Quantitative Trait Loci Controlling Light and Hormone Response in Two Accessions of Arabidopsis thaliana

Corresponding author: Joanne Chory, The Salk Institute for Biological Studies, 10010 N. Torrey Pines Rd., La Jolla, CA 92037., chory{at}salk.edu (E-mail)

Communicating editor: T. F. C. MACKAY

	ABSTRACT

TOP ABSTRACT MATERIALS AND METHODS RESULTS DISCUSSION LITERATURE CITED

We have mapped quantitative trait loci (QTL) responsible for natural variation in light and hormone response between the Cape Verde Islands (Cvi) and Landsberg erecta (Ler) accessions of Arabidopsis thaliana using recombinant inbred lines (RILs). Hypocotyl length was measured in four light environments: white, blue, red, and far-red light and in the dark. In addition, white light plus gibberellin (GA) and dark plus the brassinosteroid biosynthesis inhibitor brassinazole (BRZ) were used to detect hormone effects. Twelve QTL were identified that map to loci not previously known to affect light response, as well as loci where candidate genes have been identified from known mutations. Some QTL act in all environments while others show genotype-by-environment interaction. A global threshold was established to identify a significant epistatic interaction between two loci that have few main effects of their own. LIGHT1, a major QTL, has been confirmed in a near isogenic line (NIL) and maps to a new locus with effects in all light environments. The erecta mutation can explain the effect of the HYP2 QTL in the blue, BRZ, and dark environments, but not in far-red. LIGHT2, also confirmed in an NIL, has effects in white and red light and shows interaction with GA. The phenotype and map position of LIGHT2 suggest the photoreceptor PHYB as a candidate gene. Natural variation in light and hormone response thus defines both new genes and known genes that control light response in wild accessions.

PLANT development is coordinated to optimize the amount of light available for photosynthesis. There is an elaborate control of plant responses to light, with a variety of photoreceptors at the top of different light response signaling hierarchies (NEFF et al. 2000 ). The red/far-red light-absorbing phytochromes and the blue/UV-A absorbing cryptochromes perceive light quality and quantity and direct the plant to modify its developmental program. Cotyledon opening and inhibition of hypocotyl length (which are part of the de-etiolation response), shade avoidance, and flowering time are just some of the developmental phenotypes controlled by light. In nature, latitude, climate, vegetation, and terrain create different light environments, requiring plants to modify their light responses. For example, when plants sense light rich in far-red, indicative of shade and/or competition, many plants respond by stem and petiole elongation and accelerated flowering. The hypocotyl length of young seedlings is also affected by light quality and quantity. The adaptive nature of plant light responses is of great interest (CASAL and SMITH 1989 ; SMITH 1995 ; SCHMITT et al. 1999 ; MALOOF et al. 2000 ). Wide genetic variation exists in hypocotyl length in response to light among Arabidopsis accessions (MALOOF et al. 2001 ). This variation can be exploited using quantitative trait loci (QTL) mapping to discover new genes and new alleles of known genes in light signaling.

Traditional genetics and other molecular approaches in Arabidopsis have provided a signal transduction framework (NEFF et al. 2000 ) upon which new genes discovered from natural populations can be integrated. Arabidopsis plants with mutations in the PHYTOCHROME B gene have reduced light sensitivity and elongate much more than wild type under equal light intensities (REED et al. 1993 ). Responses to light, such as hypocotyl elongation, are also affected by hormones of the gibberellin (GA) and brassinosteroid (BR) classes (CHORY and LI 1997 ). GAs promote cell elongation in the hypocotyl, a response that is attenuated by PHYB (REED et al. 1996 ). In the dark, photomorphogenic growth is suppressed, and this suppression requires BRs. Consequently, Arabidopsis and rice mutants that fail to make or perceive BRs incorrectly de-etiolate in the dark (LI et al. 1996 ; LI and CHORY 1997 ; YAMAMURO et al. 2000 ). Application of the brassinosteroid biosynthetic inhibitor brassinazole (BRZ) mimics BR deficiency, also causing wild-type plants to de-etiolate in the dark (ASAMI and YOSHIDA 1999 ; ASAMI et al. 2000 ). Apart from seedling development, GAs and BRs affect many other developmental processes that are also controlled by light. The photoreceptor signaling pathways overlap and interact with the hormone signaling pathways, enabling plants to modify their development in response to changing environmental signals.

Understanding the cross talk between these signaling pathways has been challenging since it requires careful observation in many specific light and hormone conditions. Dissecting light signals away from internal hormone control is difficult using traditional genetics. Mutants identified in screens for seedlings altered in hypocotyl length, a common measure of light sensitivity, often show pleiotropic phenotypes due to defects in hormone production or response (LI and CHORY 1997 ; NEFF et al. 1999 ; TIAN and REED 1999 ; HSIEH et al. 2000 ; ZHAO et al. 2001 ). To determine which light and hormone response pathways naturally, polymorphic loci affect quantitative mapping can be done in multiple environments. QTL that map to similar locations in different environments may affect multiple photoreceptor pathways or may represent variation in linked genes. Tests of genotype-by-environment interaction (G x E) can confirm unique environment effects when QTL are only detected in a subset of environments. Thus, mapping QTL in different environments can dissect responses to light and hormonal control of hypocotyl length.

There are several advantages to using natural populations to discover genes affecting light response (ALONSO-BLANCO and KOORNNEEF 2000 ). Traditional genetic screens for loss-of-function mutations affecting light responses fail to identify both redundant and essential genes and in addition are limited to the genetic complement of commonly used laboratory strains. Subtle phenotypes will also likely be missed without a rigorous quantitative measurement. QTL mapping has the advantage of simultaneous detection of multiple genes that may have small effects, as well as detection of interactions between genes (epistasis) and interactions between genes and environments. In addition, change-of-function mutations and viable polymorphisms in essential genes may occur in wild populations. Perhaps most interestingly, the genes identified from natural populations may have ecological relevance and provide clues about the molecular nature of evolution. The natural variation in wild Arabidopsis accessions is extensive and represents a largely untapped pool of genetic polymorphisms (ALONSO-BLANCO and KOORNNEEF 2000 ). Tools such as a complete genome reference sequence, saturating knockout collections, large numbers of polymorphic markers, and ease of transformation make Arabidopsis an excellent model to further characterize alleles that underlie natural quantitative variation (KRYSAN et al. 1999 ; PARINOV et al. 1999 ; ARABIDOPSIS GENOME INITIATIVE 2000). Recombinant inbred lines (RILs) are available and allow a detailed investigation of variation between two parental strains. A disadvantage, however, is that QTL identify large chromosome intervals that may represent multiple genes with small effect.

