ORIGINAL PAPER

Dissecting apple tree architecture into genetic, ontogeneticand environmental effects: QTL mapping

Vincent Segura & Charles-Eric Durel & Evelyne Costes

Received: 1 February 2008 /Revised: 2 July 2008 /Accepted: 1 September 2008 / Published online: 1 November 2008# Springer-Verlag 2008

Abstract The present study aimed to dissect tree architec-tural plasticity into genetic, ontogenetic and environmentaleffects over the first 4 years of growth of an apple F1progeny by means of quantitative traits loci (QTL) map-ping. Both growth and branching processes were pheno-typed on the consecutive annual shoots of different axeswithin a tree. For each studied trait, predicted values (bestlinear unbiased predictors, BLUPs) of the genotypic (G)effect or its interaction with tree age (G×A) and climaticyear (G×Y) were extracted from mixed linear models ofrepeated data. These BLUPs, which are independent fromautocorrelations between repeated measurements, were usedfor QTL mapping. QTL detection power was improved bythis two-step approach. For each architectural process,numerous QTLs were detected and some particularlyinteresting co-localised in common genomic regions, forinternode lengthening, top diameter, and number andpercentage of axillary shoots. When several QTLs weredetected for a given trait, global models were estimated,which explained a maximum of 40% of the total variance for

both internode length and top diameter and 28% forbranching. QTLs detected for BLUPs of G×Y effects wereinterpreted as resulting from the interaction between geneticmaximal potential of growth and climatic factors, whilethose for G×A effects were interpreted in relation to treeontogeny. Most of the latter ones were found to beconcomitant with key development stages during which thetrait average started to decrease, but with different magni-tudes depending on genotype.

Keywords Malus x domestica Borkh. . Growth . BranchingRepeated data . Mixed linear model

Introduction

Plant growth and development vary as a function ofdeterministic and opportunistic factors and their interactions(Hallé et al. 1978). Whereas deterministic or genetic factorspredispose a plant toward a specific architecture, theopportunistic components cause its modification in re-sponse to the environment. Considering a perennial cropsuch as a tree, environmental factors that affect its growthand development are supplemented by age-induced mor-phological changes throughout its life. Even though treestructure often results from repetitive processes (White1979), the successive growth units are not entirely similarbecause of morphogenetic gradients during tree ontogeny(Barthélémy et al. 1997; Costes et al. 2003; Durand et al.2005; Renton et al. 2006). The observed tree phenotype isthus plastic and complex, since it results from genetic,environmental, and ontogenetic factors and their interactions.

Understanding the genetic mechanisms underlying thisphenotypic plasticity is of great interest in plant science. Tothis end, the mapping of quantitative traits loci (QTL) is akey tool that has been widely used to detect the genomic

Tree Genetics & Genomes (2009) 5:165–179DOI 10.1007/s11295-008-0181-x

Communicated by A. Dandekar

Electronic supplementary material The online version of this article(doi:10.1007/s11295-008-0181-x) contains supplementary material,which is available to authorized users.

V. Segura : E. Costes (*)INRA, UMR DAP, INRA–Montpellier SupAgro–CIRAD–Université Montpellier II,Equipe Architecture et Fonctionnement des Espèces Fruitières,2 place P. Viala,34060 Montpellier Cedex 1, Francee-mail: costes@supagro.inra.fr

C.-E. DurelINRA, UMR GenHort, INRA–INH–Université d’Angers,42 rue G. Morel, BP 57,49071 Beaucouzé Cedex, France

regions that control variations in quantitative traits. Overthe last decade, many studies have used this approach toanalyse the genetic determinism of tree growth and branch-ing in forest (Bradshaw-Jr and Stettler 1995; Plomion et al.1996; Wu and Stettler 1996, 1998; Wu 1998; Scotti-Saintagne et al. 2004) and fruit species such as apple(Conner et al. 1998; Liebhard et al. 2003; Kenis andKeulemans 2007; Segura et al. 2007). Several of thesestudies were carried out in multiple locations and/or duringseveral years of growth, and QTL analyses were performedindependently at each location or in each year of growth. Inthis case, the strategy consisted of looking for co-localisationof the QTLs detected in each analysis. Such co-localisationscould also be statistically tested by multi-trait QTL analysisinitially proposed for analysing pleiotropic effects (Jiang andZeng 1995; Korol et al. 1995; Mangin et al. 1998). Thisapproach would appear to be suitable for detecting “stable”QTLs with regard to environmental and ontogenetic effects.However, these previous studies showed that many QTLswere not common to the locations or years studied, and thechallenge is therefore to identify among these “unstable”QTLs those specific to an ontogenetic and/or an environ-mental effect. A first attempt in the analysis of ontogeneticeffects was reached by introducing an interaction termbetween genotype and age in the QTL mapping model(Verhaegen et al. 1997). However, neither autocorrelationsbetween measurements performed throughout developmentnor environmental effects were accounted for in such anapproach. More recently, Ma, Wu and colleagues proposed amethodology, called functional mapping, to detect QTLsinvolved in growth trajectories (Ma et al. 2002, 2004; Wu etal. 2004; Wu and Lin 2006). This approach based on growthmodels integrates autocorrelations between repeated mea-surements but does not allow a clear distinction betweenstable and unstable QTLs throughout tree life nor todistinguish among unstable QTLs those related to plantontogeny from those related to environmental effects.

Moreover, a clear characterisation of ontogenetic andenvironmental effects would necessitate unravelling theconsecutive years of growth and climatic years, which areconfounded in most experiments in tree species. Theseeffects might be dissected by measuring trees over severalyears of growth in a multi-locality design. However, fewgenetic studies in perennial crops have taken advantage ofmulti-locality designs, probably because they are costly andtime consuming. As an alternative, Loughin (2006) pro-posed a specific design, called a staggered-start design, inwhich plants are planted in the same field but at least 1 yearapart. Such a design appears suitable for perennial crops,since their growth years occur during different climaticyears, making the dissection of ontogenetic and climaticeffects possible. Therefore, instead of analysing eachgrowth year separately in each climatic year, data can be

gathered to form a sequence of repeated measures assessedon the same trees and analysed through mixed linearmodels of repeated data. This type of model is required toaccount for variance heterogeneity and autocorrelationsbetween repeated measures (Littell et al. 2000). In aprevious study, we applied this methodology to growthand branching traits assessed over the first 4 years ofgrowth in apple hybrids planted in a staggered-start design(Segura et al. 2008). In addition to temporal repeated datastemming from successive years of growth assessments,spatial repeated data were also considered to account formeasurements made on several types of axis within thetrees. Measurements on several axis types within a treewere assumed to provide additional information on onto-genetic effects (Costes et al. 2003; Segura et al. 2008). Inour previous study, a significant genotypic effect was foundfor most traits indicating the existence of stable geneticdeterminisms with regard to tree ontogeny and climaticcondition. However, some traits showed significant inter-actions between genotype and age and genotype andclimatic year, suggesting that specific genetic factors actdifferentially during tree ontogeny and depending onclimatic effects. To further investigate this genetic deter-minism, the present study proposes a QTL mappingapproach based on the best linear unbiased predictors(BLUPs) of the genotypic effect and its interaction withtree age and climatic year estimated from the mixed linearmodels of repeated measures previously detailed (Segura etal. 2008). Together, these two papers propose a two-stepmethod for dissecting phenotypic plasticity into genetic,ontogenetic, and environmental effects.

