Genotype-environment interactions at quantitative trait loci affecting inflorescence development in Arabidopsis thaliana

Phenotypic plasticity and genotype-environment interactions (GEI) play a prominent role in plant morphological diversity and in the potential functional capacities of plant life-history traits. The genetic basis of plasticity and GEI, however, is poorly understood in most organisms. In this report, inflorescence development patterns in Arabidopsis thaliana were examined under different, ecologically relevant photoperiod environments for two recombinant inbred mapping populations (Ler x Col and Cvi x Ler) using a combination of quantitative genetics and quantitative trait locus (QTL) mapping. Plasticity and GEI were regularly observed for the majority of 13 inflorescence traits. These observations can be attributable (at least partly) to variable effects of specific QTL. Pooled across traits, 12/44 (27.3%) and 32/62 (51.6%) of QTL exhibited significant QTL x environment interactions in the Ler x Col and Cvi x Ler lines, respectively. These interactions were attributable to changes in magnitude of effect of QTL more often than to changes in rank order (sign) of effect. Multiple QTL x environment interactions (in Cvi x Ler) clustered in two genomic regions on chromosomes 1 and 5, indicating a disproportionate contribution of these regions to the phenotypic patterns observed. High-resolution mapping will be necessary to distinguish between the alternative explanations of pleiotropy and tight linkage among multiple genes.     

Quantitative trait loci for inflorescence development in Arabidopsis thaliana

Variation in inflorescence development patterns is a central factor in the evolutionary ecology of plants. The genetic architectures of 13 traits associated with inflorescence developmental timing, architecture, rosette morphology, and fitness were investigated in Arabidopsis thaliana, a model plant system. There is substantial naturally occurring genetic variation for inflorescence development traits, with broad sense heritabilities computed from 21 Arabidopsis ecotypes ranging from 0.134 to 0.772. Genetic correlations are significant for most (64/78) pairs of traits, suggesting either pleiotropy or tight linkage among loci. Quantitative trait locus (QTL) mapping indicates 47 and 63 QTL for inflorescence developmental traits in Ler x Col and Cvi x Ler recombinant inbred mapping populations, respectively. Several QTL associated with different developmental traits map to the same Arabidopsis chromosomal regions, in agreement with the strong genetic correlations observed. Epistasis among QTL was observed only in the Cvi x Ler population, and only between regions on chromosomes 1 and 5. Examination of the completed Arabidopsis genome sequence in three QTL regions revealed between 375 and 783 genes per region. Previously identified flowering time, inflorescence architecture, floral meristem identity, and hormone signaling genes represent some of the many candidate genes in these regions.     

Pleiotropic effects of the Arabidopsis cryptochrome 2 allelic variation underlie fruit trait-related QTL

The previous molecular identification of a flowering time QTL segregating in the Arabidopsis L er x Cvi cross, demonstrated that natural allelic variation at the blue light photoreceptor CRY2 gene affects flowering time (El-Assal et al., 2001). In addition, previous works on the same cross have mapped several QTL affecting other unrelated life history traits in the CRY2 genomic region. In the present report, we have used a set of Arabidopsis L er transgenic plants carrying four different functional CRY2 transgenes for phenotypic analyses, with the aim of exploring the extent of pleiotropy of CRY2 allelic variation. It is concluded that previously identified QTL affecting fruit length, ovule number per fruit, and percentage of unfertilized ovules are caused by this same Ler/Cvi CRY2 allelic variation. In addition, dose effects of the CRY2-L er allele are detected for fruit length. A seed weight QTL at the map position of CRY2 could not be confirmed and also no effect on seed dormancy was observed. Thus, it is shown that transgenic plants carrying different alleles can be a useful tool to attribute QTL for different complex traits to a specific locus, even when the relationship among the traits has not been previously suggested.     

Genetic basis of phenotypic correlations among growth traits in hybrid willow (Salix dasycladosxS. viminalis) grown under two water regimes

Phenotypic correlations and quantitative trait loci (QTL) for important growth traits and a surrogate of intrinsic water-use efficiency (leaf delta(13)C) were analysed in a willow pedigree of 92 full-sibling clones grown under two water regimes. The major objective was to examine the genetic basis of the phenotypic correlations. Cuttings of Salix were glasshouse-grown during one growing season. The relative growth rate (RGR) and underlying traits were assessed. QTL analysis was conducted based on an available linkage map for Salix. Leaf area productivity and leaf nitrogen productivity were more important in determining RGR than leaf area ratio and specific leaf area. However, phenotypic correlations among growth traits partly varied between the two environments. QTL were detected for most growth traits, among them many common QTL for different traits. The QTL pattern reflected the phenotypic correlation pattern. None of the QTL for the complex traits was consistent across the different environments. The results demonstrate a genetic basis for phenotypic correlations among growth traits in Salix, and provide evidence for the existence of 'master switches' regulating some of the traits.     

