Hn Zhng，Jinsheng Chen，Ruyu Li，Zhiying Deng，Kunpu Zhng，Bin Liu，Jichun Tin，*Stte Key Lortory of Crop Biology，Ministry of Science nd Technology/Key Lortory of Crop Biology of Shndong Province，Deprtment of Agronomy/Group of Whet Qulity Breeding，Shndong Agriculturl University，Ti'n 271018，ChinCrop Reserch Institute，Shndong Acdemy of Agriculturl Sciences，Jinn 250100，Chin

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Conditional QTL mapping of three yield components in common wheat（Triticum aestivum L.）

Han Zhanga，b，Jiansheng Chena，Ruyu Lib，Zhiying Denga，Kunpu Zhanga，Bin Liua，b，Jichun Tiana，*
aState Key Laboratory of Crop Biology，Ministry of Science and Technology/Key Laboratory of Crop Biology of Shandong Province，Department of Agronomy/Group of Wheat Quality Breeding，Shandong Agricultural University，Tai'an 271018，China
bCrop Research Institute，Shandong Academy of Agricultural Sciences，Jinan 250100，China

A R T I C L E I N F OA B S T R A C T

Article history：

Received in revised form

27 January 2016

Accepted 15 March 2016

Available online 30 March 2016

Kernel number per spike

QTL mapping

Spike number per m2

Thousand-kernel weight

Spikenumberperm2（SN），kernelnumberperspike（KNPS）and thousand-kernelweight（TKW）are the three main components determining wheat（TriticumaestivumL.）yield.Toevaluate the relationships among them a doubled haploid（DH）population consisting of 168 lines grown at three locations for three years was analyzed by unconditional and conditional QTL mapping. Thirty-three unconditional QTL and fifty-nine conditional QTL were detected.Among them，twoQTL（QSN-DH-2BandQSN-DH-3A-1.1）improvedSN，withnoeffectonKNPS. QKNPS-DH-2B-2.1 improved KNPS，with no effect on SN.QKNPS-DH-1A-1.1，QKNPS-DH-2D-1.1 and QKNPS-DH-6Aimproved KNPS，with noeffect on SNorTKW.QKNPS-DH-6B was associated with increased SN and TKW.In addition，QTKW-DH-4B，QTKW-DH-5B and QTKW-DH-7B increased TKWwithout decreasingKNPS.Theseresultsprovideuseful informationfor marker assisted selection（MAS）and improvement in wheat yield.

?2016 Crop Science Society of China and Institute of Crop Science，CAAS.Production and hosting by Elsevier B.V.This is an open access article under the CC BY-NC-ND license

（http://creativecommons.org/licenses/by-nc-nd/4.0/）.

1.Introduction

Common wheat（Triticum aestivum L.）is one of the most important crops worldwide.Its yield is significantly correlated with spike number per m2（SN），kernel number per spike （KNPS）and thousand-kernel weight（TKW）.In wheat-breeding and agronomic studies the relationships of the three components are frequently investigated.Understanding the genetics is crucial for improving yield.Quantitative trait loci（QTL）analysis can dissect and characterize the genetic complexity of yield traits produce a better understanding of the genetic architecture of yield components.Researchers have conducted unconditional QTL analyses on KNPS［1-4］，SN［1-3，5］and TKW［3-8］in different genetic backgrounds and different environments.However，all tree traits are controlled by multiple genes and are affected by environment as well as genetic background. Previous unconditional QTL studies did not always provide an overall true expression of accumulated effects of QTL. Consequently，this method may not be suitable for analysing interactionsamongQTLorgenescontrollingrelatedtraits［1，3，4］.

Zhu［9］developed conditional analysis methods that are capable of excluding the contribution of a causal trait to variation of the resultant trait.The remaining variation in the resultant trait is defined as conditional variation，or net variation，which indicates the effects of genes that are independent of the causal trait［10］.Therefore，this methodcan also define the genetic relationships among different traits at the QTL level.To date，this method has been used not only to study the dynamic behaviour of developmental traits but also the effects of conditional variation in the resultant trait on multiple related traits in rice［10-11］，wheat ［12-16］，maize and rapeseed［17］.In wheat，many cause-effect conditional QTL，such as protein content with yield and yieldrelated traits［15］，flour components with sedimentation volume［18］，TKW with kernel length and kernel width［19］. These results indicate that conditional QTL analysis of related traits is helpful for revealing the genetic relationships of closely related individual QTL and for clarifying the positive or negative genetic relationships of two traits at the level of a single QTL or gene［9，20］.