Materials and methods

Full details of plant material, experimental design, measure-ments, and repeated data mixed linear modelling are givenin Segura et al. (2008).

Plant material, experimental design and phenotyping

The progeny studied was derived from a ‘Starkrimson’ בGranny Smith’ cross and composed of 125 genotypes. Theoffspring studied was in a staggered-start design (Loughin2006): (1) a randomly selected subsample of 50 seedlingswas replicated three times and planted in 2003 at theMelgueil INRA Montpellier experimental station in ten-treemicroplots; (2) 123 seedlings from the whole progeny (twohad died) were replicated twice and planted in 2004 at thesame site in six-tree microplots. Microplots compriseddistinct genotypes and were randomly scattered throughoutthe field. Replicates were in both cases obtained by graftingonto ‘Pajam 1’ rootstock. Trees were observed from 2004

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to 2007, i.e. the first 4 and 3 years of growth were assessedin trees planted in 2003 and 2004, respectively. In bothcases, observations were performed on the trunk, on twolong sylleptic axillary shoots (LSAS) and on two longproleptic axillary shoots (LPAS) when present. LSAS grewon the first annual shoots (AS) of the trunk during the firstyear of growth, while LPAS also grew on the first AS of thetrunk but 1 year later (during the second year of growth).The following traits ordered by architectural process wereobtained from the measurements performed on successiveAS (Fig. 1): (1) primary growth-length (L), internodenumber (INN), length of the longest internode (INLmax)and mean internode length (INL=L/INN); (2) secondarygrowth-bottom diameter (Bdia), top diameter (Tdia) andbottom diameter increment (ΔBdia) and (3) branching-number of axillary shoots (Br), number of latent buds(latents=INN-Br) and percentage of branching nodes (%Br=Br/INN).

Repeated data mixed linear modelling

To account for within-tree variability, data were analysedby considering both each axis type separately (i.e. trunk,LSAS and LPAS) and all axis types together at a whole-treescale. First, modelling was performed only with the 50genotypes present in both designs. Second, all the datafrom the design planted in 2004 (123 genotypes) wereincluded in the analysis. Consistency between models onbalanced (i.e. 50 genotypes) and unbalanced (i.e. 123genotypes) datasets was checked in order to further use

only the output of models on unbalanced data for QTLmapping. All datasets were analysed by mixed linearmodels of repeated data that included tree age (A) andyear (Y) considered as fixed effects, genotype (G),interactions between genotype and tree age (G×A), andgenotype and year (G×Y) considered as random effects.The term “repeated data” refers to multiple measurementstaken in a sequence on the same experimental unit. In ourprevious study (Segura et al. 2008), we considered twokinds of repeated data: (1) a temporal repetition for tree age(whatever the scale or the axis type) and (2) a spatialrepetition for the axes (considering repetitions of LSAS andLPAS either separately or together with the trunk on thewhole tree scale). Repeated data analysis consisted inmodelling residuals of mixed linear models using severalcovariance structures to account for both variance hetero-geneity and covariance between the repeated data. For eachtrait, axis and scale, a model selection was performedamong various covariance structures and effects included,on the basis of the Bayes Schwarz Information Criterion(BIC) minimisation. Covariance structures, effects selectedand their significance were compared between datasets thatcomprised 50 and 123 genotypes. In most cases, the modelsselected were similar enough to consider those used on the123 genotypes as acceptable despite unbalanced data. Foreach trait, when G, G×A and/or G×Y effects weresignificant in the selected model (Table 1), their best linearunbiased predictors (BLUPs) were computed. A uniqueBLUP was computed for the G effect and was consideredas independent of tree age or climatic year. This BLUP was

Fig. 1 Schematic representationof measurements made in4-year-old apple shoots. For traitabbreviation, see Table 1

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denoted by the trait name and the axis or scale considered,e.g. L_tree is the BLUP of the G effect in the modelcomputed for length of AS on the whole tree scale. ForG×A and G×Y interaction effects, the correspondingBLUPs were computed for each age and climatic yearconsidered separately. In this case, the BLUPs weredenoted as previously with trait name and the axis or scaleconsidered, but appending tree age (1 to 3) or climatic year(2004 to 2006). For example, INL1_tree, INL2_tree andINL3_tree are the BLUPs for the G×A effect in the modelcomputed for mean internode length of AS on the wholetree scale and at ages 1, 2 and 3, respectively, andINLmax04_tree, INLmax05_tree and INLmax06_tree arethe BLUPs for the G×Y effect in the model computed for

length of the longest internode of AS on the whole treescale and for climatic years 2004, 2005 and 2006,respectively. It is noteworthy that as age 4 and the 2003climatic year concerned only the 50 genotypes in the designplanted in 2003, no BLUP could be computed for the 123genotypes concerned by this age and climatic year. BLUPswere computed using the restricted maximum likelihoodmethod in the mixed procedure of SAS® v.8 software (SASInstitute 2000).

QTL detection and mapping

Both single parental genetic linkage maps and an integratedmap of ‘Starkrimson’בGranny Smith’ were used to detect

Table 1 Significance of thegenotype effect (G) and itsinteraction with age (G×A) andyear (G×Y) in selected modelsfor primary growth, secondarygrowth and branching traitsconsidered at several scales

Further details on the modelselected are given in Seguraet al. 2008ns non-significant*p≤0.05, significant;**p≤0.01, highly significant

Trait Abbreviation Axis/Scale G A Y G×A G×Y

Primary growthLength L Trunk ** ** **

LSAS ** ** **LPAS ** ** **Tree * ** ** *

Number of internodes INN Trunk ** ** **LSAS * ** ** *LPAS ** ** **Tree ** ** ** *

Mean internode length INL Trunk ** ** ** **LSAS ** ** ** **LPAS ** ** **Tree ** ** ** **

Length of the longest internode INLmax Trunk ** ** ** *LSAS ** ** ** **LPAS ** * **Tree ** ** ** **

Secondary growthBottom diameter increment ΔBdia Trunk ** ** **

LSAS ** ** **LPAS ns ** **Tree ns ** ** **

Bottom diameter Bdia Trunk ** ** ** **LSAS * ** ** **LPAS ** ** **Tree * ** ** * **

Top diameter Tdia Trunk ** ** ** **LSAS ** ** ** **LPAS ** * ** *Tree ** ** ** * **

