Quantitative trait loci mapping of phenotypic plasticity and genotype-environment interactions in plant and insect performance

Community genetic studies generally ignore the plasticity of the functional traits through which the effect is passed from individuals to the associated community. However, the ability of organisms to be phenotypically plastic allows them to rapidly adapt to changing environments and plasticity is commonly observed across all taxa. Owing to the fitness benefits of phenotypic plasticity, evolutionary biologists are interested in its genetic basis, which could explain how phenotypic plasticity is involved in the evolution of species interactions. Two current ideas exist: (i) phenotypic plasticity is caused by environmentally sensitive loci associated with a phenotype; (ii) phenotypic plasticity is caused by regulatory genes that simply influence the plasticity of a phenotype. Here, we designed a quantitative trait loci (QTL) mapping experiment to locate QTL on the barley genome associated with barley performance when the environment varies in the presence of aphids, and the composition of the rhizosphere. We simultaneously mapped aphid performance across variable rhizosphere environments. We mapped main effects, QTL × environment interaction (QTL×E), and phenotypic plasticity (measured as the difference in mean trait values) for barley and aphid performance onto the barley genome using an interval mapping procedure. We found that QTL associated with phenotypic plasticity were co-located with main effect QTL and QTL×E. We also located phenotypic plasticity QTL that were located separately from main effect QTL. These results support both of the current ideas of how phenotypic plasticity is genetically based and provide an initial insight into the functional genetic basis of how phenotypically plastic traits may still be important sources of community genetic effects.     

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.     

Two reproductive traits show contrasting genetic architectures in Plantago lanceolata

In many species, temperature‐sensitive phenotypic plasticity (i.e., an individual's phenotypic response to temperature) displays a positive correlation with latitude, a pattern presumed to reflect local adaptation. This geographical pattern raises two general questions: (a) Do a few large‐effect genes contribute to latitudinal variation in a trait? (b) Is the thermal plasticity of different traits regulated pleiotropically? To address the questions, we crossed individuals of Plantago lanceolata derived from northern and southern European populations. Individuals naturally exhibited high and low thermal plasticity in floral reflectance and flowering time. We grew parents and offspring in controlled cool‐ and warm‐temperature environments, mimicking what plants would encounter in nature. We obtained genetic markers via genotype‐by‐sequencing, produced the first recombination map for this ecologically important nonmodel species, and performed quantitative trait locus (QTL) mapping of thermal plasticity and single‐environment values for both traits. We identified a large‐effect QTL that largely explained the reflectance plasticity differences between northern and southern populations. We identified multiple smaller‐effect QTLs affecting aspects of flowering time, one of which affected flowering time plasticity. The results indicate that the genetic architecture of thermal plasticity in flowering is more complex than for reflectance. One flowering time QTL showed strong cytonuclear interactions under cool temperatures. Reflectance and flowering plasticity QTLs did not colocalize, suggesting little pleiotropic genetic control and freedom for independent trait evolution. Such genetic information about the architecture of plasticity is environmentally important because it informs us about the potential for plasticity to offset negative effects of climate change.     

Zero-inflated generalized Poisson regression mixture model for mapping quantitative trait loci underlying count trait with many zeros

Phenotypes measured in counts are commonly observed in nature. Statistical methods for mapping quantitative trait loci (QTL) underlying count traits are documented in the literature. The majority of them assume that the count phenotype follows a Poisson distribution with appropriate techniques being applied to handle data dispersion. When a count trait has a genetic basis, “naturally occurring” zero status also reflects the underlying gene effects. Simply ignoring or miss-handling the zero data may lead to wrong QTL inference. In this article, we propose an interval mapping approach for mapping QTL underlying count phenotypes containing many zeros. The effects of QTLs on the zero-inflated count trait are modelled through the zero-inflated generalized Poisson regression mixture model, which can handle the zero inflation and Poisson dispersion in the same distribution. We implement the approach using the EM algorithm with the Newton-Raphson algorithm embedded in the M-step, and provide a genome-wide scan for testing and estimating the QTL effects. The performance of the proposed method is evaluated through extensive simulation studies. Extensions to composite and multiple interval mapping are discussed. The utility of the developed approach is illustrated through a mouse F₂ intercross data set. Significant QTLs are detected to control mouse cholesterol gallstone formation.     

np2QTL: networking phenotypic plasticity quantitative trait loci across heterogeneous environments