Methods for detecting QTL depend on the size and type of population analyzed, the number of markers, and the statistical method. RILs allow the inherent environmental error to be reduced by replication, providing a powerful system of QTL analysis. Currently, the statistical methods of composite interval mapping (CIM; ZENG 1994 ) or multiple QTL model mapping (MQM; JANSEN and STAM 1994 ) have the advantage of allowing background markers to explain variation due to QTL outside the scan region, thereby increasing precision and power to detect QTL within the scan region.

The Arabidopsis RIL population derived from a cross between the Cape Verde Islands accession and the Landsberg erecta laboratory strain has been an important tool for the analysis of complex traits (ALONSO-BLANCO et al. 1998B ). This population has been used to map QTL responsible for flowering time, seed size and other life history traits, circadian rhythm, and sugar composition and seed storability (ALONSO-BLANCO et al. 1998A , ALONSO-BLANCO et al. 1999 ; BENTSINK et al. 2000 ; SWARUP et al. 1999 ). A different RIL population was used in an elegant study of natural variation in light signaling that revealed genetic differences in the very low fluence response (VLFR) between the Landsberg erecta (Ler) and Columbia (Col) accessions (YANOVSKY et al. 1997 ). Two VLF QTL were identified that control cotyledon opening under short pulses of far-red light.

Here we used the Ler/Cvi RIL set to map QTL in seven light and hormone environments. Multiple QTL were identified, some of which act across different light environments, whereas others showed genotype-by-environment interaction. Three QTL were confirmed in near isogenic lines, which define new loci, as well as loci with candidate genes. Moreover, this multienvironment analysis allows QTL to be organized into a genetic framework that can explain natural variation in different photoreceptor pathways.

	MATERIALS AND METHODS

TOP ABSTRACT MATERIALS AND METHODS RESULTS DISCUSSION LITERATURE CITED

Plant material:
The RIL set derived from a cross between Cvi and Ler accessions was used for these studies (ALONSO-BLANCO et al. 1998B ). Seeds of 162 RILs and the parents (CS22000), Col-1 (CS3176), and the Col-1 er-2 (CS3401) mutation were obtained from the Arabidopsis Biological Resource Center (ABRC) in Columbus, Ohio (http://www.arabidopsis.org) and used directly for hypocotyl measurements. Lan-1 (La ERECTA) was obtained from Carlos Alonso-Blanco. F₁ hybrids were made by reciprocal crosses for Ler x Cvi F₁ (Ler female) or Cvi x Ler F₁ (Cvi female).

Growth conditions:
Seeds were sterilized in 1.5-ml microcentrifuge tubes for 10 min in 70% ethanol, 0.01% Triton X-100, followed by a 10-min wash with 95% ethanol, and then resuspended in 1 ml sterile water. After imbibition overnight at 4° in the dark, seeds were placed individually onto 0.7% phytagar plates containing ¹/₂ Murashige and Skoog salts using a Pipetman. Seedlings were spaced at a uniform density so that they did not shade each other. Plates were kept at 4° in the dark for another 3 days, followed by 4 hr of 120 µE m^-2 sec^-1 white light to induce germination. Further incubation was at 23°. Preliminary experiments in six conditions (all except dark) with Cvi, Ler, and most of the CvL RILs revealed substantial variation in hypocotyl lengths among lines and slight variation from week to week and from plate to plate (data not shown). For the results reported here, all light environments and all RILs were done in the same week to minimize week-to-week and week-to-plate variation. Furthermore the number of RILs per plate was increased to 12, providing better statistical control of plate-to-plate variation. Plates were rotated within each incubation chamber every 12 hr for the duration of the experiment to reduce variation among plates within each incubator. Ideally, the entire experiment would be replicated several times over to reduce the contribution of uncontrolled variation in the observed differences between RILs and light environments and to provide precise estimates of the magnitudes of the components of variation. Without such replication, differences due to uncontrolled variation between growth conditions in different incubators could be attributed to light environments and lead to spurious genotype-by-light environment associations. However, a single run of 162 RILs under seven light environments requires 240 person-hours to perform. From the preliminary studies we believed that extraneous variation could be controlled sufficiently to obtain useful results from a single-week experiment alone. In all, 15–30 seedlings of each of 162 CvL RILs, Cvi, Ler, reciprocal F₁ hybrids, and photoreceptor mutants were arrayed in groups of 12 lines per plate across 15 plates. This was replicated for the seven environmental conditions.

Light/hormone conditions:
Incubators used for all environments were Percival model E30B (Percival Scientific, Boone, IA). One incubator (Percival E30LED) was equipped with LED lights and used for the far-red environment. Neutral density screens were used to vary light fluence rate. Light measurements were made with a LI-1800 instrument (Li-Cor, Lincoln, Nebraska). We wanted to identify a fluence rate that would maximize the subtle variation in light sensitivity seen in natural populations. Pilot experiments showed that at high light fluence rates CvL RILs had relatively uniform, short hypocotyls and at low light fluence rates CvL lines were much longer but more variable. We chose intermediate light fluence rates, from a fluence response curve, for each light condition, where the broad-sense heritability was maximized for subsequent experiments. White light was provided by three 35-W cool white fluorescent bulbs and two 25-W incandescent bulbs. The photosynthetic active radiation (PAR, 400–700 nm) was 35 µE m^-2 sec^-1, the Pfr/P ratio was 0.72 (KENDRICK and KRONENBERG 1994 , p. 268), and the R/FR ratio (655–665 nm)/(725–735 nm) was 1.3. The same light conditions were replicated in another incubator for the GA environment except that 30 µM GA₃ (Sigma, St. Louis) was added to the medium. Blue light was provided by three 20-W cool-white fluorescent bulbs and a filter that blocked light above 550 nm. Red light was provided by three 20-W Gro-Lux fluorescent bulbs (Osram Sylvania, Danvers, MA) and a red filter that blocked light below 600 nm. Far-red light (0.5 µE m^-2 sec^-1; 700–730 nm) was provided by LED lights. The same incubator was used for the dark and BRZ environments, and plates were wrapped in aluminum foil and received no further light after the 4-hr germination light pulse. A dose response curve, using different concentrations of the brassinosteroid biosynthetic inhibitor BRZ 91, identified 0.75 µM as the optimum concentration to maximize the heritability. A total of 0.75 µM BRZ (synthesized at RIKEN) was used unless otherwise indicated.

