Mapping quantitative trait Loci interactions from the maternal and offspring genomes

The expression of most developmental or behavioral traits involves complex interactions between quantitative trait loci (QTL) from the maternal and offspring genomes. The maternal-offspring interactions play a pivotal role in shaping the direction and rate of evolution in terms of their substantial contribution to quantitative genetic (co)variation. To study the genetics and evolution of maternal-offspring interactions, a unifying statistical framework that embraces both the direct and indirect genetic effects of maternal and offspring QTL on any complex trait is developed. This model is derived for a simple backcross design within the maximum-likelihood context, implemented with the EM algorithm. Results from extensive simulations suggest that this model can provide reasonable estimation of additive and dominant effects of the QTL at different generations and their interaction effects derived from the maternal and offspring genomes. Although our model is framed to characterize the actions and interactions of maternal and offspring QTL affecting offspring traits, the idea can be readily extended to decipher the genetic machinery of maternal traits, such as maternal care. Our model provides a powerful means for studying the evolutionary significance of indirect genetic effects in any sexually reproductive organisms.     

DEVELOPMENTAL QUANTITATIVE GENETICS AND THE EVOLUTION OF ONTOGENIES

A model is presented which permits integration of developmental information into genetic discussions about evolutionary change in morphology. Development of a trait is described in terms of an ontogenetic trajectory whose properties are defined by a small number of parameters. Some evolutionary aspects of development are examined from the perspective of this quantitative genetic model. Particular attention is given to the developmental origin of pleiotropic effects, developmental constraints, heterochrony, and the growth and morphogenesis of complex morphologies. The role of genetic maternal effects in mammalian development is briefly examined, particularly as it relates to selection on developmental traits.     

Ontogenetic stage‐specific quantitative trait loci contribute to divergence in developmental trajectories of sexually dimorphic fins between medaka populations

Sexual dimorphism can evolve when males and females differ in phenotypic optima. Genetic constraints can, however, limit the evolution of sexual dimorphism. One possible constraint is derived from alleles expressed in both sexes. Because males and females share most of their genome, shared alleles with different fitness effects between sexes are faced with intralocus sexual conflict. Another potential constraint is derived from genetic correlations between developmental stages. Sexually dimorphic traits are often favoured at adult stages, but selected against as juvenile, so developmental decoupling of traits between ontogenetic stages may be necessary for the evolution of sexual dimorphism in adults. Resolving intralocus conflicts between sexes and ages is therefore a key to the evolution of age‐specific expression of sexual dimorphism. We investigated the genetic architecture of divergence in the ontogeny of sexual dimorphism between two populations of the Japanese medaka (Oryzias latipes) that differ in the magnitude of dimorphism in anal and dorsal fin length. Quantitative trait loci (QTL) mapping revealed that few QTL had consistent effects throughout ontogenetic stages and the majority of QTL change the sizes and directions of effects on fin growth rates during ontogeny. We also found that most QTL were sex‐specific, suggesting that intralocus sexual conflict is almost resolved. Our results indicate that sex‐ and age‐specific QTL enable the populations to achieve optimal developmental trajectories of sexually dimorphic traits in response to complex natural and sexual selection.     

A hyperspace model to decipher the genetic architecture of developmental processes: allometry meets ontogeny

To better utilize limited resources for their survival and reproduction, all organisms undergo developmental changes in both body size and shape during ontogeny. The genetic analysis of size change with increasing age, i.e., growth, has received considerable attention in quantitative developmental genetic studies, but the genetic architecture of ontogenetic changes in body shape and its associated allometry have been poorly understood partly due to the lack of analytical tools. In this article, we attempt to construct a multivariate statistical framework for studying the genetic regulation of ontogenetic growth and shape. We have integrated biologically meaningful mathematical functions of growth curves and developmental allometry into the estimation process of genetic mapping aimed at identifying individual quantitative trait loci (QTL) for phenotypic variation. This model defined with high dimensions can characterize the ontogenetic patterns of genetic effects of QTL over the lifetime of an organism and assess the interplay between genetic actions/interactions and phenotypic integration. The closed forms for the residual covariance matrix and its determinant and inverse were derived to overcome the computational complexity typical of our high-dimensional model. We used a worked example to validate the utility of this model. The implications of this model for genetic research of evo-devo are discussed.     