Despite its critical importance to our understanding of plant growth and adaptation, the question of how environment‐induced plastic response is affected genetically remains elusive. Previous studies have shown that the reaction norm of an organism across environmental index obeys the allometrical scaling law of part‐whole relationships. The implementation of this phenomenon into functional mapping can characterize how quantitative trait loci (QTLs) modulate the phenotypic plasticity of complex traits to heterogeneous environments. Here, we assemble functional mapping and allometry theory through Lokta?Volterra ordinary differential equations (LVODE) into an R‐based computing platform, np²QTL, aimed to map and visualize phenotypic plasticity QTLs. Based on LVODE parameters, np²QTL constructs a bidirectional, signed and weighted network of QTL?QTL epistasis, whose emergent properties reflect the ecological mechanisms for genotype?environment interactions over any range of environmental change. The utility of np²QTL was validated by comprehending the genetic architecture of phenotypic plasticity via the reanalysis of published plant height data involving 3502 recombinant inbred lines of maize planted in multiple discrete environments. np²QTL also provides a tool for constructing a predictive model of phenotypic responses in extreme environments relative to the median environment.     

A mixed-model quantitative trait loci (QTL) analysis for multiple-environment trial data using environmental covariables for QTL-by-environment interactions, with an example in maize

Complex quantitative traits of plants as measured on collections of genotypes across multiple environments are the outcome of processes that depend in intricate ways on genotype and environment simultaneously. For a better understanding of the genetic architecture of such traits as observed across environments, genotype-by-environment interaction should be modeled with statistical models that use explicit information on genotypes and environments. The modeling approach we propose explains genotype-by-environment interaction by differential quantitative trait locus (QTL) expression in relation to environmental variables. We analyzed grain yield and grain moisture for an experimental data set composed of 976 F(5) maize testcross progenies evaluated across 12 environments in the U.S. corn belt during 1994 and 1995. The strategy we used was based on mixed models and started with a phenotypic analysis of multi-environment data, modeling genotype-by-environment interactions and associated genetic correlations between environments, while taking into account intraenvironmental error structures. The phenotypic mixed models were then extended to QTL models via the incorporation of marker information as genotypic covariables. A majority of the detected QTL showed significant QTL-by-environment interactions (QEI). The QEI were further analyzed by including environmental covariates into the mixed model. Most QEI could be understood as differential QTL expression conditional on longitude or year, both consequences of temperature differences during critical stages of the growth.     

A unified statistical model for functional mapping of environment-dependent genetic expression and genotype x environment interactions for ontogenetic development

The effects of quantitative trait loci (QTL) on phenotypic development may depend on the environment (QTL x 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 x 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 x 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.     

Bayesian quantitative trait loci mapping for multiple traits

Most quantitative trait loci (QTL) mapping experiments typically collect phenotypic data on multiple correlated complex traits. However, there is a lack of a comprehensive genomewide mapping strategy for correlated traits in the literature. We develop Bayesian multiple-QTL mapping methods for correlated continuous traits using two multivariate models: one that assumes the same genetic model for all traits, the traditional multivariate model, and the other known as the seemingly unrelated regression (SUR) model that allows different genetic models for different traits. We develop computationally efficient Markov chain Monte Carlo (MCMC) algorithms for performing joint analysis. We conduct extensive simulation studies to assess the performance of the proposed methods and to compare with the conventional single-trait model. Our methods have been implemented in the freely available package R/qtlbim (http://www.qtlbim.org), which greatly facilitates the general usage of the Bayesian methodology for unraveling the genetic architecture of complex traits.     

Genetic architecture of plastic methyl jasmonate responses in Arabidopsis thaliana

The ability of a single genotype to generate different phenotypes in disparate environments is termed phenotypic plasticity, which reflects the interaction of genotype and environment on developmental processes. However, there is controversy over the definition of plasticity genes. The gene regulation model states that plasticity loci influence trait changes between environments without altering the means within a given environment. Alternatively, the allelic sensitivity model argues that plasticity evolves due to selection of phenotypic values expressed within particular environments; hence plasticity must be controlled by loci expressed within these environments. To identify genetic loci controlling phenotypic plasticity and address this controversy, we analyzed the plasticity of glucosinolate accumulation under methyl jasmonate (MeJa) treatment in Arabidopsis thaliana. We found genetic variation influencing multiple MeJa signal transduction pathways. Analysis of MeJa responses in the Landsberg erecta x Columbia recombinant inbred lines identified a number of quantitative trait loci (QTL) that regulate plastic MeJa responses. All significant plasticity QTL also impacted the mean trait value in at least one of the two "control" or "MeJa" environments, supporting the allelic sensitivity model. Additionally, we present an analysis of MeJa and salicylic acid cross-talk in glucosinolate regulation and describe the implications for glucosinolate physiology and functional understanding of Arabidopsis MeJa signal transduction.     