BranchingNumber of axillary shoots Br Trunk * ** ** **

LSAS ** ** **Tree * ** ** ** **

Number of latent buds Latents Trunk ** ** ** * **LSAS ns ns ** * **Tree ** ** ** **

Percentage of branching nodes %Br Trunk ** ** ** **LSAS ** *Tree ** ** ** * **

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and map QTLs on the basis of previous BLUPs. Thesemaps were built using 107 microsatellite (simple sequencerepeat, SSR) markers, of which 22 were polymorphic onlyfor the female parent ‘Starkrimson’, 22 were polymorphiconly for the male parent ‘Granny Smith’ and 63 werepolymorphic for both parents. These 107 SSR markers werescattered between 17 linkage groups (LGs) and the averagedistance between two adjacent SSR markers was 10.8 cM.Segregation distortion has been checked with chi-squaretests in JoinMap™ version 2.0 software (Stam and VanOoijen 1995). On ‘Granny Smith’ parental map only, twogenomic zones comprised significantly distorted markers,on LG2 and LG10, respectively. Further details on theorigin of SSR markers and map construction are given inSegura et al. (2007). QTL analyses were carried out usingMAPQTL® 4.0 (Van Ooijen et al. 2002) on the trait BLUPsthat were normally distributed according to the Shapiro–Wilk test computed using the univariate procedure of SAS®v.8 software. The MAPQTL® 4.0 parameters used weremaximum of 200 interactions, functional tolerance value of1.0e−8 and a minimum of five flanking markers to resolveincomplete genotypes. The logarithm of the odds (LOD)threshold at which a QTL was declared significant wasdetermined according to a genome wide error rate of 0.05over 1,000 data permutations (Churchill and Doerge 1994).Then, an interval mapping analysis was performed with astep size of 1 cM to find regions with potential QTL effects,i.e. where the LOD score was greater than the LODthreshold. Subsequently, the nearest marker to each QTLpeak was selected as a cofactor to perform multiple QTLmapping (MQM, Jansen and Stam 1994). The previouslycomputed threshold was also used in MQM to detectsignificant QTLs in multiple models. Each significant QTLwas characterised by its LOD score, the percentage ofphenotypic variation it explained and its confidence intervalin cM corresponding to a LOD score drop of 1 or 2 oneither side of the likelihood peak. Allelic effects wereestimated as Af=[(μac+μad)−(μbc+μbd)]/4 for female addi-tivity, Am=[(μac+μbc)−(μad+μbd)]/4 for male additivity andD=[(μac+μbd)−(μad+μbc)]/4 for dominance, where μac,μad, μbc and μbd are estimated phenotypic means associatedwith each of the four possible genotypic classes ac, bc, adand bd, deriving from an <ab×cd> cross. QTLs with clearlyoverlapping confidence intervals, close LOD peaks andsimilar allelic effects were considered to co-localise. QTLlocation on the genetic maps was represented usingMapChart® (Voorrips 2001). When several QTLs weredetected for a trait BLUP, a global model including allcofactors and their first-order interactions, considered asfixed effects, was built to test epistatic effects betweenQTLs (i.e. interaction between cofactors). The leastsignificant effect was removed iteratively from the mostcomplete model until the BIC became minimal. In the

selected model, the significance of each factor and theglobal percentage of phenotypic variation (global R2) werethen estimated. Model selection and estimation wereperformed using the maximum likelihood method of themixed procedure and the general linear model procedure inSAS® v.8 software, respectively. To interpret QTL co-localisation and the independence of corresponding BLUPs,Pearson correlations were also computed between eachBLUP using the corr procedure of SAS® v.8 software.

Results

This section presents detailed results for QTLs that weredetected on the integrated ‘Starkrimson’בGranny Smith’map. Those that were also detected on the parentalseparated maps are mentioned in Table 2 but not repre-sented on the figures. Results are organised by architecturalprocess, and within each architectural process, the QTLsdetected for the G effect BLUPs are presented first. Second,results are provided for the QTLs of age- and/or year-specific BLUPs. When several QTLs co-localised, details(i.e. allelic effects and percentage of variation) are providedin the text only for the first one mentioned.

Primary growth

A QTL was detected on the distal part of LG 14 for the Geffect BLUP of AS length on the trunk (L_trunk; Table 2,primary growth traits, Fig. 2a). This QTL explained 14% ofthe variability and mainly resulted from a female additiveeffect.

A QTL was detected on LG 17 for the G effect BLUP ofthe number of internodes per AS considered on the wholetree scale (INN_tree). This QTL explained 18% of thevariability and was mainly due to a dominance effect. ThisQTL was also found for the same trait considered on LSAS(INN_LSAS). Two other QTLs were mapped on LGs 6 and16 for the BLUP of the number of internodes considered onthe whole tree scale during the second year of growth(INN2_tree). These QTLs explained 19% and 14% of thevariability, respectively. The QTL of LG6 was mainly dueto a female additive effect while that of LG16 to a maleadditive effect. A global model was built for these twoQTLs, showing that the QTL of LG 16 may be involved inepistatic effects (Table 3, primary growth traits). In thisstudy, the closest marker to the QTL of LG 16 was notsignificant when considered alone in the model, but ahighly significant interaction between this marker and theclosest marker to the QTL of LG 6 was found. This globalmodel explained 29% of trait variability.

Considering internode lengthening, three QTLs weredetected for the G effect BLUP of mean internode length

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Table 2 Parameters associated with the QTLs detected by multiple QTL mapping (MQM) for the best linear unbiased predictors (BLUPs) ofprimary growth, secondary growth and branching traits

BLUP LGa LODb R2c Cofactord Allelic effecte Afe Am

e De Parental mapdetectionf

Primary growthLengthL_trunk 14 3.99 (3.9) 0.14 U78948-SSR_SG Af 10.266 2.217 0.821 STKNumber of internodesINN_tree 17 4.46 (4.1) 0.19 AT00174-SSR_SG D 0.346 0.404 0.661INN_LSAS 17 4.01 (4.0) 0.18 AT00174-SSR_SG D 0.182 0.235 0.419INN2_tree 6 5.88 (3.9) 0.19 NZ23g04_SG Af −0.239 −0.114 0.065

16 4.20 (3.9) 0.14 CH02d10a_G Am 0.099 −0.182 0.069INN2_LSAS 6 4.23 (3.8) 0.17 NZ24g04_SG Af, Am −0.301 −0.271 0.030Mean internode lengthINL_tree 3 4.52 (3.8) 0.12 CH03e03_SG Af, Am, D 0.270 −0.250 −0.234

6 4.85 (3.8) 0.14 CH03d07_SG Af 0.370 0.118 −0.206 STK14 4.40 (3.8) 0.14 CH05g11_SG Af 0.402 0.200 −0.001 STK

INL_LSAS 3 5.30 (3.8) 0.16 CH03e03_SG Af, Am, D 0.222 −0.186 −0.1726 4.95 (3.8) 0.16 CH03d07_SG Af 0.281 0.066 −0.136 STK