Some studies indicated that the conditional QTL method could also detect more QTL than the traditional QTL mapping method，especiallywithregard totheidentificationofimportant QTL/genes that increase one trait without affecting others.For instance，Guo et al.［21］investigated the relationship between yieldandnumberoftillersperplant，grainsperpanicleandTKW using a population of 241 recombinant inbred lines（F9RILs）derivedfromtheelitehybridricecross‘Zhenshan97'בMinghui 63'by unconditional and conditional QTL mapping methods. Similarly Yu and Chen［22］identified 36 QTL for water logging tolerance in ITMI wheat population and 10 QTL in an SHW-L1× Chuanmai 32（SC）population，and dissected the genetic relationships between QTL for total dry weight index and its components.Zhang［19］conducted a QTL analysis of kernel weight and provided a better understanding of the relationships between yield-contributing traits at the QTL level.These results provided a theoretical basis for application in marker-assisted selection（MAS）for grain yield improvement in wheat.

In the present study the relationships among three major yield components were examined at the QTL/gene level using a DHpopulationplantedindifferentyearsandlocationsaccording to both unconditional and conditional QTL mapping methods. The aims were to 1）identify QTL for the three graincomponents conditioned on othertraits，2）analyse the relationships among the three grain components at the QTL/gene level，and 3）determine the important QTL regions controlling three yield components.

2.Materials and methods

2.1.Plant materials

A doubled haploid（DH）population consisting of 168 lines produced from a cross between Chinese wheat cultivars Huapei 3andYumai57wasusedinthisstudy.Huapei3isanelitevariety with large panicles，large grains and medium number of spikebearing tillers［23］.Yumai 57 has medium-large panicles，a large number of spike-bearing tillers，and can be cultivated under a wide range of environmental conditions［24］.Huapei 3 and Yumai 57 were released in 2006［23］and 2003［24］，respectively.

2.2.Field trials

The parental lines，together with the DH population，were evaluated at three locations:Tai'an（36°57′N，116°36′E），Jinan（36°71′N，117°09′E）and Jiyuan（112°36′E，35°05′N），and five environments:Tai'an in 2010-2011（E1），Jinan in 2011-2012 （E2），Tai'an in 2011-2012（E3），Jiyuan in 2011-2012（E4），and Jinan in 2012-2013.

All entries were planted in two replications at each location in randomized complete block designs in October 2010.At Tai'an all DH lines and parents were grown 2 m plots of four rows spaced 26 cm apart.The same materials were planted in four row plots of 2.7 m and 20 cm roe spacing，four row plots of 3 m and 25 cm roe spacing，and three row plots of 2.6 m and 20.0 cm row spacing，respectively，at Tai'an，Jinan and Jiyuan. The lines and parents were evaluated in four-row 3 m plots with row spacing of 25 cm apart at Jinan in October 2012.The population density at the different locations and environments was approximately 1.8 million per hectare.Field management was in accordance with local agronomic practices.

Data for SN and KNPS were recorded at maturity from 10 randomly selected plants grown in the central rows of each plot before harvesting.TKW was measured from the same plants harvested from central rows of each plot.

2.3.Genetic linkage map

The genetic linkage map contained 323 markers（including 284 simple sequence repeat（SSR）loci，37 expressed sequence tag （EST）loci，oneinter-simplesequencerepeat（ISSR）locus，andone high-molecular-weight glutenin subunit locus）.These linked markers formed 24 linkage groups over 21 chromosomes［25］.

2.4.Data analysis and QTL mapping

Simple correlation coefficients were calculated using SPSS version 19.0 software（SPSS，Chicago，USA）.Unconditional QTL for SN，KNPS and TKW were detected using the inclusive composite interval mapping function of QTL IciMapping 3.2 software（Beijing，China）with stepwise regression and simultaneous consideration of all marker information（http://www. isbreeding.net/）.The‘Deletion'command was used to delete missing phenotypic data.