Hypocotyl length measurements:
On day 2, poor germination was scored in white light as 1 or 0. Most lines had already germinated (and were scored as "0"), but 14 lines (CvL nos. 1, 3, 8, 15, 16, 22, 24, 27, 38, 39, 152, 185, 186, and 188) had not (and were scored as "1"). All lines except CvL 3 germinated by day 3 and were measured on day 7. The germination state seen in white light was representative of all conditions and likely reflected both environmental and genetic variation in the state of the seeds rather than light response. Therefore, germination was used as a covariate in subsequent analyses. Seedlings were transferred to acetate sheets containing moist tissue paper and scanned on a flat bed scanner. Hypocotyl lengths were measured in millimeters using National Institutes of Health (NIH) image version 1.62 (http://rsb.info.nih.gov/nih-image). The effect of the covariate germination on hypocotyl length and the average number of seedlings measured in each environment are shown in Table 1.

Statistical analysis:
Data analysis was performed using the statistical package R (IHAKA and GENTLEMAN 1996 ; http://www.R-project.org/). Hypocotyl length data are approximately normally distributed, so no transformation was needed. Hypocotyl length was fit using a statistical model that is described in detail below. Briefly, hypocotyl lengths were fit by a mixed-effects linear model with terms for germination, plate, and RIL. RIL and plate were modeled as random effects with RIL nested under plate; germination status was modeled as a fixed effect. Data for each light environment were fit separately. The variation due to plate, RIL, and residual variation is shown in Table 2. The relative variation explained by line means is an estimate of the broad-sense heritability. Best linear unbiased predictors (BLUPs) of RIL means under this model were used for QTL mapping; those lines showing poor germination had their means augmented by the coefficient for germination state. Note that these BLUPs of RIL means implicitly omit the plate effects, and this reduces the uncontrolled variation in the trait for QTL mapping. Calculations used the linear mixed effects (lme) function in the "nlme" package to R (PINHEIRO and BATES 2000 ). The genetic correlation between environments (r_GE) was calculated using cov₁₂/(_L1L2), where cov₁₂ is the covariance in line means, corrected for germination and plate effect, and _L1 and _L2 are square roots of among-line variances from the linear mixed-effects model (ROBERTSON 1959 ). Here BLUPs of RIL means used a model with RIL effects as fixed effects; this leads to unbiased estimates of cov₁₂ when the reduction in degrees of freedom is accounted for. The coefficient of genetic variation CV_G was calculated for each environment by dividing _L1 by the grand mean of line means and multiplying by 100. Confidence intervals for r_GE and CV_G were calculated, using a "leave one out" jackknife procedure on 161 lines (EFRON and TIBSHIRANI 1993 ).

The model for the dependence of hypocotyl length on germination status, RIL identity, and plate effects was

(1)

where y_ij are the measurements of hypocotyl length under a single light environment with i = 1, ... , 161 indexing the 161 RILs and j = 1, ... , n_i indexing the seedlings of the ith RIL. X_i = (1, germ_i), where germ_i = 1 if germination was poor and 0 otherwise. ß = (ß₀, ß₁)' is a column vector of two unknown coefficients; ß₀ is the mean under good germination and ß₁ is the increment due to poor germination. Z_i is a row vector of 161 elements all of which are zero except for the ith, which is 1. _RIL N(0, ²_RILI_161x161) is a column vector of 161 elements. W_i is a row vector of 14 elements, all of which are zero except for the kth, which is 1 when RIL i was incubated on plate k such that (i.e., lines "nest" within plates). _plate N(0, ²_plateI_14x14) is a column vector of 14 elements and _ij N(0, ²) is the residual and independent of other model terms. The phenotypic means are taken as and estimates are obtained by replacing the respective parameters with restricted maximum-likelihood (REML) estimates. These estimators are best linear unbiased, so phenotypic means based on _i are the BLUPs under this model.

QTL analysis:
The CvL RILs had been previously genotyped (ALONSO-BLANCO et al. 1998B ), using amplified fragment length polymorphisms (AFLP; VOS et al. 1995 ) and cleaved amplified polymorphic sequences (CAPS) markers (KONIECZNY and AUSUBEL 1993 ). Marker data and the genetic map were obtained from the web at the Nottingham Arabidopsis Stock Center (http://nasc.nott.ac.uk/). We used 163 of the 293 available markers that mapped to unique genetic loci and that had been genotyped on an average of 160 out of 162 RI lines. The BLUP data representing the line mean coefficients corrected for germination and plate effect were used as the phenotypic values for QTL mapping. The CIM (ZENG 1994 ) function of QTL Cartographer (http://statgen.ncsu.edu/qtlcart/cartographer.html) was used to map QTL. Background markers were chosen using the forward/backward stepwise multiple regression of SR map at a P value of 0.001. When SR map chose adjacent background markers in different environments, QTL models were tested where the same background marker was used in each environment to optimize the LOD score and minimize the LOD support interval. The numbers of background markers ranged from four to seven and are shown in Fig 3. Thresholds in each environment were set internally by running sets of 5000 permutations (DOERGE and CHURCHILL 1996 ). In each environment, a LOD score of 3.43–3.63 (depending on light environment) corresponded to an experiment-wise P value of 0.01 as determined by permutations. Instead of using seven different thresholds we used the largest one. A LOD of 2.8 would correspond to P = 0.05. We used a window size of 1 cM because hypocotyl length has high heritability, many QTL were in tight linkage, and many lines and many markers were used in this experiment. QTL maps with larger window sizes (1–10 cM) gave broader QTL peaks; however, the two LOD support intervals were equivalent to the 1-cM window size map. Generally the width of QTL peak was defined by the flanking markers, at various window sizes.

View larger version (15K): In this window In a new window Download PPT slide   Figure 1. Ler and Cvi seedlings. Pairs of 7-day-old Ler (left) and Cvi (right) seedlings grown in white, blue, red, far-red, GA, BRZ, and dark environments are shown.

View larger version (18K): In this window In a new window Download PPT slide   Figure 2. Distribution of CvL RILs. Histograms show the distributions of mean hypocotyl lengths in different light and hormone environments. The mean and standard deviations of Ler, Cvi, and phytochrome mutants are shown by arrows and lines, respectively.

View larger version (23K): In this window In a new window Download PPT slide   Figure 3. QTL map for light and hormone response. A QTL map generated by composite interval mapping shows the likelihood of odds (LOD) score on the y-axis along each chromosome on the x-axis. Each color represents a different environment. Markers are shown by diamonds along each chromosome. Background markers are shown as colored diamonds, with colors corresponding to the environment where they were included in the model. The dashed line is LOD 3.6, which represents a P = 0.01 threshold set by permutations. 2-LOD support intervals are shown as black bars below the x-axis.