INL_LPAS 3 4.69 (4.0) 0.13 CH03e03_SG Af, Am, D 0.304 −0.248 −0.2164 4.91 (4.0) 0.18 Hi04c10x_SG D −0.097 −0.090 −0.465

16 4.26 (4.0) 0.16 CH04f10_SG Af 0.391 −0.168 −0.164 STKINL1_trunk 7 4.41 (3.9) 0.16 Hi05b09_SG Am 0.111 0.138 0.036INL2_tree 16 5.24 (4.1) 0.22 CH05e04z_G Am 0.005 −0.195 0.049 GSINL2_trunk 2 4.50 (4.1) 0.17 NH033b_SG Am −0.081 0.103 −0.022 GSINL2_LSAS 16 4.18 (4.0) 0.17 Hi08f12_SG Am 0.011 −0.216 −0.060 GSLength of the longest internodeINLmax_tree 3 4.62 (3.8) 0.13 CH03e03_SG Af, Am, D 0.354 −0.510 −0.523

14 4.04 (3.8) 0.13 CH05g11_SG Af 0.628 0.365 0.18817 4.11 (3.8) 0.12 CH01h01_G Am 0.318 −0.676 0.055

INLmax_trunk 3 4.20 (3.9) 0.11 CH03e03_SG Af, Am, D 0.300 −0.474 −0.4305 3.98 (3.9) 0.10 CH03a09_SG Af, Am, D 0.397 −0.550 −0.348

16 4.69 (3.9) 0.12 CH04f10_SG Af 0.588 −0.241 −0.262 STKINLmax_LSAS 6 4.27 (3.9) 0.13 CH03d07_SG Af, D 0.377 0.236 −0.339

14 5.38 (3.9) 0.18 CH05g11_SG Af, Am 0.542 0.377 0.117INLmax_LPAS 14 3.90 (3.9) 0.14 CH05g11_SG Af, Am, D 0.436 0.388 0.332INLmax04_tree 10 5.59 (4.0) 0.19 COL_SG Af 0.235 0.084 −0.002 STKINLmax04_trunk 1 4.46 (4.0) 0.14 AG11_S Af 0.200 −0.031 −0.052 STK

7 5.21 (4.0) 0.17 MS06c09_SG Af 0.223 0.067 −0.070 STKINLmax04_LSAS 10 4.78 (3.8) 0.17 COL_SG Af 0.263 0.111 0.048 STKINLmax05_tree 7 4.81 (3.9) 0.14 MS06c09_SG Af −0.208 0.066 0.032 STK

16 5.84 (3.9) 0.17 CH05a04_SG Af, D 0.190 −0.058 −0.167 STKINLmax05_trunk 7 5.35 (3.9) 0.15 MS06c09_SG Af −0.188 0.045 0.063 STK

14 4.00 (3.9) 0.11 CH05g11_SG Af 0.183 0.023 −0.040 STK16 4.89 (3.9) 0.15 CH05a04_SG Af, D 0.151 −0.039 −0.162 STK

Secondary growthBottom diameter incrementΔBdia06_tree 7 4.27 (4.2) 0.18 CH04e05_S Af 0.089 0.013 0.059 STKBottom diameterBdia05_tree 1 4.17 (4.1) 0.19 CH05g08_SG Am 0.009 0.091 0.041 GSTop diameterTdia_LPAS 7 4.15 (4.0) 0.20 CH04e05_S D 0.000 0.017 0.068Tdia3_tree 10 5.49 (4.2) 0.23 CH02c11_SG Af, Am, D −0.023 −0.030 0.018 GSTdia04_tree 9 4.27 (4.2) 0.15 Hi05e07_SG Af −0.038 0.009 0.003 STKTdia05_trunk 7 4.48 (3.9) 0.21 Hi05b09_SG D −0.016 −0.009 −0.076Tdia06_tree 3 5.48 (4.0) 0.16 CH03e03_SG Af, Am, D 0.018 0.035 0.020

7 7.99 (4.0) 0.32 CH04e05_S D 0.021 0.008 0.066Tdia06_trunk 3 4.55 (4.2) 0.20 CH03e03_SG Af, Am, D 0.042 0.036 0.044

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considered on the whole tree scale (INL_tree). These QTLswere mapped on the proximal part of LG 3 and on LGs 6and 14. The QTL of LG 3 explained 12% of trait variabilityand resulted from both female and male additive anddominance effects. Each of the two other QTLs explained14% of trait variability and mainly resulted from a femaleadditive effect. Together, the three QTLs detected forINL_tree explained 39% of trait variability in the globalmodel (Table 3, primary growth traits). The QTLs of LGs 3and 6 were also mapped for the G effect BLUP of meaninternode length considered on LSAS (INL_LSAS), and theQTL on LG 3 was also detected for the BLUP of this traitconsidered on LPAS (INL_LPAS). In addition, two otherQTLs were detected on LGs 4 and 16 for INL_ LPAS. TheQTL of LG 4 explained 18% of the variability and wasmainly due to a dominance effect, while the QTL of LG 16explained 16% of the variability and was mainly due to a

female additive effect. The global model built for INL_LPAS, including the QTLs of LGs 3, 4 and 16, explained35% of trait variability. Four other QTLs were detected forage-specific BLUPs of mean internode length. Two weremapped on LGs 7 and 2 when the trait was considered onthe trunk during the first and second years of growth,respectively (INL1_trunk and INL2_trunk), while the twoothers were on LG 16 when the trait was consideredduring the second year of growth on the whole tree scaleand on LSAS (INL2_LSAS and INL2_tree). Each ofthese age-specific QTLs explained around 20% of thevariability, and they all mainly resulted from a maleadditive effect.

Three QTLs were found for the G effect BLUP of lengthof the longest internode considered on the whole tree scale(INLmax_tree), on the proximal part of LG 3 and on LGs14 and 17. Together, these three QTLs explained 35% of

Table 2 (continued)

BLUP LGa LODb R2c Cofactord Allelic effecte Afe Am

e De Parental mapdetectionf

Tdia06_LSAS 7 5.51 (4.0) 0.23 CH04e05_S D 0.003 0.014 0.0678 4.09 (4.0) 0.12 CH01c06c_G Af, Am 0.026 0.043 −0.003

Tdia06_LPAS 3 4.86 (4.1) 0.13 CH03e03_SG Af, Am, D 0.018 0.021 0.0077 7.30 (4.1) 0.26 CH04e05_S D 0.019 −0.004 0.036