Dataon conditional phenotypic values yhk（T1/T2）were obtained from QGA Station 1.0（http://ibi.zju.edu.cn/software/ Qga/index.htm）［9］，where T1/T2 means for trait 1 conditioned on trait 2（for example，SN|TKW=SN conditioned on TKW）. Conditional QTLmappingwasconductedusingQTLIciMapping 3.2 software.For all QTL，the mapping parameters of each step andtheprobability ofthestepwise regressionwere setat1.0 cM and 0.001，respectively，for each mapping method.The threshold LOD scores werecalculated using 1000 permutations，with a type I error of 0.05.The QTL LOD values below 2.5 were ignored to increase the accuracy and reliability of QTL detection.

3.Results

3.1.Phenotypic variation and correlation

The means，standard deviation，maximum，and minimum values of SN，KNPS and TKW were calculated for all five environments（Table 1）.Strong transgressive segregations for all three traits indicated control by multiple genes.

Table 1-Phenotypic mean values of traits across five environments.

The Pearson correlation coefficients revealed significant negative correlations among SN，KNPS and TKW（Table 2）. When TKW was conditioned on SN and KNPS，TKW was significantly negatively correlated with SN and KNPS.When KNPS was conditioned on SN and TKW，KNPS had significantly negative correlations with TKW.When SN was conditioned on KNPSandTKW，SNhadasignificantlynegativecorrelationwith TKW.

3.2.Unconditional and conditional QTL mapping of the three yield components

A total of 92 QTL for SN，KNPS and TKW traits were detected，including 33 unconditional QTL and 59 conditional QTL，explaining 4.48-34.07%of the phenotypic variation（Tables 3，4，and 5；Fig.1）.These QTL were located in 17 chromosomes，except 3B，3D，5A and 7D.Fifty three QTL had positive additive effects，whereas 39 had negative additive effects.

3.2.1.Unconditional and conditional QTL mapping for SN

For SN，ten unconditional QTL were detected in the five environments accounting for 5.65-18.62%of the phenotypic variation（Table 3）.Four QTL，QSN-DH-1D-1.1，QSN-DH-3A，QSN-DH-6B and QSN-DH-6D，showed positive additive effects indicating favorable alleles derived from Huapei 3，whereas six QTL，QSN-DH-2A，QSN-DH-2B，QSN-DH-2D，QSN-DH-5D，QSN-DH-6A-1.3 and QSN-DH-6A-2.1，showed negative additive effects，indicating that the favorable alleles were from Yumai 57.

For SN|TKW，eight conditioned QTL were detected in the five environments，explaining 6.85-13.77%of the phenotypic variation（Table 3）.Of these，QSN-DH-5D and QSN-DH-6B were detected by both the unconditional and conditional analysis， indicating that they partly influenced SN by the variation in TKW.Six QTL，QSN-DH-1B，QSN-DH-1D-2.1，QSN-DH-3A-2.1，QSN-DH-5B，QSN-DH-6D-2.1 and QSN-DH-7A，were detected only by conditional QTL analysis，indicating that the effects of these QTL for SN were completely determined by TKW.

Table 2-Phenotypic correlations among SN，KNPS and TKW.

ForSN|KNPS，nineconditionalQTLweredetected，accounting for 5.76-13.49%of the phenotypic variation.Among them，seven QTL were detected by both unconditional and conditional QTL mapping.The additive effects of QSN-DH-2B and QSN-DH-3A-1.1 were similar，indicating that these QTL only affected the SN without reducing KNPS.Five QTL influenced SN by affecting KNPS.Two conditional QTL were not detected in the unconditional QTL analysis，indicating that phenotypic expression of the two QTL might be masked by their effects on KNPS.Three unconditional QTL，QSN-DH-1D-1.1，QSN-DH-2A and QSN-DH-6B，were not detected when KNPS was removed，indicating that the effects of these QTL on SN were caused by their effects on KNPS.

Two QTL，QSN-DH-6A-1.3 and QSN-DH-5D，were detected both in unconditional and conditional QTL analysis when they were conditioned on KNPS and TKW.QSN-DH-1D-2.1 was detected when conditioned on KNPS and TKW，but was not found in unconditional QTL analysis.These results indicated that the phenotypic expression of this QTL was masked by KNPS and TKW.