Recombinant inbred line-by-environment testing:
The RILs are nested within plates in each light environment, so there is no "RIL-by-light environment-by-replicate" term to use as the error term for the "RIL-by-light environment" interaction. To test this interaction, two approaches were used. One was the sequential F-test of the RIL-by-light environment interaction term in a model including terms for line, light environment, plate, germination, and the germination-by-light environment interaction. In the absence of spatial or other effects on plates that increase between-RIL variation on a plate without also increasing "within RIL" variation, this is a powerful and appropriate test. The other test refers Tukey's "1 d.f. for interaction" statistic to its distribution under permutation of RIL interaction terms within plates; this yields a correct P value even in the presence of uncontrolled variation within RIL on a plate, but generally has limited power. For the first approach, Equation 1 and definitions above are extended as

(2)

where k indexes the light environment, , and with L_k being a 1 x 7 vector with a 1 in the kth element and zeroes elsewhere. _ijk N(0, ²_k) are independent residuals. Other terms on the right-hand side are suitably sized vectors of coefficients following the normalizations , summing i over 1, ... , 161 and k over 1, ... , 7. The mean square for the RIL-by-light environment interaction, _ikRIL·light, has 876 d.f. after accounting for the other terms and the F-statistic takes the residual mean square to be the error. The Tukey 1 d.f. for interaction statistic (SCHEFFE 1959 , section 4.8) decomposes the sum of the squared RIL-by-light environment terms into two parts,

where

(3)

The statistic is F = SS_G/(SS_res/d.f.), taking d.f. as 875. A permutation test can be constructed by permuting (_RIL·light)_7(j-1)+i with respect to the index j and calculating F under each permutation. Possible plate effects should be preserved in the reference distribution, so permutations of j must respect the assignment of RILs to plates. This type of permutation honors the normalizations above.

Multienvironment QTL mapping:
The multitrait CIM (mCIM) program JZmapqtl in QTL Cartographer was used (JIANG and ZENG 1995 ). mCIM mapping calculates a joint likelihood to detect QTL in multiple environments and a genotype-by-environment likelihood to determine if QTL are specific to certain environments. Light and hormone interactions were tested separately by including four light environments (white, blue, red, and far-red) in one analysis, white light and GA in a second analysis, and dark and BRZ in a third. A common set of background markers was used for each analysis (Fig 3, Table 4), to avoid problems of overparameterization. When SRmap chose adjacent background markers closer than 3 cM apart in different environments, a common marker was chosen that was selected in the majority of environments. An experiment-wise P = 0.01 threshold for both the joint likelihood (main effects) and G x E likelihood was determined separately for each analysis by performing 5000 permutations (DOERGE and CHURCHILL 1996 ; G x E LOD = 5.7 for four light environments and 3.6 for each of the hormone comparisons). These routines were provided by Chris Basten and are available upon request. The likelihood of the G x E test at each QTL was compared to the threshold to determine if that QTL showed a significant G x E interaction. This occurs when the estimated QTL effect is different from the joint effect in at least one of the tested environments.

Tests of epistasis:
We tested interactions between QTL and then performed an exhaustive search for pairwise marker interactions using BQTL. Each environment was analyzed separately and included main effect QTL as background markers (Fig 3, Table 4) and the covariate germination. A total of 43,956 pairwise tests were done between 296 loci. These included 163 actual markers and 133 pseudomarkers, at marker intervals <2 cM, creating an 2-cM walking speed. The test statistic is the LOD score difference between a model with only additive effects and one that included an epistatic term. Thresholds for statistical tests used a sequential permutation procedure (NETTLETON and DOERGE 2000 ) to ensure that enough permutations were performed to assert that each test attained (or failed at) P = 0.05. This is discussed in detail below. A total of 5000 permutations were done in the white light environment. Each permutation tested 43,956 pairs of markers. A LOD score of 4.6 corresponded to an experiment-wise threshold of P = 0.05 and was similar across light environments. The effect of the epistatic interaction is shown as 4i (Table 4), which represents the difference between the homotypic and heterotypic means (JUENGER et al. 2000 ). The interacting loci on chromosome 5 were also detected as the pair with the largest test statistic from the preliminary experiment in white light.

The maximum-likelihood method provides good power for detecting epistasis (KAO 2000 ) but requires more time for computation than linear methods for QTL mapping (KNAPP et al. 1990 ; HALEY and KNOTT 1992 ). To obtain correct P values with a model with covariates and additional loci, a permutation procedure is needed—further increasing the computational burden. Hybrid procedures for QTL mapping that are linear with respect to some, but not all, loci (JANSEN 1993 ; ZENG 1994 ) are widely used and provide some of the benefits of a full maximum-likelihood approach at a reduced computational cost. Such a hybrid approach and an associated permutation test for scanning for epistasis were implemented as follows. The log-likelihood used for scanning for epistasis is

(4)

where

(5)

y_i = _i, is the intercept, x_i is zero if the ith line had good germination and one otherwise with ß as the coefficient for germination, j and k index the parental lines of the alleles at loci l₁ and l₂ being tested for epistasis, z_j = 2(j - 1.5), z_k = 2(k - 1.5), ₁ and ₂ are the main effects at those alleles and ₁₂ is the epistatic effect, E_Z|M(z_l3, ... , z_ln|m_i) is the expectation of a vector of z's corresponding to n - 2 other loci given the marker information for subject i and is a vector of coefficients, _Z|M(Z = (z_j, z_k)|M = m_i) is the probability that the two loci are in states j and k given the marker information for subject i, ² is the residual variance, and (y; µ, ²) is the normal density function. The maximum-likelihood solution of (4) and (5) with respect to all of the coefficients is carried out. In addition, the maximum-likelihood solution under ₁₂ = 0 (no epistasis) is found. The log-likelihood ratio statistic X²(l₁, l₂) = 2(sup L(; y, x, l₁, l₂) - sup₀ L(₀; y, x, l₁, l₂)) is formed for all pairwise combinations of loci, l₁ = 1, ... , 295, l₂ = l₁ + 1, ... , 296, taking as the vector of free parameters and ₀ as that vector with ₁₂ fixed at zero. Statistical significance is ascertained via permutation testing using the "residual empirical threshold" method (DOERGE and CHURCHILL 1996 ). Predicted values and residuals are formed using a model in which ; i.e., only the germination effect and the effects of the n - 2 loci used in all models are included. A new vector of trait values is formed by adding the fitted values to a permutation of the residuals from that model. The log-likelihood ratio statistic is found as above for every combination of loci, and the maximum of these is found for each permutation. Attained P values are found as the fraction of permuted maxima that equals or exceeds X²(l₁, l₂). This produces genome-wide P values that are nominally correct under the null hypothesis of no epistasis anywhere on the genome. However, the randomness in the procedure is considered objectionable especially when claiming to have attained a fixed significance level. This can be overcome by following the recommendations of NETTLETON and DOERGE 2000 , requiring that the 95% confidence interval for P values exclude 0.05 and 0.01. Calculations were performed by the function "bqtl" available in the R package, BQTL (http://hacuna.ucsd.edu/bqtl and http://cran.r-project.org).