A conceptual framework for mapping quantitative trait Loci regulating ontogenetic allometry

Although ontogenetic changes in body shape and its associated allometry has been studied for over a century, essentially nothing is known about their underlying genetic and developmental mechanisms. One of the reasons for this ignorance is the unavailability of a conceptual framework to formulate the experimental design for data collection and statistical models for data analyses. We developed a framework model for unraveling the genetic machinery for ontogenetic changes of allometry. The model incorporates the mathematical aspects of ontogenetic growth and allometry into a maximum likelihood framework for quantitative trait locus (QTL) mapping. As a quantitative platform, the model allows for the testing of a number of biologically meaningful hypotheses to explore the pleiotropic basis of the QTL that regulate ontogeny and allometry. Simulation studies and real data analysis of a live example in soybean have been performed to investigate the statistical behavior of the model and validate its practical utilization. The statistical model proposed will help to study the genetic architecture of complex phenotypes and, therefore, gain better insights into the mechanistic regulation for developmental patterns and processes in organisms.     

Bayesian model choice and search strategies for mapping interacting quantitative trait Loci

Most complex traits of animals, plants, and humans are influenced by multiple genetic and environmental factors. Interactions among multiple genes play fundamental roles in the genetic control and evolution of complex traits. Statistical modeling of interaction effects in quantitative trait loci (QTL) analysis must accommodate a very large number of potential genetic effects, which presents a major challenge to determining the genetic model with respect to the number of QTL, their positions, and their genetic effects. In this study, we use the methodology of Bayesian model and variable selection to develop strategies for identifying multiple QTL with complex epistatic patterns in experimental designs with two segregating genotypes. Specifically, we develop a reversible jump Markov chain Monte Carlo algorithm to determine the number of QTL and to select main and epistatic effects. With the proposed method, we can jointly infer the genetic model of a complex trait and the associated genetic parameters, including the number, positions, and main and epistatic effects of the identified QTL. Our method can map a large number of QTL with any combination of main and epistatic effects. Utility and flexibility of the method are demonstrated using both simulated data and a real data set. Sensitivity of posterior inference to prior specifications of the number and genetic effects of QTL is investigated.     

Genetic mapping of developmental instability: design, model and algorithm

Developmental instability or noise, defined as the phenotypic imprecision of an organism in the face of internal or external stochastic disturbances, has been thought to play an important role in shaping evolutionary processes and patterns. The genetic studies of developmental instability have been based on fluctuating asymmetry (FA) that measures random differences between the left and the right sides of bilateral traits. In this article, we frame an experimental design characterized by a spatial autocorrelation structure for determining the genetic control of developmental instability for those traits that cannot be bilaterally measured. This design allows the residual environmental variance of a quantitative trait to be dissolved into two components due to permanent and random environmental factors. The degree of developmental instability is quantified by the relative proportion of the random residual variance to the total residual variance. We formulate a mixture model to estimate and test the genetic effects of quantitative trait loci (QTL) on the developmental instability of the trait. The genetic parameters including the QTL position, the QTL effects, and spatial autocorrelations are estimated by implementing the EM algorithm within the mixture model framework. Simulation studies were performed to investigate the statistical behavior of the model. A live example for poplar trees was used to map the QTL that control root length growth and its developmental instability from cuttings in water culture.     

Molecular dissection of developmental behavior of tiller number and plant height and their relationship in rice (Oryza sativa L.)