BranchingNumber of axillary shootsBr_tree 4 4.70 (3.9) 0.20 CH02h11a_S Am −0.087 0.527 0.229 GSBr2_tree 13 7.47 (3.9) 0.26 CH05f04_G Am 0.089 −0.608 0.286 GSBr2_trunk 13 4.96 (3.9) 0.18 CH05f04_G Am 0.136 −0.536 0.310 GSBr05_tree 13 4.55 (3.9) 0.16 CH05f04_G Am 0.132 −0.528 0.188 GSNumber of latent budsLatents_tree 17 3.90 (3.9) 0.16 CH01h01_G Af 0.911 0.404 0.534 STKLatents_trunk 17 4.76 (4.1) 0.22 Hi02f12_G Af 1.165 −0.143 0.125 STKLatents05_trunk 17 4.90 (4.1) 0.23 Hi02f12_G Af 1.113 −0.553 0.004 STKPercentage of branching nodes%Br_tree 4 5.02 (4.1) 0.20 CH04e02_SG Am −0.001 0.017 0.011 GS%Br_trunk 17 4.20 (4.0) 0.19 Hi02f12_G Af −0.024 0.004 −0.005 STK%Br_LSAS 4 5.70 (3.9) 0.22 CH04e02_SG Am 0.001 0.018 0.009 GS%Br2_tree 13 4.57 (4.2) 0.17 CH05f04_G Am 0.001 −0.006 0.004 GS%Br2_LSAS 1 4.19 (4.1) 0.14 CH05g08_SG Af, Am −0.007 −0.006 0.000

13 4.23 (4.1) 0.13 CH05f04_G Am −0.001 −0.008 0.005%Br3_tree 7 5.84 (4.1) 0.21 Hi03a10_SG Am −0.001 −0.007 −0.003 GS

11 4.37 (4.1) 0.13 CH04h02_SG D 0.002 0.002 0.006%Br3_LSAS 7 6.26 (4.1) 0.25 Hi03a10_SG Am −0.001 −0.011 −0.006

11 4.18 (4.1) 0.13 CH04h02_SG D 0.003 0.003 0.008

a Linkage GroupbMaximum LOD score value with the considered threshold in bracketsc Percentage of phenotypic variation explained by the QTLdMarkers used as cofactors in the MQM analysise Female (Af) and male (Am) additive effects computed as [(μac+μad)−(μbc+μbd)]/4 and [(μac+μbc)−(μad+μbd)]/4 respectively; dominance (D)effect computed as [(μac+μbd)−(μad+μbc)]/4, where μab, μad, μbc and μbd are estimated phenotypic means associated with each of the fourpossible genotypic classes ab, ac, ad and bd, deriving from a <ab×cd> crossf QTLs detected on the parental separated maps: Starkrimson (STK) and Granny Smith (GS)

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trait variability in the global model (Table 3, primarygrowth traits). The QTL mapped on LG 17 explained 12%of INLmax_tree variability and mainly resulted from a maleadditive effect. The QTLs of LG 3 and 14 co-localised withthose previously mapped for mean internode length. Inaddition, these QTLs were also detected for the G effectBLUP of length of the longest internode considered on thetrunk (INLmax_trunk on LG 3), LSAS and LPAS(INLmax_LSAS, INLmax_LPAS on LG14). However,another QTL was detected on LG 6 for INLmax_LSAS.This QTL co-localised with the QTLs previously detectedfor INL_LSAS and INL_tree. For INLmax_trunk, twoother QTLs were mapped on LGs 5 and 16, the firstresulted from both female and male additive effects and adominance effect, while the second mainly resulted from afemale additive effect. Together, the three QTLs detectedfor INLmax_tr explained 41% of trait variability. OtherQTLs were detected for year-specific BLUPs of length ofthe longest internode, on LGs 1, 7, 10, 14 and 16. Each ofthese QTLs explained between 11% and 19% of thevariability, and some of them were either common toseveral climatic years or to different positions within thetrees. For instance, the QTL on LG 10 was detected forINLmax04 considered both on the whole tree scale and onLSAS; the QTL on LG 7 was detected for INLmax04_trunk, INLmax05_trunk and INLmax05_tree, and the QTLon LG 16 was detected for both INLmax05_tree andINLmax05_trunk. In addition, the QTL detected on LG 14for INLmax05_trunk co-localised with that previouslymapped for INL_tree, INLmax_tree, INLmax_LSAS andINLmax_LPAS.

Secondary growth

For both bottom diameter and bottom diameter increment,QTLs were detected only for year-specific BLUPs (Table 2,secondary growth; Fig. 2b.). A QTL was detected on LG 1for the BLUP of bottom diameter considered on the wholetree scale in 2005 (Bdia05_tree). This QTL explained 19%of trait variability and mainly resulted from a male additiveeffect. A QTL was detected for the BLUP of bottomdiameter increment estimated on the whole tree scale in2006 (ΔBdia06_tree). This QTL was mapped on LG 7,explained 18% of trait variability and mainly resulted froma female additive effect.

Only one QTL was detected for the G effect BLUP oftop diameter when the trait was considered on LPAS(Tdia_LPAS). This QTL was mapped on LG 7, explained20% of the variability and mainly resulted from adominance effect. Three other QTLs were detected in thisgenomic position for the BLUPs of top diameter consideredeither on the whole tree scale or on LSAS and LPAS duringthe 2006 climatic year (Tdia06_tree, Tdia06_LSAS and

Tdia06_LPAS). Other QTLs were mapped for the BLUPsof top diameter considered in 2006: on LG 8 forTdia06_LSAS and on LG3 for both Tdia06_tree andTdia06_LPAS. Global model estimations were carried outon these three BLUPs, but since the QTL of LG7 wasmainly due to a dominance effect, its closest marker(CH04e05_S), which was only polymorphic for the femaleparent, was replaced by Hi03a10_SG, the closest markerthat was polymorphic for both parents (Table 3, secondarygrowth). For Tdia06_LSAS, the global model showedhighly significant effects for both QTLs of LGs 7 and8 but explained only 16% of trait variability. For Tdia06_-tree and Tdia06_LPAS, in addition to the highly significanteffects found for both QTLs of LGs 7 and 3, a highlysignificant interaction between them was also included inthe model, underlining the existence of epistatic effects.These global models explained around 40% of both traitsvariability. Other year-specific QTLs were detected for topdiameter on LG 9 (Tdia04_tree) and on the distal part ofLG 7 (Tdia05_trunk). The QTL on LG 9 explained 15% ofthe variability and mainly resulted from a female additiveeffect. The QTL on the distal part of LG 7 explained 21%of trait variability and was mainly due to a dominanceeffect. Only one QTL was detected on LG 10 for an age-specific BLUP of top diameter: Tdia3_tree. This QTLexplained 23% of trait variability and was mainly due to amale additive effect.

Branching

A QTL was detected on the median part of LG 4 for the Geffect BLUP of the total number of axillary shoots per ASconsidered on the whole tree scale (Br_tree) (Table 2,branching traits; Fig. 2c). This QTL explained 20% of thevariability and mainly resulted from a male additive effect.Three other QTLs were detected on the distal part of LG 13for the total number of axillary shoots, but for age- andyear-specific BLUPs of this trait considered either on thewhole tree scale or on the trunk (Br2_tree, Br05_tree, andBr2_trunk). Each of them explained between 16% and 26%of the variability, and they mainly resulted from a maleadditive effect.