Strategies for genetic mapping of categorical traits

The search for efficient and powerful statistical methods and optimal mapping strategies for categorical traits under various experimental designs continues to be one of the main tasks in genetic mapping studies. Methodologies for genetic mapping of categorical traits can generally be classified into two groups, linear and non-linear models. We develop a method based on a threshold model, termed mixture threshold model to handle ordinal (or binary) data from multiple families. Monte Carlo simulations are done to compare its statistical efficiencies and properties of the proposed non-linear model with a linear model for genetic mapping of categorical traits using multiple families. The mixture threshold model has notably higher statistical power than linear models. There may be an optimal sampling strategy (family size vs number of families) in which genetic mapping reaches its maximal power and minimal estimation errors. A single large-sibship family does not necessarily produce the maximal power for detection of quantitative trait loci (QTL) due to genetic sampling of QTL alleles. The QTL allelic model has a marked impact on efficiency of genetic mapping of categorical traits in terms of statistical power and QTL parameter estimation. Compared with a fixed number of QTL alleles (two or four), the model with an infinite number of QTL alleles and normally distributed allelic effects results in loss of statistical power. The results imply that inbred designs (e.g. F₂ or four-way crosses) with a few QTL alleles segregating or reducing number of QTL alleles (e.g. by selection) in outbred populations are desirable in genetic mapping of categorical traits using data from multiple families. This revised version was published online in July 2006 with corrections to the Cover Date.     

Generalized Linear Model for Mapping Discrete Trait Loci Implemented with LASSO Algorithm

Generalized estimating equation (GEE) algorithm under a heterogeneous residual variance model is an extension of the iteratively reweighted least squares (IRLS) method for continuous traits to discrete traits. In contrast to mixture model-based expectation–maximization (EM) algorithm, the GEE algorithm can well detect quantitative trait locus (QTL), especially large effect QTLs located in large marker intervals in the manner of high computing speed. Based on a single QTL model, however, the GEE algorithm has very limited statistical power to detect multiple QTLs because of ignoring other linked QTLs. In this study, the fast least absolute shrinkage and selection operator (LASSO) is derived for generalized linear model (GLM) with all possible link functions. Under a heterogeneous residual variance model, the LASSO for GLM is used to iteratively estimate the non-zero genetic effects of those loci over entire genome. The iteratively reweighted LASSO is therefore extended to mapping QTL for discrete traits, such as ordinal, binary, and Poisson traits. The simulated and real data analyses are conducted to demonstrate the efficiency of the proposed method to simultaneously identify multiple QTLs for binary and Poisson traits as examples.     

QTL analysis and QTL-based prediction of flowering phenology in recombinant inbred lines of barley

Combining ecophysiological modelling and genetic mapping has increasingly received attention from researchers who wish to predict complex plant or crop traits under diverse environmental conditions. The potential for using this combined approach to predict flowering time of individual genotypes in a recombinant inbred line (RIL) population of spring barley (Hordeum vulgare L.) was examined. An ecophysiological phenology model predicts preflowering duration as affected by temperature and photoperiod, based on the following four input traits: f(o) (the minimum number of days to flowering at the optimum temperature and photoperiod), theta1 and theta2 (the development stages for the start and the end of the photoperiod-sensitive phase, respectively), and delta (the photoperiod sensitivity). The model-input trait values were obtained from a photoperiod-controlled greenhouse experiment. Assuming additivity of QTL effects, a multiple QTL model was fitted for the model-input traits using composite interval mapping. Four to seven QTL were identified for each trait. Each trait had at least one QTL specific to that trait alone. Other QTL were shared by two or all traits. Values of the model-input traits predicted for the RILs from the QTL model were fed back into the ecophysiological model. This QTL-based ecophysiological model was subsequently used to predict preflowering duration (d) for eight field trial environments. The model accounted for 72% of the observed variation among 94 RILs and 94% of the variation among the two parents across the eight environments, when observations in different environments were pooled. However, due to the low percentage (34-41%) of phenotypic variation accounted for by the identified QTL for three model-input traits (theta1, theta2 and delta), the QTL-based model accounted for somewhat less variation among the RILs than the model using original phenotypic input trait values. Nevertheless, days to flowering as predicted from the QTL-based ecophysiological model were highly correlated with days to flowering as predicted from QTL-models per environment for days to flowering per se. The ecophysiological phenology model was thus capable of extrapolating (QTL) information from one environment to another.     