Plant height and tiller number are two important characters related to yield in rice (Oriza sativa L.). Zhenshan97 x Minghui63 recombinant inbred lines were employed to dissect the genetic basis of development of plant height and tiller number using conditional and unconditional composite interval mapping approaches. The traits were normally distributed with transgressive segregation in both directions. Increasingly negative correlations were observed between tiller number and plant height at five consecutive growth stages. A total of 23 and 24 QTL were identified for tiller number and plant height, respectively. More QTL were detected by conditional mapping than by conventional mapping. Different QTL/genes apparently controlled the traits at different developmental stages. Three genomic regions were identified as putative co-located QTL, which showed opposite additive effects on tiller number and plant height. Furthermore, in the period reaching maximum tiller number, the expression of QTL for tiller number was active, whereas that of QTL for plant height was inactive. These facts provided a possible genetic explanation for the negative correlations between the traits. The research demonstrates conditional mapping to be superior to conventional mapping for this type of research. Implications of the results for hybrid rice improvement are discussed.     

Elucidating genomic regions determining enhanced leaf growth and delayed senescence in elevated CO2

Limited information is available on the genetic variation and control for plant growth response to elevated CO(2) (e[CO(2)]). Such information is necessary to understand plant adaptation and evolution in future rising CO(2). Here, quantitative trait loci (QTL) for leaf growth, development, quality and leaf senescence were determined in a tree pedigree - an F(2) hybrid of Populus trichocarpa T. & G and Populus deltoides Marsh, following season-long exposure to either current day ambient carbon dioxide (a[CO(2)]) or e[CO(2)] at 600 microL L(-1). Leaf growth and development differed between the grandparents such that P. trichocarpa showed greater response to e[CO(2)]. In the F(2) generation, leaf development and quality traits including leaf area, leaf shape, epidermal cell area, and stomatal number, specific leaf area (SLA), and the phenology trait, canopy senescence index, were sensitive to e[CO(2)]. Sixty-nine QTL were mapped for the 19 traits of plants in a[CO(2)] while 60 QTL were mapped for plants in e[CO(2)]. The results suggest that although many QTL mapped to common positions in a[CO(2)] and e[CO(2)], confirming their importance in determining growth, there was also differential genetic control for a number of traits including leaf senescence. Candidate genes were shown to collocate to regions where response QTL mapped. This study is the first to identify candidate genes that may be important in determining plant adaptation to future high-CO(2) world.     

Functional mapping of quantitative trait loci underlying the character process: a theoretical framework

Unlike a character measured at a finite set of landmark points, function-valued traits are those that change as a function of some independent and continuous variable. These traits, also called infinite-dimensional characters, can be described as the character process and include a number of biologically, economically, or biomedically important features, such as growth trajectories, allometric scalings, and norms of reaction. Here we present a new statistical infrastructure for mapping quantitative trait loci (QTL) underlying the character process. This strategy, termed functional mapping, integrates mathematical relationships of different traits or variables within the genetic mapping framework. Logistic mapping proposed in this article can be viewed as an example of functional mapping. Logistic mapping is based on a universal biological law that for each and every living organism growth over time follows an exponential growth curve (e.g., logistic or S-shaped). A maximum-likelihood approach based on a logistic-mixture model, implemented with the EM algorithm, is developed to provide the estimates of QTL positions, QTL effects, and other model parameters responsible for growth trajectories. Logistic mapping displays a tremendous potential to increase the power of QTL detection, the precision of parameter estimation, and the resolution of QTL localization due to the small number of parameters to be estimated, the pleiotropic effect of a QTL on growth, and/or residual correlations of growth at different ages. More importantly, logistic mapping allows for testing numerous biologically important hypotheses concerning the genetic basis of quantitative variation, thus gaining an insight into the critical role of development in shaping plant and animal evolution and domestication. The power of logistic mapping is demonstrated by an example of a forest tree, in which one QTL affecting stem growth processes is detected on a linkage group using our method, whereas it cannot be detected using current methods. The advantages of functional mapping are also discussed.     