Fig. 2 Genomic positions of QTLs detected on the linkage groups ofthe integrated ‘Starkrimson’בGranny Smith’ map (STK×GS) bymultiple QTL mapping (MQM) for the best linear unbiased predictors(BLUPs) of primary growth (a), secondary growth (b) and branchingtraits (c). QTLs are represented by boxes extended by lines represent-ing the LOD-1 and LOD-2 confidence intervals. Triangle LOD peak.Boxes are coloured according to the trait from which the BLUPswhere computed and are hatched when the BLUPs were computedfrom the interaction between genotype and age or genotype and year.For trait abbreviation, see Table 1

b

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Two QTLs were detected on LG 17 for the G BLUP ofthe number of latent buds considered either on the wholetree scale (Latents_tree) or on the trunk (Latents_trunk).However, they were located in two distinct genomic zonesof the LG 17. Each of these QTLs explained between 16%and 22% of the variability and mainly resulted from afemale additive effect. Another QTL was detected on LG 17for the BLUP of the number of latent buds considered onthe trunk in 2005 (Latents05_trunk). This QTL co-localisedwith the QTL previously detected for Latents_trunk.

For the percentage of branching nodes, a QTL wasdetected on the proximal part of LG 4 for its G BLUPconsidered either on the whole tree scale (%Br_tree) or onLSAS (%Br_LSAS). Each of these QTLs explained around20% of trait variability, and they were mainly due to a maleadditive effect. Another QTL was detected on LG 17 for theG effect BLUP of the percentage of branching nodes of thetrunk (%Br_trunk). This QTL co-localised with the QTLspreviously mapped for Latents_trunk and Latents05_trunk.Other QTLs were detected on LG 13 for the BLUPs of thepercentage of branching nodes considered during thesecond year of growth (%Br2_tree and %Br2_LSAS).These QTLs co-localised with the QTLs previously mappedfor age- and year-specific BLUPs of the total number ofaxillary shoots (Br2_tree, Br05_tree and Br2_trunk).Another QTL was detected on LG 1 for %Br2_LSAS. ThisQTL explained 14% of trait variability and was due to bothfemale and male additive effects. Together the QTLs of LG1 and 13 explained 23% of %Br2_LSAS variability in theglobal model (Table 3, branching traits). Two other QTLswere detected on LG 7 and 11 for the BLUPs of thepercentage of branching nodes considered in the thirdyear of growth either on the whole tree scale or on LSAS

(%Br3_tree, %Br3_LSAS). The QTL on LG 7 explainedbetween 21% and 25% of the variability of both traits andwas mainly due to a male additive effect, while the QTL onLG 11 explained 13% of the variability and mainly resultedfrom a dominance effect. A global model was estimated forboth %Br3_tree and %Br3_LSAS and explained 28% and26% of the variability, respectively.

Discussion

Improvement in QTL mapping through mixed linearmodelling of repeated data

Several strategies might be used to detect QTLs for datacollected at different times or positions in the sameindividual. The most classic approach has been to associatemarkers with phenotype at each time or position and tocompare the QTLs detected (e.g., for architectural traits inapple Conner et al. 1998; Kenis and Keulemans 2007). Afirst step in improving QTL detection power may be madeby considering the data all together and employing amultivariate approach (Jiang and Zeng 1995; Korol et al.1995; Mangin et al. 1998). However, as argued by Wu andLin (2006), the statistical power to detect significant QTLsmight be affected by not modelling autocorrelations. To thisend, these authors proposed a dynamic method called‘functional mapping’, which is especially adapted to thedetection of genetic effects involved in growth trajectories,i.e. ontogenetic effects. But the genetic effects that areindependent of ontogeny and also environmental effectsmight not be accounted for in such an approach. In the pres-ent study, a two-step method was preferred, dissociating the

Fig. 2 (continued)

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modelling of autocorrelation and QTL mapping on the basisof BLUP estimation. BLUPs of genotypic effect wereconsidered as independent of both ontogenetic and environ-mental effects, while BLUPs of interaction effects betweengenotype and age and genotype and year were assumed to bespecific of ontogenetic and climatic effects, respectively.Correlation analysis between BLUPs confirmed these

assumptions. Indeed, correlations between BLUPs of thesame trait considered either on different axes or at differentscales were always higher than those between G BLUP andA or Y BLUPs (Supplementary material, Table S1.a.), eventhough these latter were significant for most traits (note thatfor 122 observations correlation higher than 0.15 inabsolute value are significant). In addition, all these BLUPs

Table 3 Global model estima-tions for the best linear unbi-ased predictors (BLUPs) ofprimary growth, secondarygrowth and branching traitswith several QTLs detected bymultiple QTL mapping (MQM)

a Linkage groupb Effects selected for modelestimationc Effect probabilityd Percentage of variationexplained by the global modele Replaced by Hi03a10_SG thenearest marker with the fourgenotypic classes (ac, bc, adand bd)

BLUP LGa Markerb p valuec Global R2d

Primary gowthNumber of internodesINN2_tree 6 NZ23g04_SG <0.0001 0.29

6*16 NZ23g04_SG*CH02d10a_G 0.0004Mean internode lengthINL_tree 3 CH03e03_SG <0.0001 0.39

6 CH03d07_SG 0.000214 CH05g11_SG 0.0008

INL_LSAS 3 CH03e03_SG <0.0001 0.316 CH03d07_SG 0.0001

INL_LPAS 3 CH03e03_SG 0.0002 0.354 Hi04c10x_SG 0.000316 CH04f10_SG 0.0022

Length of the longest internodeINL_max_tree 3 CH03e03_SG 0.0002 0.35

14 CH05g11_SG 0.000617 CH01h01_G 0.0002

INLmax05_tree 7 MS06c09_SG 0.0001 0.3216 CH05a04_SG <0.0001

INLmax_trunk 3 CH03e03_SG 0.0006 0.415 CH03a09_SG 0.008416 CH04f10_SG <0.0001

INLmax04_trunk 1 AG11_S <0.0001 0.307 MS06c09_SG <0.0001

INLmax05_trunk 7 MS06c09_SG <0.0001 0.4214 CH05g11_SG 0.000316 CH05a04_SG 0.0003

INLmax_LSAS 6 CH03d07_SG 0.0005 0.2814 CH05g11_SG <0.0001

Secondary growthTop diameterTdia06_tree 3 CH03e03_SG 0.0002 0.39

7 CH04e05_Se 0.00023*7 CH03e03_SG*CH04e05_Se 0.0053

Tdia06_LSAS 7 CH04e05_Se 0.0079 0.168 CH01c06c_G 0.001

Tdia06_LPAS 3 CH03e03_SG 0.0001 0.427 CH04e05_Se 0.00033*7 CH03e03_SG*CH04e05_Se 0.0037

