# QTL×QTL×QTL Interaction Effects for Total Phenolic Content of Wheat Mapping Population of CSDH Lines under Drought Stress by Weighted Multiple Linear Regression

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

_{gw}parameter compared to aaa

_{p}in five cases, with the exception of severe drought in 2012. The results show that by using weighted regression on marker observations, the obtained estimates are closer to the ones obtained by the phenotypic method. The coefficients of determination for the weighted regression model were significantly higher than for the unweighted regression and ranged from 46.2% (control in 2010) to 95.0% (control in 2011). Considering this, it is clear that a three-way interaction had a significant effect on the expression of quantitative traits.

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Plant Material

#### 2.2. Estimation of the QTL×QTL×QTL Interaction Effects

#### 2.2.1. Estimation Based on the Phenotype

#### 2.2.2. Estimation Based on the Genotype

_{g}was based on the assumption that genes responsible for the total phenolic content were completely linked to observed molecular markers. After the selection of p markers (among all observed), determining the total phenolic content, the phenotypic observation model for DH lines is given as

**1**is the n-vector of ones, $\mu $ is the general mean,

**A**is the (n×p)-matrix of the form $\mathit{A}=\left[\begin{array}{cc}\begin{array}{cc}{\mathit{m}}_{{l}_{1}}& {\mathit{m}}_{{l}_{2}}\end{array}& \begin{array}{cc}\cdots & {\mathit{m}}_{{l}_{p}}\end{array}\end{array}\right]$, l

_{1}, l

_{2}, …, l

_{p}∈ {1, 2, …, q}, $\mathit{\beta}$ is the p-vector of unknown parameters of the form ${\mathit{\beta}}^{\prime}=\left[\begin{array}{cc}\begin{array}{cc}{a}_{{l}_{1}}& {a}_{{l}_{2}}\end{array}& \begin{array}{cc}\cdots & {a}_{{l}_{p}}\end{array}\end{array}\right]$,

**E**is the matrix for which columns are products of some columns of matrix

**A**, $\mathit{\gamma}$ is the vector of unknown parameters of the form ${\mathit{\gamma}}^{\prime}=\left[\begin{array}{cc}\begin{array}{cc}a{a}_{{l}_{1}{l}_{2}}& a{a}_{{l}_{1}{l}_{3}}\end{array}& \begin{array}{cc}\cdots & a{a}_{{l}_{p-1}{l}_{p}}\end{array}\end{array}\right]$,

**T**is the matrix for which columns are three-way products of some columns of matrix

**A**, $\mathit{\delta}$ is the vector of unknown parameters of the form ${\mathit{\delta}}^{\prime}=\left[\begin{array}{cc}\begin{array}{cc}aa{a}_{{l}_{1}{l}_{2}{l}_{3}}& aa{a}_{{l}_{1}{l}_{2}{l}_{4}}\end{array}& \begin{array}{cc}\cdots & aa{a}_{{l}_{p-2}{l}_{p-1}{l}_{p}}\end{array}\end{array}\right]$, and

**e**is the n-vector of random variables such that E(e

_{i}) = 0, Cov(e

_{i}, e

_{j}) = 0 for i≠j, i, j = 1, 2, …, n. The parameters ${a}_{{l}_{1}}$, ${a}_{{l}_{2}}$, …, ${a}_{{l}_{p}}$ are the additive effects of the genes controlling the total phenolic content, parameters $a{a}_{{l}_{1}{l}_{2}}$, $a{a}_{{l}_{1}{l}_{3}}$, …, $a{a}_{{l}_{p-1}{l}_{p}}$ are the additive×additive interaction effects and parameters $aa{a}_{{l}_{1}{l}_{2}{l}_{3}}$, $aa{a}_{{l}_{1}{l}_{2}{l}_{4}}$, …, $aa{a}_{{l}_{p-2}{l}_{p-1}{l}_{p}}$ are the additive×additive×additive interaction effects. It was assumed that epistatic and three-way epistatic interaction effects show only loci with significant additive gene action effects. Consequently, this assumption results in a decrease in the number of possible significant effects and makes the regression model more useful. Loci with significant additive effects of genes were located and estimated previously by Czyczyło-Mysza et al. [42].

#### Unweighted Regression

**G**is of full rank, the estimate of ${\mathit{\alpha}}_{\mathit{u}}$ from traditional (unweighted) multiple linear regression model is given by [46]

_{gu}effect of genes influencing the total phenolic content from a traditional (unweighted) multiple linear regression model can be found as

#### Weighted Regression

**W**of unknown variances of observations, which, however, may be empirically found by estimation. The selection of markers for the weighted regression is made by a similar method described for the unweighted case but concerns the weights for lines. In this model, the estimate of ${\mathit{\alpha}}_{\mathit{w}}$ is

_{gw}effect of genes influencing the total phenolic content from the weighted multiple linear regression model can be found as

## 3. Results

#### 3.1. Estimation Based on the Phenotype

_{p}) are presented in Table 1. In four of the six cases, the total aaa

_{p}effect was positive. A negative effect was observed for the 2011 and 2012 control groups. The highest total additive×additive×additive effect was observed for the 2012 severe drought group and the lowest for the 2011 control group. Triples interaction effects were statistically significant for all groups except the control group in 2012.

#### 3.2. Estimation Based on the Genotype

_{gu}) and weighted (aaa

_{gw}) multiple linear regression are presented in Table 2.