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.     

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.     

Identification of Botrytis cinerea susceptibility loci in Arabidopsis thaliana

Botrytis cinerea is a major pathogen of fruit and vegetable crops causing both pre- and post-harvest grey mould. We have analysed 16 Arabidopsis thaliana ecotypes for natural variation in B. cinerea susceptibility. Susceptibility was associated with lower camalexin accumulation, and three ecotypes (Cape Verdi Islands (Cvi-0), Slavice (Sav-0) and Kindalville (Kin-0)) showed differential susceptibility to the two B. cinerea isolates used. Subsequently, to better understand the genetic control of grey mould disease, we assayed the Arabidopsis Landsberg erecta (Ler) x Columbia (Col-0) recombinant inbred population with the two isolates, and identified multiple small-to-medium-effect quantitative trait loci (QTL) governing susceptibility. Interestingly, the QTL for each isolate are distinct, suggesting that different mechanisms govern defence against these two isolates. Two QTL for each isolate exhibited epistatic interactions with specific allele combinations generating heightened B. cinerea susceptibility.     

Ecological genetics of an induced plant defense against herbivores: additive genetic variance and costs of phenotypic plasticity

Abstract.— Adaptive phenotypic plasticity in chemical defense is thought to play a major role in plant-herbivore interactions. We investigated genetic variation for inducibility of defensive traits in wild radish plants and asked if the evolution of induction is constrained by costs of phenotypic plasticity. In a greenhouse experiment using paternal half-sibling families, we show additive genetic variation for plasticity in glucosinolate concentration. Genetic variation for glucosinolates was not detected in undamaged plants, but was significant following herbivory by a specialist herbivore, Pieris rapae . On average, damaged plants had 55% higher concentrations of glucosinolates compared to controls. In addition, we found significant narrow-sense heritabilities for leaf size, trichome number, flowering phenology, and lifetime fruit production. In a second experiment, we found evidence of genetic variation in induced plant resistance to P. rapae . Although overall there was little evidence for genetic correlations between the defensive and life-history traits we measured, we show that more plastic families had lower fitness than less plastic families in the absence of herbivory (i.e., evidence for genetic costs of plasticity). Thus, there is genetic variation for induction of defense in wild radish, and the evolution of inducibility may be constrained by costs of plasticity.     

Quantitative trait loci for floral morphology in Arabidopsis thaliana

A central question in biology is how genes control the expression of quantitative variation. We used statistical methods to estimate genetic variation in eight Arabidopsis thaliana floral characters (fresh flower mass, petal length, petal width, sepal length, sepal width, long stamen length, short stamen length, and pistil length) in a cosmopolitan sample of 15 ecotypes. In addition, we used genome-wide quantitative trait locus (QTL) mapping to evaluate the genetic basis of variation in these same traits in the Landsberg erecta x Columbia recombinant inbred line population. There was significant genetic variation for all traits in both the sample of naturally occurring ecotypes and in the Ler x Col recombinant inbred line population. In addition, broad-sense genetic correlations among the traits were positive and high. A composite interval mapping (CIM) analysis detected 18 significant QTL affecting at least one floral character. Eleven QTL were associated with several floral traits, supporting either pleiotropy or tight linkage as major determinants of flower morphological integration. We propose several candidate genes that may underlie these QTL on the basis of positional information and functional arguments. Genome-wide QTL mapping is a promising tool for the discovery of candidate genes controlling morphological development, the detection of novel phenotypic effects for known genes, and in generating a more complete understanding of the genetic basis of floral development.     

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.     

Genetic Control of Water Use Efficiency and Leaf Carbon Isotope Discrimination in Sunflower (Helianthus annuus L.) Subjected to Two Drought Scenarios

