then the aligned curves are analysed. The second approach adopts the perspective of looking at the aligned curve and the warping function as a joint functional object. In both cases, we propose a functional mixed-effects framework that uses functional principal components as the data-driven basis for genetically correlated data. The proposed procedure is applied to simulations and a real-case study of Tribolium castaneum growth trajectories.
ER -