Academic journal article Genetics

Varying Coefficient Models for Mapping Quantitative Trait Loci Using Recombinant Inbred Intercrosses

Academic journal article Genetics

Varying Coefficient Models for Mapping Quantitative Trait Loci Using Recombinant Inbred Intercrosses

Article excerpt

ABSTRACT There has been a great deal of interest in the development of methodologies to map quantitative trait loci (QTL) using experimental crosses in the last 2 decades. Experimental crosses in animal and plant sciences provide important data sources for mapping QTL through linkage analysis. The Collaborative Cross (CC) is a renewable mouse resource that is generated from eight genetically diverse founder strains to mimic the genetic diversity in humans. The recombinant inbred intercrosses (RIX) generated from CC recombinant inbred (RI) lines share similar genetic structures of F^sub 2^ individuals but with up to eight alleles segregating at any one locus. In contrast to F^sub 2^ mice, genotypes of RIX can be inferred from the genotypes of their RI parents and can be produced repeatedly. Also, RIX mice typically do not share the same degree of relatedness. This unbalanced genetic relatedness requires careful statistical modeling to avoid false-positive findings. Many quantitative traits are inherently complex with genetic effects varying with other covariates, such as age. For such complex traits, if phenotype data can be collected over a wide range of ages across study subjects, their dynamic genetic patterns can be investigated. Parametric functions, such as sigmoidal or logistic functions, have been used for such purpose. In this article, we propose a flexible nonparametric time-varying coefficient QTL mapping method for RIX data. Our method allows the QTL effects to evolve with time and naturally extends classical parametric QTL mapping methods. We model the varying genetic effects nonparametrically with the B-spline bases. Our model investigates gene-by-time interactions for RIX data in a very flexible nonparametric fashion. Simulation results indicate that the varying coefficient QTL mapping has higher power and mapping precision compared to parametric models when the assumption of constant genetic effects fails. We also apply a modified permutation procedure to control overall significance level.

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DURING the past 2 decades, there has been considerable development in statistical methodologies for mapping quantitative trait loci (QTL), since Lander and Botstein (1989) implemented a maximum-likelihood approach to the interval-mapping technique (Goldgar 1990; Amos 1994; Jansen and Stam 1994; Zeng 1994; Almasy and Blangero 1998; Kao et al. 1999; Zou et al. 2001; Xu et al. 2005). In addition to the interval-mapping approach, many other statistical approaches have been used in QTL mapping, such as regression analyses (Haley and Knott 1992) and Bayesian approaches (Satagopan et al. 1996; Sillanpaa and Arjas 1998; Yi and Xu 2000; Yi 2004; Hoeschele 2007).

While these methods have been instrumental for QTL identification, they are not able to capture the temporal pattern of QTL effect. Many quantitative traits, such as body size, are inherently too complex to be described by a single value, because their phenotypes, for example, change with age. Instead of being measured at one fixed time point, each subject's phenotype may be measured at different time points across samples, which allows us to study genetic effects that vary with the change of time. For example, genetic correlations among age-specific weights in a laboratory population of rats were shown to involve variable gene action at different ages (Cheverud et al. 1983). Vaughn et al. (1999) located QTL responsible for age-specific weights in mice, and they found that some QTL affect the early growth patterns and some affect the late growth patterns. To study genetic determination of such functional traits, Wu and colleagues (Ma et al. 2002; Wu et al. 2002, 2004; Lin and Wu 2006) developed the functional mapping approach. They used growth curve data as an example of functional traits, and the genetic effect was modeled by a parametric function such as sigmoidal or logistic function (Ma et al. 2002). While the parametric nature of functional mapping offers tremendous biological and statistical advantages, a reliance on the availability of mathematical functions limits its applicability (Yang et al. …

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