Mapping Quantitative Trait Loci for Longitudinal Traits in Line Crosses

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Abstract

Quantitative traits whose phenotypic values change over time are called longitudinal traits. Genetic analyses of longitudinal traits can be conducted using any of the following approaches: (1) treating the phenotypic values at different time points as repeated measurements of the same trait and analyzing the trait under the repeated measurements framework, (2) treating the phenotypes measured from different time points as different traits and analyzing the traits jointly on the basis of the theory of multivariate analysis, and (3) fitting a growth curve to the phenotypic values across time points and analyzing the fitted parameters of the growth trajectory under the theory of multivariate analysis. The third approach has been used in QTL mapping for longitudinal traits by fitting the data to a logistic growth trajectory. This approach applies only to the particular S-shaped growth process. In practice, a longitudinal trait may show a trajectory of any shape. We demonstrate that one can describe a longitudinal trait with orthogonal polynomials, which are sufficiently general for fitting any shaped curve. We develop a mixed-model methodology for QTL mapping of longitudinal traits and a maximum-likelihood method for parameter estimation and statistical tests. The expectation-maximization (EM) algorithm is applied to search for the maximum-likelihood estimates of parameters. The method is verified with simulated data and demonstrated with experimental data from a pseudobackcross family of Populus (poplar) trees.

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A simple regression method for mapping quantitative trait loci in line crosses using flanking markers.

C S Haley, S Knott (1992)

The use of flanking marker methods has proved to be a powerful tool for the mapping of quantitative trait loci (QTL) in the segregating generations derived from crosses between inbred lines. Methods to analyse these data, based on maximum-likelihood, have been developed and provide good estimates of QTL effects in some situations. Maximum-likelihood methods are, however, relatively complex and can be computationally slow. In this paper we develop methods for mapping QTL based on multiple regression which can be applied using any general statistical package. We use the example of mapping in an F(2) population and show that these regression methods produce very similar results to those obtained using maximum likelihood. The relative simplicity of the regression methods means that models with more than a single QTL can be explored and we give examples of two lined loci and of two interacting loci. Other models, for example with more than two QTL, with environmental fixed effects, with between family variance or for threshold traits, could be fitted in a similar way. The ease, speed of application and generality of regression methods for flanking marker analysis, and the good estimates they obtain, suggest that they should provide the method of choice for the analysis of QTL mapping data from inbred line crosses.

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A general model for ontogenetic growth.

G. B. West, J. Brown, B Enquist (2001)

Several equations have been proposed to describe ontogenetic growth trajectories for organisms justified primarily on the goodness of fit rather than on any biological mechanism. Here, we derive a general quantitative model based on fundamental principles for the allocation of metabolic energy between maintenance of existing tissue and the production of new biomass. We thus predict the parameters governing growth curves from basic cellular properties and derive a single parameterless universal curve that describes the growth of many diverse species. The model provides the basis for deriving allometric relationships for growth rates and the timing of life history events.