3.2.2.Unconditional and conditional QTL mapping for KNPS

Eleven QTL controlling KNPS were detected using unconditional QTLmapping，explaining6.23-34.07%ofthephenotypicvariation （Table4）.SixQTLQKNPS-DH-1A，QKNPS-DH-2A，QKNPS-DH-2D-1.1，QKNPS-DH-2D-1.2，QKNPS-DH-3A-1.2andQKNPS-DH-7B-2.1，had positive additive effects，indicating that the favorable alleles were derived from Huapei 3，whereas five QTL，QKNPS-DH-2B-1.1，QKNPS-DH-2B-2.1，QKNPS-DH-6A，QKNPS-DH-6B and QKNPS-DH-7B-1.1，had negative additive effects，indicating that the favorable alleles were from Yumai 57.

For KNPS|TKW，twelve QTL were detected in the five environmentsexplaining4.80-14.91%ofthephenotypic variation（Table 4）.Eight QTL，QKNPS-DH-3A-2.2，QKNPS-DH-7B-2.1，QKNPS-DH-2D-1.2，QKNPS-DH-6B，QKNPS-DH-2B-2.1，QKNPSDH-1A-1.1，QKNPS-DH-2D-1.1 and QKNPS-DH-6A，were detected in both unconditional and conditional analysis，indicating that the QTL partly influenced KNPS by increasing or decreasing variation in TKW.Four QTL QKNPS-DH-1A-2.1，QKNPS-DH-3A-1.1，QKNPSDH-4A and QKNPS-DH-4D-2.1，were detected only by conditional QTL analysis，indicating that their effects on KNPS were completely determined by TKW.

For KNPS|SN，eleven QTL were detected in the five environments，accounting for 6.45-15.36%of the phenotypic variation（Table4）.TenQTL，QKNPS-DH-2B-1.1，QKNPS-DH-7B-2.1，QKNPS-DH-2D-1.2，QKNPS-DH-6B，QKNPS-DH-2B-2.1，QKNPSDH-4D-1.1，QKNPS-DH-1A-1.1，QKNPS-DH-2D-1.1，QKNPS-DH-6A and QKNPS-DH-2A，were detected in both unconditional and conditional QTL analysis.QKNPS-DH-4D-1.1 was not detected in unconditional QTL analysis，indicating that its expression was masked by TKW.QKNPS-DH-7B-2.1，which is located in the Xbarc276.1-Xwmc396regiononchromosome7B，hadthe greatest genetic contribution to KNPS，explaining 34.07%of the phenotypic variance.The positive allele of this QTL was derived from Huapei 3.

Table 3 - Unconditional and conditional QTL for spike number per m2 （SN）.

Table 4 - Unconditional and conditional QTL for kernel number per spike （KNPS）.

Table 5 - Unconditional and conditional QTL for thousand kernel weight （TKW）. a

Fig.1-Genome locations for conditional and unconditional QTL for SN，KNPS and TKW.

3.2.3.Unconditional and conditional QTL mapping for TKW

For TKW，twelve QTL were detected by unconditional QTL mapping，explaining 4.48-17.68%of the total trait variation （Table 5）.Four QTL QTKW-DH-2B-2.1，QTKW-DH-5B and QTKWDH-7B，had negative additive effects，whereas eight，QTKW-DH-2B-1.2，QTKW-DH-2D-1.5，QTKW-DH-3A-1.1，QTKW-DH-3A-2.1，QTKW-DH-4A-1.2，QTKW-DH-4B，QTKW-DH-5B2，QTKW-DH-6A-1.2 and QTKW-DH-6A-2.4，had positive additive effects，with favorable alleles from Huapei 3.

For TKW|KNPS，ten QTL were detected，explaining 4.59-16.70%of the phenotypic variation（Table 5）.Of these，nine QTL were detected by both unconditional and conditional analysis. QTKW-DH-2B-1.2，QTKW-DH-2B-2.1 and QTKW-DH-3A-2.1 were not detected when conditioned on KNPS，indicating that these QTL influenced TKW through variation in KNPS.QTKW-DH-1A was not detected in unconditional QTL analysis.The results suggest that its phenotypic expression might be masked completely by its effects on KNPS.