The role of epistasis in the manifestation of heterosis: a systems-oriented approach

Heterosis is widely used in breeding, but the genetic basis of this biological phenomenon has not been elucidated. We postulate that additive and dominance genetic effects as well as two-locus interactions estimated in classical QTL analyses are not sufficient for quantifying the contributions of QTL to heterosis. A general theoretical framework for determining the contributions of different types of genetic effects to heterosis was developed. Additive x additive epistatic interactions of individual loci with the entire genetic background were identified as a major component of midparent heterosis. On the basis of these findings we defined a new type of heterotic effect denoted as augmented dominance effect di* that comprises the dominance effect at each QTL minus half the sum of additive x additive interactions with all other QTL. We demonstrate that genotypic expectations of QTL effects obtained from analyses with the design III using testcrosses of recombinant inbred lines and composite-interval mapping precisely equal genotypic expectations of midparent heterosis, thus identifying genomic regions relevant for expression of heterosis. The theory for QTL mapping of multiple traits is extended to the simultaneous mapping of newly defined genetic effects to improve the power of QTL detection and distinguish between dominance and overdominance.     

Genetic effects at pleiotropic loci are context-dependent with consequences for the maintenance of genetic variation in populations

Context-dependent genetic effects, including genotype-by-environment and genotype-by-sex interactions, are a potential mechanism by which genetic variation of complex traits is maintained in populations. Pleiotropic genetic effects are also thought to play an important role in evolution, reflecting functional and developmental relationships among traits. We examine context-dependent genetic effects at pleiotropic loci associated with normal variation in multiple metabolic syndrome (MetS) components (obesity, dyslipidemia, and diabetes-related traits). MetS prevalence is increasing in Western societies and, while environmental in origin, presents substantial variation in individual response. We identify 23 pleiotropic MetS quantitative trait loci (QTL) in an F₁₆ advanced intercross between the LG/J and SM/J inbred mouse strains (Wustl:LG,SM-G16; n = 1002). Half of each family was fed a high-fat diet and half fed a low-fat diet; and additive, dominance, and parent-of-origin imprinting genotypic effects were examined in animals partitioned into sex, diet, and sex-by-diet cohorts. We examine the context-dependency of the underlying additive, dominance, and imprinting genetic effects of the traits associated with these pleiotropic QTL. Further, we examine sequence polymorphisms (SNPs) between LG/J and SM/J as well as differential expression of positional candidate genes in these regions. We show that genetic associations are different in different sex, diet, and sex-by-diet settings. We also show that over- or underdominance and ecological cross-over interactions for single phenotypes may not be common, however multidimensional synthetic phenotypes at loci with pleiotropic effects can produce situations that favor the maintenance of genetic variation in populations. Our findings have important implications for evolution and the notion of personalized medicine.     

Functional mapping of quantitative trait loci that interact with the hg mutation to regulate growth trajectories in mice

The high growth (hg) mutation increases body size in mice by 30-50%. Given the complexity of the genetic regulation of animal growth, it is likely that the effect of this major locus is mediated by other quantitative trait loci (QTL) with smaller effects within a web of gene interactions. In this article, we extend our functional mapping model to characterize modifier QTL that interact with the hg locus during ontogenetic growth. Our model is derived within the maximum-likelihood context, incorporated by mathematical aspects of growth laws and implemented with the EM algorithm. In an F2 population founded by a congenic high growth (HG) line and non-HG line, a highly additive effect due to the hg gene was detected on growth trajectories. Three QTL located on chromosomes 2 and X were identified to trigger significant additive and/or dominant effects on the process of growth. The most significant finding made from our model is that these QTL interact with the hg locus to affect the shapes of the growth process. Our model provides a powerful means for understanding the genetic architecture and regulation of growth rate and body size in mammals.     