QTL effect estimation:
QTL effects were estimated by applying the method of maximum likelihood to the QTL model (KAO 2000 ). This model included main effect QTL identified by CIM, significant epistatic loci, and the covariate germination. QTL effects are estimated using a likelihood analogous to (4) and (5). Since the number of loci is manageably small and there are only a few models to be fit, no use of linearized terms E_Z|M is needed, and full maximum-likelihood fitting is used. The modifications required are to replace µ_ijk by where j₁, ... , j_K index K loci included in the QTL model, L epistatic terms are included with r_l and s_l indexing the main effects upon which they depend. Obvious modifications are made to the summation and to _Z|M, the joint allele state probabilities, in (4). These calculations were also performed by the function bqtl available in the R package. The additive effect is shown as 2a, the difference between homozygous classes. The percentage of change caused by a single QTL is the effect in millimeters (2a) divided by the average RIL hypocotyl length for that environment (Table 4) multiplied by 100. The percentage of variance explained for each QTL was determined by squaring the coefficient (a) and by dividing the residual variance in a null model without genetic loci (²_rN). Total variance explained was determined as , where (²_rG) is the residual variance in the model with all genetic terms.

Near isogenic lines:
The LIGHT1 near isogenic line (NIL) was derived from line N42 created to map EDI (ALONSO-BLANCO et al. 1998A ). N42 contains only 35 cM of Cvi from the top of chromosome 1 in a Ler background determined by selection against other markers throughout the rest of the genome (gift from Carlos Alonso-Blanco and Maarten Koornneef). N42 was crossed to Ler, and F₂ plants that had the Ler allele at EDI and were heterozygous at marker g2395 were selected. The LIGHT1 NIL is an F₃ line (F₃-77), derived by selfing, that is heterozygous for the AFLP marker GD143L-Col and the CAPS marker m235 at 22 and 34 cM on chromosome 1, respectively. After hypocotyl lengths in white light were measured, individual seedlings were genotyped at g2395 as a marker for the LIGHT1 QTL. The LIGHT2 and HYP2 NILs were made by crossing the RIL CvL 125 to Ler. The CvL125 x Ler F₂ cross segregates Cvi DNA from 34 to 63 cM on chromosome 2 containing the PHYB and ERECTA loci, as well as from 84 to 107 cM on chromosome 5. For LIGHT2, 100 F₂ plants were measured in white light and genotyped at PHYB and GPA1 as markers for the LIGHT2 QTL. Interval mapping was done between these two markers. For HYP2, F₂ plants were measured in the far-red and BRZ environments and genotyped at BAS1 (NEFF et al. 1999 ). The additive and dominance effects of each marker were assessed using linear regression.

Genotyping:
Genotyping was done using CAPS markers. GPA1, g2395, and m235 information was from TAIR (http://www.arabidopsis.org). PHYB oligonucleotide primers were 5' CTGCTGACGAGAACACG 3' and 5' GAAAGTTGGCTTAAATGG 3'; Ler has a PstI restriction site absent from Cvi. BAS1 oligonucleotide primers were 5' ATATAATAGGCGTTCATCTAATG 3' and 5' CTCGGAGTTCGTACATG 3'; Cvi has an AccI restriction site absent in Ler. The BAS1 marker is 170 kb from the ERECTA gene, on the same bacterial artificial chromosome (BAC) T9J22.

Data and statistical routines are available on our web page (http://naturalvariation.org).

	RESULTS

TOP ABSTRACT MATERIALS AND METHODS RESULTS DISCUSSION LITERATURE CITED

Genetic variation in CvL RILs:
Light quality (wavelength) and light quantity (fluence rate) affect hypocotyl length. We chose wavelengths of light that corresponded to the absorption maximum for the red and far-red absorbing forms of phytochrome and blue for cryptochrome to dissect the light responses controlled by individual photoreceptor pathways.

We then measured hypocotyl length of Cvi and Ler parental lines, reciprocal F₁ hybrids, 162 Cvi/Ler RILs, and phytochrome mutants in seven different environments. The results are summarized in Table 1. In total, 17,787 hypocotyl length measurements made up the data set. Fig 1 shows the phenotype of the parental lines after 7 days of growth under the different experimental conditions. Cvi was generally less sensitive to light with a longer hypocotyl than the common lab strain Ler (t-test P < 0.05 all environments). Hypocotyl length differences were dramatic in white, blue, red, GA, and BRZ environments, but less so in the far-red and dark environments. F₁ hybrids had long hypocotyls and were generally similar to the Cvi parent (Table 1). The difference between reciprocal crosses is likely due to the maternal effect of the erecta mutation (ALONSO-BLANCO et al. 1999 ) as crosses using Ler as females were generally shorter. The distribution of mean hypocotyl lengths among CvL RILs in each environment is broad and continuous, typical of polygenic traits (Fig 2). Transgression was also observed in each environment. The phyB-5 null mutant has a very severe defect in light signaling in the white and red light environments. Variation of this magnitude was not expected in natural populations. Surprisingly, some transgressive RILs were found to have a hypocotyl length equal to phyB-5 in white light, and beyond that of phyB-5 in the GA environment. This may be due to the action of several genes and illustrated the magnitude of natural variation in this trait. In comparison, variation in far-red light was not as dramatic as that caused by a phyA null mutant. Nevertheless, the large amount of transgression seen in the far-red environment showed that there was considerable genetic variation segregating, even though the parental lines did not differ by much.

The genetic coefficient of variation (CV_G), a unitless measure of genetic variability (HOULE 1992 ), was 20% of the mean for each environment except dark, where it was only 10% of the mean. The variance explained by RILs is an estimate of broad-sense heritability (Table 2). This ranged from 65 to 77% across environments except dark, which was lower (38%) due to a relatively large environmental component. This low level of background variation in the dark environment indicates that the variation seen in other environments was due largely to the specific effects of light and hormone treatments. Tests for RIL-by-environment interactions (see MATERIALS AND METHODS) were highly significant (Table 2).