BranchingPercentage of branching nodes%Br3_tree 7 Hi03a10_SG <0.0001 0.28

11 CH04h02_SG 0.0003%Br2_LSAS 1 CH05g08_SG 0.0006 0.23

13 CH05f04_G 0.0004%Br3_LSAS 7 Hi03a10_SG <0.0001 0.26

11 CH04h02_SG 0.0004

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are independent from autocorrelations, since they wereextracted from the mixed linear models of repeated data. Toevaluate the relevance of this two-step approach, wecompared the number of genomic regions and QTLsdetected to those found in a classic univariate approach.The results obtained from the classic univariate approach,which was conducted for the design comprising the entireprogeny planted in 2004, are provided as a case in point forprimary growth traits only (Supplementary material,Figure S1). For both primary growth and branching traits,a larger number of QTLs covering a larger number ofgenomic regions were found by the two-step method thanby the classic approach. For secondary growth, the numberof QTLs was similar in both methods, but the two-stepmethod detected a larger number of genomic regions (datanot shown). Thus, the two-step method increased QTLdetection power for all architectural processes. Neverthe-less, in some cases, genomic regions detected with theclassic approach were not found with the two-step method.However, these genomic regions always carried only oneQTL and thus were considered as weak. Another argumentis also provided by the QTLs of BLUPs for traitsconsidered on the whole tree scale compared to thosedetected from separated axes, which are also repeatedmeasures on the same individuals. This comparison showedthat (1) the LOD score was higher in most cases (e.g. LODscores increased from 4.96 to 7.47 on LG 13 when thenumber of axillary shoots was considered on the whole treescale rather than on the trunk) and (2) some genomicregions were only detected for BLUPs of traits consideredon the whole tree scale (e.g. length of the longest internodeon LG17, or number of axillary shoots on LG 4). Such amethod might still be improved by performing QTLmapping directly from the mixed linear model and replac-ing the genotype effect by a molecular marker effect.Interval mapping could also be considered to improve themethod, but this would involve a high number of repeateddata models that require high computational time. More-over, it would be difficult to estimate interactions betweenQTLs in such a single step model because of the highnumber of parameters included.

Genetic analysis of architectural processes

This section focuses on the QTLs considered as the mostinteresting as they co-localised with other QTLs found forthe same process either in the present study or in previousgenetic studies for the same traits (for linkage groupcorrespondence, see Conner et al. 1997; Maliepaard et al.1998; Hemmat et al. 2003; Kenis and Keulemans 2005;Silfverberg-Dilworth et al. 2006). For primary growth traits,two QTLs co-localised on LG 17 for the number ofinternodes considered either on the whole tree scale or on

LSAS. This co-localisation is consistent with the correlationbetween these two BLUPs (r=0.84). It is also noteworthythat Conner et al. (1998) mapped a QTL for the number ofinternodes on an LG homologous to LG17, but since theseauthors did not use SSR markers, no final conclusion canbe drawn with regard to QTL co-localisation between thestudies. For both mean internode length and length of thelongest internode, many QTL co-localisations were ob-served in the present study especially when the traits wereconsidered at different positions within the tree (LGs 3, 6,7, 10, 14 and 16). In addition, some of these genomicregions carried QTLs for both mean internode length andlength of the longest internode. This was the case for LGs3, 6 and 14. Even though these traits are related to the sameprocess, i.e. internode elongation, and thus are highlycorrelated (r between G effect BLUPs of INL and INLmaxranged from 0.74 to 0.88, Supplementary material, TableS1.b.), the independence of their measurements underlinesthe robustness of the corresponding QTLs. In addition,Kenis and Keulemans (2007) mapped QTLs for internodelengthening on LGs homologous to LGs 3 and 14. TheQTL mapped by Kenis and Keulemans (2007) on the LGhomologous to LG 3 could be in the same genomic regionas the QTLs mapped in this study, but the low number ofSSR markers used in their study did not allow a finalconclusion to be drawn with regard to the respectivepositions of QTLs detected on the LG 14 in both studies.

Considering secondary growth traits, two genomicregions carried several QTLs on LGs 3 and 7. On LG 3,co-locolising QTLs were detected for top diameter whenconsidered at whole tree scale, on trunk or on LPAS. Hereagain, these co-localisations were consistent with thecorrelations between the corresponding BLUPs (r rangedbetween 0.61 and 0.85).These QTLs were also in the samegenomic region as the QTLs previously mapped forinternode lengthening. Even though for both top diameterand internode lengthening the QTLs mapped were mainlydue to combined female and male additive and dominanceeffects, the male and dominance effects showed oppositesigns between the two traits. This is consistent with thecorrelation values detected between these traits, which werealways negative, even though quite low (Supplementarymaterial, Table S1.b.) and suggests a common underlyingdeterminism that impacts both primary and secondarygrowth and the final organ dimensions. On LG 7, fourQTLs were detected for top diameter considered on differentaxes, and one QTL was found for bottom diameterincrement. As previously discussed for internode lengthen-ing, bottom diameter increment and top diameter werecorrelated (r ranged from 0.47 to 0.60 between ΔBdia06_-tree and either Tdia06_tree, Tdia06_trunk or Tdia06_LSAS)but stemmed from independent measures which reinforcesthe robustness of the QTLs mapped.

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For branching traits, the distal part of LG 13 carried fiveQTLs detected for the number of axillary shoots and thepercentage of branching nodes, considered either on severalaxes or on the whole tree scale. Four of these were specificto the second year of growth, while the fifth one wasspecific to year 2005. It is noteworthy that the corre-sponding BLUPs displayed significant correlation betweeneach other (r ranged between 0.42 and 0.89). This genomicregion has previously been detected for both the totalnumber of sylleptic and proleptic axillary shoots develop-ing over the first and second years of growth, respectively(Segura et al. 2007, and unpublished data), suggesting acommon locus acting on both syllepsis and prolepsisprocesses. The present results are consistent with thishypothesis, since both the number of axillary shoots andthe proportion of branching nodes on the first AS includethe sylleptic and proletic laterals that developed during thefirst and second years of growth, respectively (Fig. 1).Another QTL was mapped on the distal part of LG 17 forthe percentage of branching nodes and co-localised withtwo QTLs detected for the number of latent buds. In bothcases, the QTLs were mainly due to a female additiveeffect. This effect was inverse on the two traits, as thesetraits were negatively correlated (r=−0.84).