For TKW|SN，nine QTL were detected.Ofthese，QTKW-DH-1B，QTKW-DH-4D-1.1，QTKW-DH-4D-2.1 and QTKW-DH-6D were not detected in unconditional QTL analysis，suggesting that the phenotypic expression of these QTL was masked by their effects on SN.QTKW-DH-2D-1.5 and QTKW-DH-7B were detected in unconditional and conditional QTL analysis，indicating that the two QTL partly influenced TKW through variation of SN.The other three QTL also partly influenced the TKW by affecting SN.

4.Discussion

4.1.ThedifferencesinunconditionalandconditionalQTLanalysis

The relationships between yield and its components are very complex due to varietal diversity of and environmental differences.Genes controlling SN，KNPS and TKW are considered to have a‘pleiotropic effect'or‘multigenic effect'，as they do not function in isolation.Zhu［9］and Wu et al.［20］introduced conditional QTL analysisbased onthe net effect of a QTL，which is helpful for detailed investigation of the genetic effects and can improve the sensitivity and accuracy of QTL mapping.In this study，SN，KNPS and TKW were analysed using both unconditional and conditional QTL mapping methods.Thirtythree unconditional QTL and 59 conditional QTL were detected. These QTL could be divided into 4 types for each trait.To illustrate using the example of KNPS conditioned on TKW）: （1）QTLthatweredetectedonlyinunconditionalQTLanalysison KNPS were detected when the genetic effect of TKW was excluded.This pattern indicates that the effects of these QTLon KNPS are completely dependent on their effects on TKW；（2）QTLthatwere detected in unconditional and conditional QTL analysis with very similar genetic effect values improved KNPS while not affecting the TKW；（3）QTL that were detected in unconditional and conditional QTL analysis with quite different genetic effects influenced KNPS through variation in TKW；and（4）QTL that were detected only in conditional QTL analysis had effects indicating that their phenotypic expression was masked by their effects on TKW.These QTL were detected only by conditional QTL analysis when the influence of TKW was excluded［10，17］.TheseQTLcouldbeusedtoselecthigh-yielding wheat cultivars with large spikes and a large number of heavy grains.

4.2.Stability of QTL

In the present study，eight QTL，QKNPS-DH-2D-1.2，QKNPS-DH-3A-2.2，QTKW-DH-2B-1.2，QTKW-DH-4A-1.2，QTKW-DH-6A-1.2，QSN-DH-6A-1.3，QTKW-DH-6A-2.4 and QTKW-DH-2D-1.5，were detected repeatedly in two or more environments.For example，QTKW-DH-2D-1.5 was detected in all five environments.The genetic contributions of this QTL to TKW in three environments （E1，E2 and E4）was more than 10%，indicating that QTKW-DH-2D-1.5 might be a major QTL consistently expressed in different environments.QTKW-DH-2D-1.5，located in the Xwmc170.2-Xgwm539 interval，had markers in common with QTKW.ncl-2D.2 （Xwmc181-Xwmc41）and Xgwm539［8］.QTKW-DH-6A-2.4，detected in four environments（E3-E5，P），was located in the interval Xbarc1055-Xwmc553 on chromosome 6A and accounted for 14.90%，6.18%，11.76%and 15.02%of total variation of TKW for E3，E4，E5 and P，respectively.It was located in the same region as QTgw.wa-6AL.e3［26］and qTgw6Ab［27］.These QTL were likely the same locus derived from of Huapei 3.These QTL were relatively stable and had the potential to be used in molecular markerassisted breeding.

4.3.Comparison of the present study with previous work It is widely accepted that detection of stable，major QTL has high significance for marker-assisted selection in different environments.In the present study eight QTL detected by unconditional and conditional analysis were located in similar chromosome intervals of chromosomes as detected in previous studies.

QSN-DH-1D-1.1，located in region Xcfd19-Xwmc93 on chromosome 1D，explained 9.78%of the phenotypic variation in SN. This interval includes marker Xwmc93 for QSn.sdau-1A.e4，which was located in the region of Xwmc93-Xgwm135.［28］.QSN-DH-1D and QSn.sdau-1A.e4 were likely the same QTL controlling SN.