Response is correlated across environments:
We estimated the cross-environment genetic correlation (r_GE) between environments and found significant correlations between responses in all light and hormone conditions (Table 3). This indicates that much of the genetic control is shared among environments but that it is not identical. The highest correlation was between white and GA, . In contrast, the correlation between dark and BRZ is 0.69. Differences in genetic correlations between the hormone environments may be due to true differences in the hormone response. Alternatively, differences in genetic correlations between these environments may reflect differences caused by adding additional GA hormone in one environment and using an inhibitor to remove BR hormone in another. Furthermore differences may reflect variation in endogenous levels of GA and BR levels.

Quantitative trait loci:
We first mapped QTL for each environment independently, using different background markers for each trait. The LOD score map is shown for each chromosome in Fig 3. QTL with LOD scores >3.6 (P < 0.01 threshold set by permutations) were considered significant. We chose a higher threshold because the many more QTL detected at P < 0.05 had rather small effects. A summary of the significant QTL including their effects is shown in Table 4. The effects were estimated by including significant markers and germination as covariates, using a maximum-likelihood approach that included main and epistatic terms (BQTL, see MATERIALS AND METHODS).

We named the QTL according to the environment in which they were detected and the chromosome to which they mapped (Fig 3). Three QTL mapped to chromosome 1. DARK1 maps to the top (0–7 cM) and was detected only in the dark environment. LIGHT1 was detected in all light environments and is one of the major QTL, explaining 22% of the phenotypic variance (_p) in white light. LIGHT1 had the highest LOD score of all the QTL in the white, blue, and red environments. The effect of LIGHT1 was similar in white, blue, and red environments but was weaker in the far-red environment (Table 4). HYPOCOTYL1 (HYP1) contributes to r_GE since it was detected in all environments; however, the LOD score was below the threshold in the dark environment (Fig 3). The Ler allele of the HYP1 QTL increased hypocotyl length and may explain the transgression seen in many environments. LIGHT2, a major QTL on chromosome 2 (32–40 cM), was detected in white, red, and GA environments. The largest effect of LIGHT2 was seen in the GA environment where homozygous allele substitutions caused 1.3 mm change in length and explained 22% of the phenotypic variance. Another QTL on chromosome 2, HYPOCOTYL2 (HYP2), mapped to the ERECTA locus and was detected in the blue, far-red, BRZ, and dark environments. A third QTL, FARRED2, was detected only in the far-red environment. On chromosome 3 we detected only one QTL, RED3, where again the Ler allele increases hypocotyl length. Chromosome 4 contained four significant QTL that were specific to single environments, BRZ4, WHITE4, BLUE4, and FARRED4. Last, chromosome 5 contained one QTL that was specific to the blue environment, BLUE5 (0–3 cM). Taken together, multiple QTL were detected across the seven environments that explain up to 61% of the variation in light response (Table 4). A surprisingly large amount of linkage was seen between QTL (Fig 3). The high genetic correlations among environments can be explained in part by QTL detected in multiple environments as well as linked QTL whose effects are specific to certain environments.

Genotype-by-environment interaction:
To understand how the natural variation seen at these light response QTL is controlled across different environments we used mCIM (JIANG and ZENG 1995 ). A genome scan, using common background markers, was performed in a single joint analysis using white, blue, red, and far-red environments as four traits. All QTL detected using single-environment CIM mapping were confirmed, using mCIM mapping (joint likelihood exceeded the threshold), with the exception of light QTL on chromosome 4 (BLUE4, WHITE4, and FARRED4). Loci where the G x E likelihood exceeded the significance threshold (P = 0.01 by permutations) are shown in italics in Table 4. As expected, the QTL unique to single environments or to a subset of environments, DARK1, FARRED2, RED3, BLUE5, LIGHT2, and HYP2, showed significant G x E. LIGHT1 also showed significant G x E, even though it was detected by single-trait analysis in all light environments, reflecting the fact that LIGHT1 has a larger effect in white, blue, and red than in the far-red environment. As expected, the HYP1 QTL did not show G x E.

To assess the effects of the hormone GA, a multitrait analysis was conducted, including the white and GA environments. The only QTL that showed significant G x E was LIGHT2, due to the difference in effects at this locus between the GA and white environments. In the GA environment Cvi alleles increased the phenotype by 1.3 mm, whereas in white light, they caused only a 0.7 mm increase (Table 4). However, the effect of LIGHT2, expressed as percentage of change in length, is similar between the GA and white environments. The effect of the BR inhibitor BRZ was investigated in the same way using mCIM by including dark and BRZ environments as traits. As expected the unique loci DARK1 and BRZ4 showed significant G x E as they were only detected in a single environment. HYP2 did not show G x E as it has a similar additive effect in dark and BRZ environments, 1.3 and 1.5 mm respectively. However, the difference in effects expressed as percentage of change in length is dramatic, 8% in dark and 20% in the BRZ environment (Table 4).

Epistatic interactions:
We performed a genome scan for pairwise interactions. Each environment was analyzed separately using models that included specific background markers (see MATERIALS AND METHODS). Again an appropriate significance threshold was set by permutations to account for the type of population, any segregation distortion, and the large number of tests. A single epistatic pair was identified in the white light environment that was significant under this stringent criterion (-1.4 mm in white light, Table 4). In all other environments, this pair had an effect (-0.8–1.5 mm) similar to that seen in white light and was point-wise significant (P < 0.007). These epistatic loci are linked on chromosome 5, separated by 15 cM. Forty-four of 162 RILs fall into this recombinant class. The negative interaction coefficient indicates that Ler and Cvi allele classes act cooperatively in this case. Fig 4 depicts a genetic model that illustrates the statistical epistatic interaction. Apparently, one of these markers acts as a "controller locus." There is an allele-specific interaction that is the basis for the significant epistatic term in the statistical model. When BF.269C is Ler, allele changes at GH.117C have no effect, but when BF.269C is Cvi, allele changes at GH.117C have a large effect. Thus, BF.269C could act as a controller locus and GH.117C as the "effector locus." By reversing the order of the middle genotypes in Fig 4, GH.117C could be the controller locus governing the direction of the effect of BF.269C. These two genetic models (Fig 4) are equally plausible interpretations of the statistical interaction.