Mapping quantitative trait loci for longitudinal traits in line crosses

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.     

Genetics of phenotypic plasticity: QTL analysis in barley, Hordeum vulgare

Phenotypic plasticity is the variation in phenotypic traits produced by a genotype in different environments. In contrast, environmental canalization is defined as the insensitivity of a genotype's phenotype to variation in environments. Despite the extensive literature on the evolutionary significance and potential genetic mechanisms driving plasticity and canalization, few studies tried to unravel the genetic basis of this phenomenon. Using both simulations and real data from barley (Hordeum vulgare), we used QTL mapping to obtain insights into the genetics of phenotypic plasticity. We explored two ways of quantifying phenotypic plasticity, namely the phenotypic variance across environments and the Finlay-Wilkinson's regression slope. Each relates to a different concept of stability. Through QTL detection with real and simulated data, we show that each measure of plasticity detects specific types of plasticity QTL. Most of the plasticity QTLs were detected in the data set with the lowest number of environments. All plasticity QTL co-located with loci showing QTL x E interaction and there were no QTL that only affected plasticity. The number of environments that are considered and their homogeneity is a key to interpret the genetic control of phenotypic plasticity. Regulatory pathways of plasticity may vary from one set of environments to another due to unique features of each environment. Therefore, with an increasing number of environments, it may become impossible to detect a single 'consistent' regulatory pathway for all environments.     

Mapping phenotypic plasticity and genotype-environment interactions affecting life-history traits in Caenorhabditis elegans

Phenotypic plasticity and genotype-environment interactions (GEI) play an important role in the evolution of life histories. Knowledge of the molecular genetic basis of plasticity and GEI provides insight into the underlying mechanisms of life-history changes in different environments. We used a genomewide single-nucleotide polymorphism map in a recombinant N2 x CB4856 inbred panel of the nematode Caenorhabditis elegans to study the genetic control of phenotypic plasticity to temperature in four fitness-related traits, that is, age at maturity, fertility, egg size and growth rate. We mapped quantitative trait loci (QTL) for the respective traits at 12 and 24 degrees C, as well as their plasticities. We found genetic variation and GEI for age at maturity, fertility, egg size and growth rate. GEI in fertility and egg size was attributed to changes in rank order of reaction norms. In case of age at maturity and growth rate, GEI was caused mainly by differences in the among-line variance. In total, 11 QTLs were detected, five QTL at 12 degrees C and six QTL at 24 degrees C, which were associated with life-history traits. Five QTL associated with age at maturity, fertility and growth rate showed QTL x environment interaction. These colocalized with plasticity QTL for the respective traits suggesting allelic sensitivity to temperature. Further fine mapping, complementation analyses and gene silencing are planned to identify candidate genes underlying phenotypic plasticity for age at maturity, fertility and growth.     

Phenotypic integration plasticity in Daphnia magna: an integral facet of G × E interactions

Phenotypic integration can be defined as the network of multivariate relationships among behavioural, physiological and morphological traits that describe the organism. Phenotypic integration plasticity refers to the change in patterns of phenotypic integration across environments or ontogeny. Because studies of phenotypic plasticity have predominantly focussed on single traits, a G × E interaction is typically perceived as differences in the magnitude of trait expression across two or more environments. However, many plastic responses involve coordinated responses in multiple traits, raising the possibility that relative differences in trait expression in different environments are an important, but often overlooked, source of G × E interaction. Here, we use phenotypic change vectors to statistically compare the multivariate life‐history plasticity of six Daphnia magna clones collected from four disparate European populations. Differences in the magnitude of plastic responses were statistically distinguishable for two of the six clones studied. However, differences in phenotypic integration plasticity were statistically distinguishable for all six of the clones studied, suggesting that phenotypic integration plasticity is an important component of G × E interactions that may be missed unless appropriate multivariate analyses are used.     