High water use efficiency (WUE) can be achieved by coordination of biomass accumulation and water consumption. WUE is physiologically and genetically linked to carbon isotope discrimination (CID) in leaves of plants. A population of 148 recombinant inbred lines (RILs) of sunflower derived from a cross between XRQ and PSC8 lines was studied to identify quantitative trait loci (QTL) controlling WUE and CID, and to compare QTL associated with these traits in different drought scenarios. We conducted greenhouse experiments in 2011 and 2012 by using 100 balances which provided a daily measurement of water transpired, and we determined WUE, CID, biomass and cumulative water transpired by plants. Wide phenotypic variability, significant genotypic effects, and significant negative correlations between WUE and CID were observed in both experiments. A total of nine QTL controlling WUE and eight controlling CID were identified across the two experiments. A QTL for phenotypic response controlling WUE and CID was also significantly identified. The QTL for WUE were specific to the drought scenarios, whereas the QTL for CID were independent of the drought scenarios and could be found in all the experiments. Our results showed that the stable genomic regions controlling CID were located on the linkage groups 06 and 13 (LG06 and LG13). Three QTL for CID were co-localized with the QTL for WUE, biomass and cumulative water transpired. We found that CID and WUE are highly correlated and have common genetic control. Interestingly, the genetic control of these traits showed an interaction with the environment (between the two drought scenarios and control conditions). Our results open a way for breeding higher WUE by using CID and marker-assisted approaches and therefore help to maintain the stability of sunflower crop production.     

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.     

Phenotypic integration may constrain phenotypic plasticity in plants

Phenotypic plasticity is essential for plant adaptation to changing environments but some factors limit its expression, causing plants to fail in producing the best phenotype for a given environment. Phenotypic integration refers to the pattern and magnitude of character correlations and it might play a role as an internal constraint to phenotypic plasticity. We tested the hypothesis that phenotypic integration – estimated as the number of significant phenotypic correlations between traits – constrains phenotypic plasticity of plants. The rationale is that, for any phenotypic trait, the more linked with other traits it is, the more limited is its range of variation. In the perennial species Convolvulus chilensis (Convolvulaceae) and Lippia alba (Verbenaceae) we determined the relationship between phenotypic plasticity to relevant environmental factors – shading for C. chilensis and drought for L. alba– and the magnitude of phenotypic integration of morphological and biomass allocation traits. In C. chilensis plants, plasticity to shading of a given trait decreased with the number of significant correlations that it had with the other traits. Likewise, the characters that showed greater plasticity to experimental drought in L. alba plants had fewer significant phenotypic correlations with other characters. We report a novel limit to phenotypic plasticity of plants by showing that the phenotypic trait architecture may constrain their plastic, functional responses to the environment.     

Quantitative genetics and functional-structural plant growth models: simulation of quantitative trait loci detection for model parameters and application to potential yield optimization

BACKGROUND AND AIMS: Prediction of phenotypic traits from new genotypes under untested environmental conditions is crucial to build simulations of breeding strategies to improve target traits. Although the plant response to environmental stresses is characterized by both architectural and functional plasticity, recent attempts to integrate biological knowledge into genetics models have mainly concerned specific physiological processes or crop models without architecture, and thus may prove limited when studying genotype x environment interactions. Consequently, this paper presents a simulation study introducing genetics into a functional-structural growth model, which gives access to more fundamental traits for quantitative trait loci (QTL) detection and thus to promising tools for yield optimization. METHODS: The GREENLAB model was selected as a reasonable choice to link growth model parameters to QTL. Virtual genes and virtual chromosomes were defined to build a simple genetic model that drove the settings of the species-specific parameters of the model. The QTL Cartographer software was used to study QTL detection of simulated plant traits. A genetic algorithm was implemented to define the ideotype for yield maximization based on the model parameters and the associated allelic combination. KEY RESULTS AND CONCLUSIONS: By keeping the environmental factors constant and using a virtual population with a large number of individuals generated by a Mendelian genetic model, results for an ideal case could be simulated. Virtual QTL detection was compared in the case of phenotypic traits--such as cob weight--and when traits were model parameters, and was found to be more accurate in the latter case. The practical interest of this approach is illustrated by calculating the parameters (and the corresponding genotype) associated with yield optimization of a GREENLAB maize model. The paper discusses the potentials of GREENLAB to represent environment x genotype interactions, in particular through its main state variable, the ratio of biomass supply over demand.     

Identification of quantitative trait loci controlling symptom development during viral infection in Arabidopsis thaliana

In compatible interactions between plants and viruses that result in systemic infection, symptom development is a major phenotypic trait. However, host determinants governing this trait are mostly unknown, and the mechanisms underlying it are still poorly understood. In a previous study on the Arabidopsis thaliana-Plum pox virus (PPV) pathosystem, we showed a large degree of variation in symptom development among susceptible accessions. In particular, Cvi-1 (Cape Verde islands) accumulates viral particules but remains symptomless, Col-0 (Columbia) sometimes shows weak symptoms compared with Ler (Landsberg erecta), which always shows severe symptoms. Genetic analyses of Col x Ler and Cvi x Ler F2 and recombinant inbred line (RIL) populations suggested that symptom development as well as viral accumulation traits are polygenic and quantitative. Three of the symptom quantitative trait loci (QTL) identified could be confirmed in near-isogenic lines, including PSI1 (PPV symptom induction 1), which was identified on the distal part of chromosome 1 in both RIL populations. With respect to viral accumulation, several factors have been detected and, interestingly, in the Col x Ler population, two out of three viral accumulation QTL colocalized with loci controlling symptom development, although correlation analysis showed weak linearity between symptom severity and virus accumulation. In addition, in the Cvi x Ler RIL population, a digenic recessive determinant controlling PPV infection was identified.     