View larger version (18K): In this window In a new window Download PPT slide   Figure 4. Epistatic interaction. A genetic model is shown of the significant epistatic interaction between two loci on chromosome 5, in the white light environment. BF.269C is shown as a controller locus and GH.117C is shown as the effector locus. Other genetic models are possible.

Near isogenic lines:
To confirm and better characterize the major QTL, we introgressed them into an isogenic Ler background. NIL-QTL effects were measured in segregating progeny of a single line to minimize seed variation between different mother plants (Fig 5). The LIGHT1 NIL is heterozygous and segregates the LIGHT1 QTL. The effect of LIGHT1 in an isogenic background confirms the prediction by QTL analysis in the RIL population and also shows that the gene is unlikely to act dominantly . The effects of LIGHT2 and HYP2 QTL were investigated in an isogenic Ler background (see MATERIALS AND METHODS). Surprisingly, the less sensitive Cvi allele of LIGHT2 was dominant . The effect of the HYP2 QTL was confirmed in two environments using CvL125 x Ler F₂ seedlings. In the far-red environment HYP2 showed no evidence of a dominant effect , whereas in the BRZ environment the Cvi allele of HYP2 was clearly dominant .

View larger version (48K): In this window In a new window Download PPT slide   Figure 5. Near isogenic lines. LIGHT1, LIGHT2, and HYP2 NILs show the effect of a single QTL in segregating populations. Plants were grown in the indicated environment, measured, and genotyped at the marker g2395 for LIGHT1, PHYB for LIGHT2, or BAS1 for HYP2; L, Ler; H, heterozygote; C, Cvi. The QTL effect (2a) and dominance/additive ratio were estimated using linear regression. n, the number of seedlings genotyped in each class. Error bars represent 95% confidence intervals. The WHITE* environment has a reduced light fluence rate of 20 µE m-2 sec-1.

ERECTA and HYP2:
The erecta mutation segregating in these lines has been shown to have many pleiotropic effects in Ler (TORII et al. 1996 ). Since the HYP2 QTL spans the ERECTA locus, we wanted to test whether it might correspond to the erecta mutation. In the BRZ environment the Ler allele of HYP2 acts recessively as does the loss-of-function erecta mutation (Fig 5). In contrast, the HYP2 QTL seems to act additively in the far-red environment. HYP2 also has an effect in the blue environment (Fig 3, Table 4). We used two alleles of the erecta mutation in different backgrounds to determine its effect on hypocotyl length. The Lan-1 (La ERECTA) line is isogenic to Ler (La erecta) except that it does not contain the erecta mutation (ALONSO-BLANCO and KOORNNEEF 2000 ). The er-2 mutation was isolated in the Columbia background. We measured the four genotypes Col erecta, La erecta, Col ERECTA, La ERECTA on different concentrations of BRZ and in blue and far-red light (Fig 6). In both Col and La genetic backgrounds erecta causes a shortening of hypocotyl length in the dark and at different concentrations of BRZ. This shortening seemed independent of BRZ concentration as erecta mutant lines were 0.8 mm shorter at all inhibitor concentrations (Fig 6A), consistent with the HYP2 QTL not showing a G x E interaction with BRZ (Table 4). Scale remains a complicating issue; in terms of percentage of change erecta has a much larger effect at higher inhibitor concentrations. In blue light erecta also has an effect; loss-of-function mutations are 1.0 mm (P = 0.002) shorter in both genetic backgrounds (Fig 6B). In far-red light, however, we did not detect a significant effect of erecta (P = 0.56). Additionally, the erecta effect in blue was significantly different (P < 0.01) from that in far-red (Fig 6B). We conclude that the effect of HYP2 in the blue, BRZ, and dark environments is caused by the erecta mutation, and another tightly linked gene must be responsible for the effect of HYP2 in far-red light.

View larger version (32K): In this window In a new window Download PPT slide   Figure 6. Erecta effect. (A) BRZ dose response curve shows that erecta mutations in both the Col and La backgrounds reduce hypocotyl length equally across all inhibitor concentrations. The x-axis is on a log scale. (B) The erecta mutation causes a 1.0-mm decrease in hypocotyl length in blue light in both genetic backgrounds; however, no significant effect of erecta in far-red light was observed. The erecta effect is significantly different in blue and far-red light.

PHYTOCHROME B is a candidate for LIGHT2:
Arabidopsis phyB mutants have elongated hypocotyls in the white and red environments but not in the blue or far-red environments (Table 1). phyB mutants are also hypersensitive to GA (REED et al. 1996 ). The phenotype of the LIGHT2 QTL matches that of phyB (Table 4) and LIGHT2 maps very close to PHYB (Fig 3). Segregating LIGHT2 NIL progeny (Fig 5) were also genotyped at GPA1, a marker 14 cM distal to PHYB. Interval mapping using the PHYB and GPA1 markers and 100 CvL125 x Ler F₂ plants showed that the likelihood and effect were greatest at PHYB, indicating that LIGHT2 was closer to PHYB than GPA1. phyB loss-of-function mutations are recessive in these conditions; however, the less functional Cvi allele of LIGHT2 is dominant (Fig 5). The Cvi allele of LIGHT2 may therefore represent a dominant negative polymorphism in PHYB; however, 200 other genes are in the 8-cM LIGHT2 QTL interval.

	DISCUSSION

TOP ABSTRACT MATERIALS AND METHODS RESULTS DISCUSSION LITERATURE CITED

We have identified 12 QTL that correspond to both candidate and unknown genes. Several QTL map to positions where no published candidate genes or photomorphogenic mutations map, such as HYP1, RED3, WHITE4, BLUE4, FARRED4, and BLUE5. The major QTL BRZ4 also describes a novel locus and has an effect that is large enough to make positional cloning a possibility. If the molecular nature of BRZ4 can be identified it will uncover a new gene involved in brassinosteroid signaling and may help explain variation in hormone response among Arabidopsis accessions. In contrast, the confidence limits of the DARK1 QTL overlap that of a Cvi/Ler QTL affecting seed quality (ALONSO-BLANCO et al. 1999 ). Cvi alleles at this locus result in fewer seeds per fruit that are larger and heavier. Consequently more seed reserves may allow for an increased hypocotyl length in the dark. Cvi alleles also increase seed storability at this locus (BENTSINK et al. 2000 ). DARK1 may be allelic to the QTL for seed quality traits. The FARRED2 QTL maps to a region including the SUPPRESSOR OF PHYA1 (SPA1) locus (HOECKER et al. 1998 , HOECKER et al. 1999 ).