QTL mapping of ontogenetic factors

The QTLs detected in the present study for age- or axis-specific BLUPs were interpreted as resulting from ontoge-netic effects. A marked decrease in primary growthexpression and variability was observed in the progeny(Segura et al. 2008). But the decrease in AS length over theyears was too homogenous between the progeny genotypesto detect any G×A interaction. Consequently, no age-specific QTLs were detected for AS length. By contrast,two QTLs were detected for BLUPs of the number ofinternodes considered during the second year of growth.Since the decrease in the number of internodes was shownto be exponential (Costes et al. 2003; Segura et al. 2008),the second year of growth appears to be a key stage duringwhich the most pronounced decrease in primary growthoccurs. The QTL highlighted in this study shows that themorphogenetic activity of the terminal meristems differsbetween the genotypes during this key stage and that thisvariability is under genetic control. Other age-specificQTLs were also found for mean internode length on LG 7for the first year of growth and on LGs 2 and 16 for thesecond year of growth. But the combined nature of the traitmakes it difficult to interpret these different genomicregions detected for the first 2 years of growth and theirisolated positions on the genome. Six axis-specific QTLswere also detected for primary growth traits. It isnoteworthy that most of these were specific to the trunk,

which is characterised by the highest growth potential,while growth decreased as branching order increased(Barthélémy et al. 1997; Durand et al. 2005). The QTLshighlighted here might therefore be responsible for thevariability in the maximum growth observed on the trunk.

For secondary growth, the only age-specific QTLdetected in this study was on LG 10 for the BLUP of topdiameter considered in the third year of growth. As the treeages, top diameter increases from the first to second yearsof growth and decreases from the third year of growth(Segura et al. 2008). As previously discussed for thenumber of internodes, the QTL highlighted in this studyis concomitant with the first year from which the decreasestarts. This QTL might therefore be related to tree ontogenyand may be involved in shoot shape (Niklas 1994; Almeraset al. 2002). For the top diameter, two axis-specific QTLswere mapped on LGs 7 and 8 (trunk and LSAS,respectively). But both these two QTLs were also specificto a climatic year, which makes their interpretation difficultfrom the point of view of tree ontogeny.

For branching traits, an age-specific QTL was detectedon LG 13 for both the number of axillary shoots and thepercentage of branching nodes considered on the first ASand observed during the second year of growth, but noQTLs were mapped for this trait on the second AS. Aspreviously discussed, this QTL is likely to result from bothsyllepsis and prolepsis branching that developed on the AS.Syllepsis expression has been shown to increase withprimary growth potential in both forest and fruit species

Fig. 3 Changes in the percentage of branching nodes on the three firstannual shoots of an axis, considering the data of all axes gathered onthe whole tree scale. Mean values were considered for the wholedataset and for two extreme genotypes among the 16 possiblecombinations resulting from alleles at the nearest markers to the twoQTLs mapped for Br3_tree (Hi03a10_SG on LG7 and CH04h02_SGon LG11). These two extreme genotypes combine ad or bc at the firstQTL (LG7) with ac or ad at the second QTL (LG11). DiamondDataset mean value, triangle and square mean values for ad–ac andbc–ad, respectively

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(Powell 1987; Genard et al. 1994). In our dataset, thenumber of sylleptic axillary shoots dramatically decreasedfrom AS 2 so that this branching process was very weaklyexpressed at this age (data not shown). This decrease wasinterpreted as resulting from the marked decrease inprimary growth observed (previously discussed). Theabsence of QTL for the total number of axillary shoots onAS 2 might thus be related to the weak expression ofsyllepsis at this age. By contrast, for the percentage ofbranching nodes, two QTLs were found on LGs 7 and 11for this trait considered on the AS 2. During tree ontogeny,even though the expression of both the number andproportion of axillary shoots decreases, these traits do notshow exactly the same behaviour. Here, the variability inthe amount of branching decreased as the tree ages, whilefor the proportion of laterals, this variability remained highand was under strong genetic control. As an illustration ofthe relationship between the QTLs mapped on LGs 7 and11 and changes in the percentage of branching nodes, themean values for two particular genotypic classes obtainedfrom the combination of these two QTLs (ad–ac vs. bc–ad)are shown in Fig. 3. Relatively to the progeny mean, thevalues for the extreme ‘ad–ac’ genotypes did not decreasebetween the two first AS, while the ‘bc–ad’ genotypesshowed a marked decrease. These results highlighted thatthe part of ontogenetic changes for branching that is undergenetic control is likely to affect the branching potential ofa given AS rather than its branching amount. With regard tothe age-specific QTLs detected for the percentage ofbranching nodes, the low number of axis-specific QTLs(only 1 on LG 1) suggests that the ontogenetic factors forbranching process are related to tree age rather thanpositions within the tree.

QTL mapping of climatic factors

Many climatic year-specific QTLs were found in thepresent study, especially for length of the longest internodeand top diameter. As already suggested, these traits mightbe involved in architectural adaptation to climatic con-ditions (Segura et al. 2008). As the trees were regularlyirrigated throughout the study, the QTLs highlighted in thisstudy cannot be interpreted as resulting from limitations inwater resources. By contrast, an examination of ambienttemperatures during the summer of the climatic years understudy (data from Fréjorgues Météo-France meteorologicalstation) showed that 2004 and 2005 were fairly similar andin the norm, while 2006 was characterised by temperaturessubstantially above average (Segura et al. 2008). The factthat all the year-specific QTLs for length of the longestinternode were for 2004 and 2005 suggests that normaltemperatures combined with the highest growth potential oftrees in their first years of growth, resulted in the expression

of maximum internode elongation potential and that thispotential is under genetic control. This provides a geneticbackground to the concept of maximum growth potential,which has been proposed in a carbon modelling approach torepresent the genetic potential of organ growth (Allen et al.2005). By contrast for top diameter, even though year-specific QTLs were found for all the climatic years understudy, most of these QTLs were specific to 2006. Thissuggests that these QTLs may be related to tree adaptation tohigh temperature constraints even though a relationship withtree age cannot be entirely excluded. Indeed, 2006 corre-sponded to the third and fourth years of growth for treesplanted in 2004 and 2003, respectively, and one shouldnotice that the fourth year of growth of trees planted in 2004has not been phenotyped. Further investigations, for examplein control conditions, could help to clarify this hypothesis.

To conclude, an original two-step method was employedin this study and allowed us to detect QTLs that were eitherindependent of or specific to ontogenetic and environmen-tal effects. This method was shown to increase the power ofQTL detection in comparison with a classic approach. As aconsequence, interesting QTLs were detected, since manyco-localised in similar genomic regions. This geneticdissection of architectural plasticity was performed for thefirst years of growth during which the tree establishes itself.The analysis of ontogenetic factors was facilitated by thesubstantial variability in growth and branching potentialsduring these developmental stages. Indeed, both growth andbranching processes were shown to decrease very rapidlyfrom the second year of growth so that very little variabilitysubsisted for most traits from the third year of growth.From this age, trees start to reach the mature developmentalstage characterised by fruiting. This process is likely togreatly interfere with growth and branching in the consec-utive developmental stages, as previously shown in applecultivars (Lauri et al. 1995). Since production is of greateconomic importance, the genetic analysis of apple treearchitectural development and its interaction with fruitingbehaviour constitute a prospect for the present study.

Acknowledgements We acknowledge Mark Jones for improving theEnglish. This research was partly funded by a grant from the INRAgenetic and plant breeding department and Languedoc-Roussillonregion, allocated to Vincent Segura.

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