Conditional QTL mapping of oil content in rapeseed with respect to protein content and traits related to plant development and grain yield

Oil content in rapeseed (Brassica napus L.) is generally regarded as a character with high heritability that is negatively correlated with protein content and influenced by plant developmental and yield related traits. To evaluate possible genetic interrelationships between these traits and oil content, QTL for oil content were mapped using data on oil content and on oil content conditioned on the putatively interrelated traits. Phenotypic data were evaluated in a segregating doubled haploid population of 282 lines derived from the F₁ of a cross between the old German cultivar Sollux and the Chinese cultivar Gaoyou. The material was tested at four locations, two each in Germany and in China. QTLMapper version 1.0 was used for mapping unconditional and conditional QTL with additive (a) and locus pairs with additive × additive epistatic (aa) effects. Clear evidence was found for a strong genetic relationship between oil and protein content. Six QTL and nine epistatic locus pairs were found, which had pleiotropic effects on both traits. Nevertheless, two QTL were also identified, which control oil content independent from protein content and which could be used in practical breeding programs to increase oil content without affecting seed protein content. In addition, six additional QTL with small effects were only identified in the conditional mapping. Some evidence was apparent for a genetic interrelationship between oil content and the number of seeds per silique but no evidence was found for a genetic relationship between oil content and flowering time, grain filling period or single seed weight. The results indicate that for closely correlated traits conditional QTL mapping can be used to dissect the genetic interrelationship between two traits at the level of individual QTL. Furthermore, conditional QTL mapping can reveal additional QTL with small effects that are undetectable in unconditional mapping.     

Dissecting Genetic Architecture Underlying Seed Traits in Multiple Environments

The seeds of flowering plants develop from double fertilization and play a vital role in reproduction and supplying human and animal food. The genetic variation of seed traits is influenced by multiple genetic systems, e.g., maternal, embryo, and/or endosperm genomes. Understanding the genetic architecture of seed traits is a major challenge because of this complex mechanism of multiple genetic systems, especially the epistasis within or between different genomes and their interactions with the environment. In this study, a statistical model was proposed for mapping QTL with epistasis and QTL-by-environment (QE) interactions underlying endosperm and embryo traits. Our model integrates the maternal and the offspring genomes into one mapping framework and can accurately analyze maternal additive and dominant effects, endosperm/embryo additive and dominant effects, and epistatic effects of two loci in the same or two different genomes, as well as interaction effects of each genetic component of QTL with environment. Intensive simulations under different sampling strategies, heritabilities, and model parameters were performed to investigate the statistical properties of the model. A set of real cottonseed data was analyzed to demonstrate our methods. A software package, QTLNetwork-Seed-1.0.exe, was developed for QTL analysis of seed traits.     

Simultaneous mapping of epistatic QTL in chickens reveals clusters of QTL pairs with similar genetic effects on growth

We used simultaneous mapping of interacting quantitative trait locus (QTL) pairs to study various growth traits in a chicken F2 intercross. The method was shown to increase the number of detected QTLs by 30 % compared with a traditional method detecting QTLs by their marginal genetic effects. Epistasis was shown to be an important contributor to the genetic variance of growth, with the largest impact on early growth (before 6 weeks of age). There is also evidence for a discrete set of interacting loci involved in early growth, supporting the previous findings of different genetic regulation of early and late growth in chicken. The genotype-phenotype relationship was evaluated for all interacting QTL pairs and 17 of the 21 evaluated QTL pairs could be assigned to one of four clusters in which the pairs in a cluster have very similar genetic effects on growth. The genetic effects of the pairs indicate commonly occurring dominance-by-dominance, heterosis and multiplicative interactions. The results from this study clearly illustrate the increase in power obtained by using this novel method for simultaneous detection of epistatic QTL, and also how visualization of genotype-phenotype relationships for epistatic QTL pairs provides new insights to biological mechanisms underlying complex traits.     