LIGHT1 represents a major locus responsible for light response variation between Ler and Cvi across multiple light environments. Confidence limits of a major QTL affecting circadian rhythm, ESPRESSO, overlap with LIGHT1 (SWARUP et al. 1999 ). This region also overlaps a minor QTL affecting flowering time (ALONSO-BLANCO et al. 1998A ). The pleiotropic effects at the LIGHT1 locus may be due to the action of more than one gene. However, several Arabidopsis mutants are known to affect hypocotyl length, circadian rhythm, and flowering time such as LHY and CCA1 (SCHAFFER et al. 1998 ; WANG and TOBIN 1998 ), suggesting that there may be a single gene responsible for the effects in the LIGHT1 region as well. The cloning of LIGHT1 may identify a new and vital signaling component, as well as provide clues about the mechanisms of light response adaptation in natural populations.

Both the phenotype and map position of the LIGHT2 QTL indicate PHYB as a candidate gene. We have sequenced PHYB from Cvi and Ler and found considerable nucleotide variation in the promoter as well as synonymous and replacement changes in the coding region (J. N. MALOOF, J. LUTES, J. O. BOREVITZ, D. WEIGEL and J. CHORY, unpublished data). It is surprising that a photoreceptor may be a major light QTL, as loss-of-function phyB mutations have dramatic, deleterious effects throughout development. phyB null mutations also have a large effect on flowering time (REED et al. 1993 ). However, Ler/Cvi flowering time QTL do not map to PHYB (ALONSO-BLANCO et al. 1998A ). Thus, if PHYB is LIGHT2, this natural allele must affect only a subset of downstream processes controlled by PHYB. Further fine mapping of the LIGHT2 QTL, as well as transgenic experiments with Cvi and Ler alleles of PHYB, are needed to determine if LIGHT2 is PHYB.

The HYP2 locus exemplifies the difficulty in distinguishing between a single gene with effects in multiple environments and multiple genes in tight linkage with effects in specific environments. HYP2 has effects in blue, far-red, BRZ, and dark and contributes to the high correlation between these environments (Table 3). The effect of HYP2 in the blue and BRZ and dark environments is due to erecta (Fig 6A and Fig B). The far-red phenotype of HYP2, however, is likely not due to erecta (Fig 5 and Fig 6B) and thus represents variation at another tightly linked gene. QTL analysis of the VLFR in the Ler/Col RILs identified two QTL, VLF1 and VLF2 (YANOVSKY et al. 1997 ). VLF1 affects cotyledon unfolding under short pulses of far-red light. The confidence limits of VLF1 and HYP2 overlap and they may be allelic. Differences in phenotypes between VLF1 and HYP2 may be due to differences between the Col and Cvi alleles at VLF1/HYP2, to other background effects, or to different genes responsible for VLF1 and HYP2 QTL.

Identifying epistatic interactions is a powerful advantage of QTL mapping over traditional approaches. The interacting loci on chromosome 5 together have an effect equal to that of the major light response QTL (Table 4), indicating that epistasis does account for some of the variation in hypocotyl length. Flowering time experiments have identified epistasis as an important factor in quantitative variation, with one interaction explaining up to 31% of the phenotypic variance (ALONSO-BLANCO et al. 1998A ). The synergistic effect of FRI and FLC on late flowering, which is suppressible by vernalization, is also well established (LEE and AMASINO 1995 ). Approaches such as ours to detect epistasis may identify smaller but significant interactions that may be quite informative when candidate genes are considered. Others have also tested all markers for pairwise interactions and identified significant marker pairs that do not have large main effects on their own (SHOOK and JOHNSON 1999 ; SHIMOMURA et al. 2001 ).

In conclusion, we have mapped 12 highly significant hypocotyl length light and hormone response QTL from the Ler/Cvi RIL population. Some QTL are unique to specific environments and have genotype-by-environment interactions, while others have effects in multiple environments. Fig 7 depicts a model in which QTL are placed into a genetic framework according to the environments in which they have phenotypes. Individual QTL can be crossed to other Arabidopsis photomorphogenic and hormone mutants and be integrated with the known signal transduction network (NEFF et al. 2000 ). BLUE4 and BLUE5 are specific to blue light and likely act downstream of the cryptochrome photoreceptors (Fig 7). The far-red light-specific effects of HYP2, FARRED2, and FARRED4 suggest that they transduce signals from PHYA, the major photoreceptor in far-red light. The unique red light effect of RED3 makes it a PHYB pathway candidate, since PHYB is the major photoreceptor in red light (Fig 7). The effect of BRZ4 is specific to the BRZ environment and therefore may represent variation in brassinosteroid signaling or biosynthesis. The DARK1 QTL affects hypocotyl length; however, its effect is overridden by light signals. The HYP1 QTL may control length through a mechanism that is independent of light signals, possibly controlling cell size or cell number. LIGHT1 may act downstream of multiple light and/or hormone signaling pathways and may serve to integrate multiple environmental cues. Finally LIGHT2 may represent variation in a photoreceptor at the top of the light signaling hierarchy.

View larger version (17K): In this window In a new window Download PPT slide   Figure 7. QTL framework. A potential genetic pathway showing how light response QTL could act in different environments to control hypocotyl length. A strict gene order of action is not implied.

	FOOTNOTES

¹ These authors contributed equally to this work.

	ACKNOWLEDGMENTS

We thank Ben Sadrian for help with hypocotyl measurements; Chris Basten and R. Doerge for help with QTL Cartographer; Josh Kohn, Jennifer Nemhauser, Marcelo Yanovsky, Pablo Cerdan, and José Dinneny for discussion and advice on the manuscript; Ming Ji for discussion on the experimental design and analysis; and Carlos Alonso-Blanco and Maarten Koornneef for seeds and discussion. Seeds were obtained from the Arabidopsis Biological Resource Center at Ohio State University, which is funded by the National Science Foundation (NSF). The joint program in quantitative genetics in the Weigel and Chory laboratories is supported by National Institutes of Health (NIH) training grant GM08666 (J.O.B.), by a Helen Hay Whitney Fellowship (J.M.N.), an NSF Predoctoral Fellowship (J.D.W.), funds from the Howard Hughes Medical Institute (HHMI) and NIH (GM52413) to J.C., by an REU supplement to NSF grant IBN-9723818 to D.W., and by a grant from Torrey Mesa Research Institute/Syngenta to D.W. J.C. is an Associate Investigator of the HHMI. Charles Berry is funded by NIH grant AR40770 and Tadao Asami by a Bio-architect Research Program. D.W. is a director of the Max Planck Institute.

Manuscript received March 9, 2001; Accepted for publication November 8, 2001.

	LITERATURE CITED

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