Reaction norms of Arabidopsis. I. Plasticity of characters and correlations across water,nutrient and light gradients

The univariate and multivariate study of variation for phenotypic plasticity is central to providing a clear understanding of hypotheses about the genetic control and evolution of reaction norms in natural populations. Arabidopsis thaliana is an ideal organism for the study of Genotype × Environment interactions (i.e., genetic variation for plasticity), because of the ease with which it can be grown in large numbers and due to the amount of information already available on its genetics, physiology and developmental biology. In this paper, we report on the plasticity, genetic variation and G × E interactions of four populations of A. thaliana in response to three environmental gradients (water, light and nutrients), each characterized by four levels of the controlled parameter. We measured nine traits and obtained their reaction norms. Path analysis was used to study the plasticity of character correlations. We found a tendency for A. thaliana reaction norms to be linear (either flat, i.e. no plasticity, or with a significant slope), in accordance with previous studies. We detected substantial amounts of genetic variation for plasticity in the light and nutrient gradients, but not in the water gradient. Dramatic restructuring of character correlations was induced by changes in environmental conditions, although some paths tended to be stable irrespective of the environment, thereby suggesting some degree of canalization.     

The impact of plasticity and maternal effect on the evolution of leaf resin production in Diplacus aurantiacus

Our previous quantitative genetic study of leaf resin production in Diplacus aurantiacus revealed large environmental and maternal effects on variation in resin production, which suggests the possibility of a genotype×environment interaction for this trait when plants grow in heterogeneous environments. Our objectives in this study were to observe the genetic variation in plasticity of resin production under field and chamber conditions, compare phenotypic correlations of resin content with growth traits under these two environmental conditions, and distinguish the possible basis of the maternal effect on resin production using parents and half-sib progeny. A significant genotype×environment interaction (P<0.0001) in leaf resin production was found, which suggests a potential for the evolution of plasticity of these secondary metabolites under heterogeneous environments. The phenotypic correlation between resin content and growth rate also exhibited plasticity. In addition, the resin content of dam half-sib families grown in the chamber had a closer relationship with their maternal parents in the field (r=0.65, P=0.059) than in the chamber (r=0.39, P=0.34), suggesting an environmentally based maternal effect on the secondary chemicals. We suggest that the maternal environmental effect may act as a contributor to plasticity of resin production and, while it may not diminish the appearance of the genotype×environment interaction, the heritable variation of plasticity of resin production may be confounded.     

Population size and identity influence the reaction norm of the rare,endemic plant Cochlearia bavarica across a gradient of environmental stress

Habitat degradation and loss can result in population decline and genetic erosion, limiting the ability of organisms to cope with environmental change, whether this is through evolutionary genetic response (requiring genetic variation) or through phenotypic plasticity (i.e., the ability of a given genotype to express a variable phenotype across environments). Here we address the question whether plants from small populations are less plastic or more susceptible to environmental stress than plants from large populations. We collected seed families from small (<100) versus large natural populations (>1,000 flowering plants) of the rare, endemic plant Cochlearia bavarica (Brassicaceae). We exposed the seedlings to a range of environments, created by manipulating water supply and light intensity in a 2 x 2 factorial design in the greenhouse. We monitored plant growth and survival for 300 days. Significant effects of offspring environment on offspring characters demonstrated that there is phenotypic plasticity in the responses to environmental stress in this species. Significant effects of population size group, but mainly of population identity within the population size groups, and of maternal plant identity within populations indicated variation due to genetic (plus potentially maternal) variation for offspring traits. The environment x maternal plant identity interaction was rarely significant, providing little evidence for genetically- (plus potentially maternally-) based variation in plasticity within populations. However, significant environment x population-size-group and environment x population-identity interactions suggested that populations differed in the amount of plasticity, the mean amount being smaller in small populations than in large populations. Whereas on day 210 the differences between small and large populations were largest in the environment in which plants grew biggest (i.e., under benign conditions), on day 270 the difference was largest in stressful environments. These results show that population size and population identity can affect growth and survival differently across environmental stress gradients. Moreover, these effects can themselves be modified by time-dependent variation in the interaction between plants and their 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.     

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.