A Unified Statistical Model for Functional Mapping of Environment-Dependent Genetic Expression and Genotype × Environment Interactions for Ontogenetic Development

The effects of quantitative trait loci (QTL) on phenotypic development may depend on the environment (QTL × environment interaction), other QTL (genetic epistasis), or both. In this article, we present a new statistical model for characterizing specific QTL that display environment-dependent genetic expressions and genotype × environment interactions for developmental trajectories. Our model was derived within the maximum-likelihood-based mixture model framework, incorporated by biologically meaningful growth equations and environment-dependent genetic effects of QTL, and implemented with the EM algorithm. With this model, we can characterize the dynamic patterns of genetic effects of QTL governing growth curves and estimate the global effect of the underlying QTL during the course of growth and development. In a real example with rice, our model has successfully detected several QTL that produce differences in their genetic expression between two contrasting environments. These detected QTL cause significant genotype × environment interactions for some fundamental aspects of growth trajectories. The model provides the basis for deciphering the genetic architecture of trait expression adjusted to different biotic and abiotic environments and genetic relationships for growth rates and the timing of life-history events for any organism.

[1]  W. G. Hill,et al.  Estimating the covariance structure of traits during growth and ageing, illustrated with lactation in dairy cattle. , 1994, Genetical research.

[2]  Trudy F. C. Mackay,et al.  Quantitative trait loci in Drosophila , 2001, Nature Reviews Genetics.

[3]  David Ruppert,et al.  Power Transformations When Fitting Theoretical Models to Data , 1984 .

[4]  F. J. Richards.  A Flexible Growth Function for Empirical Use , 1959 .

[5]  N. Hübner,et al.  Conserved synteny in rat and mouse for a blood pressure QTL on human chromosome 17. , 2002, Hypertension.

[6]  Rongling Wu,et al.  Quantitative trait loci for growth trajectories in Populus. , 2003, Genetical research.

[7]  James H. Brown,et al.  The fourth dimension of life: fractal geometry and allometric scaling of organisms. , 1999, Science.

[8]  William R. Atchley,et al.  Ontogeny, Timing of Development, and Genetic Variance-Covariances Structure , 1984, The American Naturalist.

[9]  A. Gregorczyk,et al.  Richards Plant Growth Model , 1998 .

[10]  G. Casella,et al.  A General Framework for Analyzing the Genetic Architecture of Developmental Characteristics , 2004, Genetics.

[11]  G. S. Khush,et al.  QTL × environment interactions in rice. I. Heading date and plant height , 2003, Theoretical and Applied Genetics.

[12]  G. Casella,et al.  Joint linkage and linkage disequilibrium mapping of quantitative trait loci in natural populations. , 2002, Genetics.

[13]  S. Rice,et al.  The analysis of ontogenetic trajectories: when a change in size or shape is not heterochrony. , 1997, Proceedings of the National Academy of Sciences of the United States of America.

[14]  L. Bertalanffy.  Quantitative Laws in Metabolism and Growth , 1957 .

[15]  Z B Zeng,et al.  Genotype-environment interaction for quantitative trait loci affecting life span in Drosophila melanogaster. , 2000, Genetics.

[16]  W. Atchley,et al.  Developmental quantitative genetics, conditional epigenetic variability and growth in mice. , 1997, Genetics.

[17]  E. Lander,et al.  Mapping mendelian factors underlying quantitative traits using RFLP linkage maps. , 1989, Genetics.

[18]  P. Diggle,et al.  Analysis of Longitudinal Data. , 1997 .

[19]  H. Piepho,et al.  A mixed-model approach to mapping quantitative trait loci in barley on the basis of multiple environment data. , 2000, Genetics.

[20]  G. Casella,et al.  Functional mapping of quantitative trait loci underlying the character process: a theoretical framework. , 2002, Genetics.

[21]  J. Cheverud,et al.  Quantitative trait loci for murine growth. , 1996, Genetics.

[22]  C. Geyer,et al.  The genetic analysis of age-dependent traits: modeling the character process. , 1999, Genetics.

[23]  James H. Brown,et al.  A General Model for the Origin of Allometric Scaling Laws in Biology , 1997, Science.

[24]  S. Pletcher,et al.  Statistical models for estimating the genetic basis of repeated measures and other function-valued traits. , 2000, Genetics.

[25]  W. Arthur,et al.  The emerging conceptual framework of evolutionary developmental biology , 2002, Nature.

[26]  D. Cox,et al.  An Analysis of Transformations , 1964 .

[27]  Rudolf A. Raff,et al.  Evo-devo: the evolution of a new discipline , 2000, Nature Reviews Genetics.

[28]  James H. Brown,et al.  A general model for ontogenetic growth , 2001, Nature.

[29]  Rongling Wu,et al.  A logistic mixture model for characterizing genetic determinants causing differentiation in growth trajectories. , 2002, Genetical research.

[30]  Karl J. Niklas,et al.  Botanical Scaling. (Book Reviews: Plant Allometry. The Scaling of Form and Process.) , 1994 .

[31]  L. von Bertalanffy.  Quantitative Laws in Metabolism and Growth , 1957, The Quarterly Review of Biology.

[32]  Wei Zhao,et al.  A unifying statistical model for QTL mapping of genotype x sex interaction for developmental trajectories. , 2004, Physiological genomics.

[33]  M. Kenward,et al.  Parametric modelling of growth curve data: An overview , 2001 .

[34]  G. Casella,et al.  Functional Mapping of Quantitative Trait Loci Underlying Growth Trajectories Using a Transform‐Both‐Sides Logistic Model , 2004, Biometrics.

[35]  Rongling Wu,et al.  FunMap: functional mapping of complex traits , 2004, Bioinform..

[36]  Jun Zhu,et al.  Molecular dissection of developmental behavior of plant height in rice (Oryza sativa L.). , 1998, Genetics.

[37]  R. Doerge,et al.  Empirical threshold values for quantitative trait mapping. , 1994, Genetics.

[38]  S. Iwahori,et al.  Genetic manipulation of gibberellin metabolism in transgenic rice , 2003, Nature Biotechnology.

[39]  Susan McCouch,et al.  RFLP mapping of isozymes, RAPD and QTLs for grain shape, brown planthopper resistance in a doubled haploid rice population , 2004, Molecular Breeding.