QKNPS-DH-2B-2.1 was located in interval Xwmc179-Xbarc373 on chromosome 2B.This QTL was close to QKer.macs-2B（interval Xbarc55-Xbarc167）with the distance between Xbarc167 and Xwmc179 being 1 cM in the linkage map of Patil et al.［4］.

QSN-DH-2D，located in region Xwmc170.2-Xgwm539，had markers in common with QTKW.ncl-2D.2（Xwmc181-Xwmc41）and marker Xgwm539［8］.It was detected in both unconditional and conditional QTL analysis，and the absolute value of the additive effects varied only slightly.This locus controlled both KNPS and SN.This QTL was located in a region different from qSgn2D（Xgwm261-Xgwm296）［27］indicating that it may be a different QTL.A QTL at the same or a similar location on chromosome 2D detected by B?rner et al.［6］controlled yield and was associated with photoperiod gene Ppd-D1.This QTL was speculated to control both yield and photoperiod.Rht8，which is located on chromosome 2DS，was reported to increase KNPS［29］.In the present study，we also detected a QTL that controlled SN，KNPS and TKW.Further investigations are required to confirm the relationship of these QTL with Rht8.

4.4.Implications of QTL for wheat improvement

Unconditional and conditionalmapping methodshelptoreveal the genetic basis of target traits and relationships among relevant traits.The findings can be used in MAS for precise selection of a desirable trait［10］or for simultaneous improvements of several target traits［30］.In the present study，QKNPSDH-1A-1.1，QKNPS-DH-2D-1.1andQKNPS-DH-6A，explaining8.60，6.23 and 6.67%of the phenotypic variation，respectively，increased KNPS without decreasing SN and TKW.QSN-DH-2B and QSN-DH-3A-1.1，accounting for 5.65%and 5.76%of the phenotypicvariation，respectively，improvedSNwithout decreasing KNPS.QKNPS-DH-2B-2.1 accounting for 11.39%of the phenotypic variation improved KNPS without decreasing SN.QTKW-DH-4B，QTKW-DH-5BandQTKW-DH-7B，which explained 5.08%，6.92%and 4.48%of the phenotypic variation，respectively，increased TKW without decreasing KNPS.These findings may be helpful in resolving contradictions among KNPS，SN and TKW and may have theoretical and practical importance for development of high yielding wheat varieties.

5.Conclusion

Thirty-three unconditional QTL and 59 conditional QTL controlling SN，KNPS and TKW were detected.QSN-DH-2B and QSNDH-3A-1.1 improved SN without decreasing KNPS.QKNPS-DH-2B-2.1 improved KNPS without decreasing SN.QKNPS-DH-1A-1.1，QKNPS-DH-2D-1.1 and QKNPS-DH-6A influenced KNPS，TKW and SN.The overall analysis showed that improvement of KNPS had no negative effects on TKW and SN.QTKW-DH-4B，QTKW-DH-5BandQTKW-DH-7BimprovedTKWwithout decreasing KNPS.These QTL could improve one or two yield traits with only slight or no detriment effects on other yield components.Their use may help to reduce the problem of negative correlations among the three yield component traits. The findings could support molecular breeding of wheat and could be useful for breeders attempting to combine genes for high-yielding traits in developing wheat varieties with the best balance of KNPS，TKW and SN.

Acknowledgments

This work was funded by the National Natural Science Foundation ofChina（No.31171554），Major Projects for DevelopmentofNewGeneticallyModifiedCrops（No. 2011ZX08002-003），F(xiàn)und for the Doctoral Program of Higher Education of China（No.20123702110016），and the Natural Science Foundation of Shandong（No.ZR2015CM036）.

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19 November 2015

*Corresponding author.Tel./fax:+86 538 8242040.

E-mail address:jctian9666@163.com（J.Tian）.

Peer review under responsibility of Crop Science Society of China and Institute of Crop Science，CAAS.

http://dx.doi.org/10.1016/j.cj.2016.01.007

2214-5141/?2016 Crop Science Society of China and Institute of Crop Science，CAAS.Production and hosting by Elsevier B.V.This is an open access article under the CC BY-NC-ND license（http://creativecommons.org/licenses/by-nc-nd/4.0/）.