Dynamic QTL and epistasis analysis on seedling root traits in upland cotton

Roots are involved in acquisition of water and nutrients, as well as in providing structural support to plant. The root system provides a dynamic model for developmental analysis. Here, we investigated quantitative trait loci (QTL), dynamic conditional QTL and epistatic interactions for seedling root traits using an upland cotton F₂ population and a constructed genetic map. Totally, 37 QTLs for root traits, 35 dynamic conditional QTLs based on the net increased amount of root traits (root tips, forks, length, surface area and volume) (i) after transplanting 10 days compared to 5 days, and (ii) after transplanting 15 days to 10 days were detected. Obvious dynamic characteristic of QTL and dynamic conditional QTL existed at different developmental stages of root because QTL and dynamic conditional QTL had not been detected simultaneously. We further confirmed that additive and dominance effects of QTL qRSA-chr1-1 in interval time 5 to 10 DAT (days after transplant) offset the effects in 10 to 15 DAT. Lots of two-locus interactions for root traits were identified unconditionally or dynamically, and a few epistatic interactions were only detected simultaneously in interval time of 5–10 DAT and 10–15 DAT, suggesting different interactive genetic mechanisms on root development at different stages. Dynamic conditional QTL and epistasis effects provide new attempts to understand the dynamics of roots and provide clues for root architecture selection in upland cotton.     

Advances in Bayesian multiple quantitative trait loci mapping in experimental crosses

Many complex human diseases and traits of biological and/or economic importance are determined by interacting networks of multiple quantitative trait loci (QTL) and environmental factors. Mapping QTL is critical for understanding the genetic basis of complex traits, and for ultimate identification of genes responsible. A variety of sophisticated statistical methods for QTL mapping have been developed. Among these developments, the evolution of Bayesian approaches for multiple QTL mapping over the past decade has been remarkable. Bayesian methods can jointly infer the number of QTL, their genomic positions and their genetic effects. Here, we review recently developed and still developing Bayesian methods and associated computer software for mapping multiple QTL in experimental crosses. We compare and contrast these methods to clearly describe the relationships among different Bayesian methods. We conclude this review by highlighting some areas of future research.     

Functional mapping of ontogeny in flowering plants

All organisms face the problem of how to perform a sequence of developmental changes and transitions during ontogeny. We revise functional mapping, a statistical model originally derived to map genes that determine developmental dynamics, to take into account the entire process of ontogenetic growth from embryo to adult and from the vegetative to reproductive phase. The revised model provides a framework that reconciles the genetic architecture of development at different stages and elucidates a comprehensive picture of the genetic control mechanisms of growth that change gradually from a simple to a more complex level. We use an annual flowering plant, as an example, to demonstrate our model by which to map genes and their interactions involved in embryo and postembryonic growth. The model provides a useful tool to study the genetic control of ontogenetic growth in flowering plants and any other organisms through proper modifications based on their biological characteristics.     

Evolutionary quantitative genetics of nonlinear developmental systems

In quantitative genetics, the effects of developmental relationships among traits on microevolution are generally represented by the contribution of pleiotropy to additive genetic covariances. Pleiotropic additive genetic covariances arise only from the average effects of alleles on multiple traits, and therefore the evolutionary importance of nonlinearities in development is generally neglected in quantitative genetic views on evolution. However, nonlinearities in relationships among traits at the level of whole organisms are undeniably important to biology in general, and therefore critical to understanding evolution. I outline a system for characterizing key quantitative parameters in nonlinear developmental systems, which yields expressions for quantities such as trait means and phenotypic and genetic covariance matrices. I then develop a system for quantitative prediction of evolution in nonlinear developmental systems. I apply the system to generating a new hypothesis for why direct stabilizing selection is rarely observed. Other uses will include separation of purely correlative from direct and indirect causal effects in studying mechanisms of selection, generation of predictions of medium‐term evolutionary trajectories rather than immediate predictions of evolutionary change over single generation time‐steps, and the development of efficient and biologically motivated models for separating additive from epistatic genetic variances and covariances.