Genetic analysis of growth curves using the SAEM algorithm

Cristian Meza,Jean-Louis Foulley,Marc Lavielle,Florence Jaffrézic

doi:10.1186/1297-9686-38-6-583

Abstract

The analysis of nonlinear function-valued characters is very important in genetic studies, especially for growth traits of agricultural and laboratory species. Inference in nonlinear mixed effects models is, however, quite complex and is usually based on likelihood approximations or Bayesian methods. The aim of this paper was to present an efficient stochastic EM procedure, namely the SAEM algorithm, which is much faster to converge than the classical Monte Carlo EM algorithm and Bayesian estimation procedures, does not require specification of prior distributions and is quite robust to the choice of starting values. The key idea is to recycle the simulated values from one iteration to the next in the EM algorithm, which considerably accelerates the convergence. A simulation study is presented which confirms the advantages of this estimation procedure in the case of a genetic analysis. The SAEM algorithm was applied to real data sets on growth measurements in beef cattle and in chickens. The proposed estimation procedure, as the classical Monte Carlo EM algorithm, provides significance tests on the parameters and likelihood based model comparison criteria to compare the nonlinear models with other longitudinal methods.

Highlights

Many traits of interest in genetic studies are function-valued characters, i.e. they change in a continuous manner over time or some other independent continuous variable
The aim of this paper was to present an extension of the stochastic approximation EM algorithm (SAEM) proposed in the statistical literature [15] and to apply it to the genetic analysis of growth curves
The Stochastic Approximation EM (SAEM) algorithm presented in this paper is conceptually very simple and has several advantages compared to a classical Monte Carlo EM algorithm [28]

Summary

Introduction

Many traits of interest in genetic studies are function-valued characters, i.e. they change in a continuous manner over time or some other independent continuous variable. A different approach for function-valued characters, especially growth traits, is to use a parametric nonlinear function of time, with a few interpretable parameters, that are decomposed into a genetic and an environmental component. It has three parameters that have an interesting biological interpretation in terms of adult body weight and maturation rate This modeling is similar in spirit to the random regression approach, but it overcomes the drawbacks encountered with the use of polynomimal functions. This nonlinear modeling of growth curves has been used in QTL detection by Ma et al [20]

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Conclusion