Multiple trait multiple interval mapping of quantitative trait loci from inbred line crosses

ABSTRACT: BACKGROUND: Although many experiments have measurements on multiple traits, most studies performed the analysis of mapping of quantitative trait loci (QTL) for each trait separately using single trait analysis. Single trait analysis does not take advantage of possible genetic and environmental correlations between traits. In this paper, we propose a novel statistical method for multiple trait multiple interval mapping (MTMIM) of QTL for inbred line crosses. We also develop a novel score-based method for estimating genome-wide significance level of putative QTL effects suitable for the MTMIM model. The MTMIM method is implemented in the freely available and widely used Windows QTL Cartographer software. RESULTS: Throughout the paper, we provide compelling empirical evidences that: (1) the score-based threshold maintains proper type I error rate and tends to keep false discovery rate within an acceptable level; (2) the MTMIM method can deliver better parameter estimates and power than single trait multiple interval mapping method; (3) an analysis of Drosophila dataset illustrates how the MTMIM method can better extract information from datasets with measurements in multiple traits. CONCLUSIONS: The MTMIM method represents a convenient statistical framework to test hypotheses of pleiotropic QTL versus closely linked nonpleiotropic QTL, QTL by environment interaction, and to estimate the total genotypic variance-covariance matrix between traits and to decompose it in terms of QTL-specific variance-covariance matrices, therefore, providing more details on the genetic architecture of complex traits.     

A dissection model for mapping complex traits

Many quantitative traits are composites of other traits that contribute differentially to genetic variation. Quantitative trait locus (QTL) mapping of these composite traits can benefit by incorporating the mechanistic process of how their formation is mediated by the underlying components. We propose a dissection model by which to map these interconnected components traits under a joint likelihood setting. The model can test how a composite trait is determined by pleiotropic QTLs for its component traits or jointly by different sets of QTLs each responsible for a different component. The model can visualize the pattern of time‐varying genetic effects for individual components and their impacts on composite traits. The dissection model was used to map two composite traits, stemwood volume growth decomposed into its stem height, stem diameter and stem form components for Euramerican poplar adult trees, and total lateral root length constituted by its average lateral root length and lateral root number components for Euphrates poplar seedlings. We found the pattern of how QTLs for different components contribute to phenotypic variation in composite traits. The detailed understanding of the genetic machineries of composite traits will not only help in the design of molecular breeding in plants and animals, but also shed light on the evolutionary processes of quantitative traits under natural selection.     

On the generalized poisson regression mixture model for mapping quantitative trait loci with count data

Statistical methods for mapping quantitative trait loci (QTL) have been extensively studied. While most existing methods assume normal distribution of the phenotype, the normality assumption could be easily violated when phenotypes are measured in counts. One natural choice to deal with count traits is to apply the classical Poisson regression model. However, conditional on covariates, the Poisson assumption of mean-variance equality may not be valid when data are potentially under- or overdispersed. In this article, we propose an interval-mapping approach for phenotypes measured in counts. We model the effects of QTL through a generalized Poisson regression model and develop efficient likelihood-based inference procedures. This approach, implemented with the EM algorithm, allows for a genomewide scan for the existence of QTL throughout the entire genome. The performance of the proposed method is evaluated through extensive simulation studies along with comparisons with existing approaches such as the Poisson regression and the generalized estimating equation approach. An application to a rice tiller number data set is given. Our approach provides a standard procedure for mapping QTL involved in the genetic control of complex traits measured in counts.     

Identification of quantitative trait loci (QTL) for fruit-quality traits and number of weeks of flowering in the cultivated strawberry

Fruit quality and repeat flowering are two major foci of several strawberry breeding programs. The identification of quantitative trait loci (QTL) and molecular markers linked to these traits could improve breeding efficiency. In this work, an F₁ population derived from the cross ‘Delmarvel’ × ‘Selva’ was used to develop a genetic linkage map for QTL analyses of fruit-quality traits and number of weeks of flowering. Some QTL for fruit-quality traits were identified on the same homoeologous groups found in previous studies, supporting trait association in multiple genetic backgrounds and utility in multiple breeding programs. None of the QTL for soluble solids colocated with a QTL for titratable acids, and, although the total soluble solid contents were significantly and positively correlated with titratable acids, the correlation coefficient value of 0.2452 and independence of QTL indicate that selection for high soluble solids can be practiced independently of selection for low acidity. One genomic region associated with the total number of weeks of flowering was identified quantitatively on LG IV-S-1. The most significant marker, FxaACAO2I8C-145S, explained 43.3 % of the phenotypic variation. The repeat-flowering trait, scored qualitatively, mapped to the same region as the QTL. Dominance of the repeat-flowering allele was demonstrated by the determination that the repeat-flowering parent was heterozygous. This genomic region appears to be the same region identified in multiple mapping populations and testing environments. Markers linked in multiple populations and testing environments to fruit-quality traits and repeat flowering should be tested widely for use in marker-assisted breeding.