#### 3.2.1. Unweighted Regression

_{gu}effect ranged from –0.043 (control, 2010) to 0.688 (severe drought, 2012) (Table 2). The phenotypic variation of total phenolic content explained by the total triples interaction was similar in all five cases where the number of triples interactions was greater than zero and ranged from 32.4% (control, 2010) to 44.5% (severe drought, 2012) (Table 2).

#### 3.2.2. Weighted Regression

_{gu}), and weighted (aaa

_{gw}) multiple linear regression are presented in Table 3. Sixty-seven statistically significant triples interactions were observed. None of the QTL×QTL×QTL threes were significant in at least two cases: threes significant using weighted regression were not significant using unweighted regression and vice versa (Table 3). The QTLs most frequently found in triples interaction were gwm165.3 (22 times), gwm269.2 (11 times) and wmc429 (11 times). Using unweighted regression, the genes most frequently found in triples interaction were gwm165.3 (19 times), gwm269.2 (11 times) and wPt-0391 (9 times) (Table 3). Using weighted regression, the genes most frequently observed in triples interaction were wmc429 (eleven times), wPt-3738 (five times), wPt-6239 (five times) and wPt-6316 (also five times) (Table 3).

## 4. Discussion

_{gu}compared to assessment based on phenotypes alone in three cases (severe drought in 2010, control in 2012 and severe drought in 2012). In contrast, weighted regression yielded an improvement (in absolute value) in the evaluation of the aaa

_{gw}parameter compared to aaa

_{p}in five cases, with the exception of severe drought in 2012 (Table 1 and Table 2).

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Brodersen, C.R.; Roddy, A.B.; Wason, J.W.; McElrone, A.J. Functional Status of Xylem Through Time. Annu. Rev. Plant Biol.
**2019**, 70, 407–433. [Google Scholar] [CrossRef] [PubMed][Green Version] - Khan, M.A.; Iqbal, M.; Akram, M.; Ahmad, M.; Hassan, M.W.; Jamil, M. Recent Advances in Molecular Tool Development for Drought Tolerance Breeding in Cereal Crops: A Review. Zemdirb.-Agric.
**2013**, 100, 325–334. [Google Scholar] [CrossRef] - Seleiman, M.F.; Al-Suhaibani, N.; Ali, N.; Akmal, M.; Alotaibi, M.; Refay, Y.; Dindaroglu, T.; Abdul-Wajid, H.H.; Battaglia, M.L. Drought Stress Impacts on Plants and Different Approaches to Alleviate Its Adverse Effects. Plants
**2021**, 10, 259. [Google Scholar] [CrossRef] - Daryanto, S.; Wang, L.; Jacinthe, P.-A. Global Synthesis of Drought Effects on Cereal, Legume, Tuber and Root Crops Production: A Review. Agric. Water Manag.
**2017**, 179, 18–33. [Google Scholar] [CrossRef][Green Version] - Lisar, S.Y.S.; Motafakkerazad, R.; Hossain, M.M.; Rahman, I.M.M.; Lisar, S.Y.S.; Motafakkerazad, R.; Hossain, M.M.; Rahman, I.M.M. Water Stress in Plants: Causes, Effects and Responses; IntechOpen: Rijeka, Croatia, 2012; ISBN 978-953-307-963-9. [Google Scholar]
- Yadav, B.; Jogawat, A.; Rahman, M.S.; Narayan, O.P. Secondary Metabolites in the Drought Stress Tolerance of Crop Plants: A Review. Gene Rep.
**2021**, 23, 101040. [Google Scholar] [CrossRef] - Naikoo, M.I.; Dar, M.I.; Raghib, F.; Jaleel, H.; Ahmad, B.; Raina, A.; Khan, F.A.; Naushin, F. Chapter 9—Role and Regulation of Plants Phenolics in Abiotic Stress Tolerance: An Overview. In Plant Signaling Molecules; Khan, M.I.R., Reddy, P.S., Ferrante, A., Khan, N.A., Eds.; Woodhead Publishing: Duxford, UK, 2019; pp. 157–168. ISBN 978-0-12-816451-8. [Google Scholar]
- Hura, T.; Hura, K.; Ostrowska, A.; Grzesiak, M.; Dziurka, K. The Cell Wall-Bound Phenolics as a Biochemical Indicator of Soil Drought Resistance in Winter Triticale. Plant Soil Environ.
**2013**, 59, 189–195. [Google Scholar] [CrossRef][Green Version] - Latif, F.; Ullah, F.; Mehmood, S.; Khattak, A.; Khan, A.U.; Khan, S.; Husain, I. Effects of Salicylic Acid on Growth and Accumulation of Phenolics in Zea Mays L. under Drought Stress. Acta Agric. Scand. Sect. B
**2016**, 66, 325–332. [Google Scholar] [CrossRef] - Hussain, W.; Baenziger, P.S.; Belamkar, V.; Guttieri, M.J.; Venegas, J.P.; Easterly, A.; Sallam, A.; Poland, J. Genotyping-by-Sequencing Derived High-Density Linkage Map and Its Application to QTL Mapping of Flag Leaf Traits in Bread Wheat. Sci. Rep.
**2017**, 7, 16394. [Google Scholar] [CrossRef][Green Version] - Cyplik, A.; Bocianowski, J. Analytical and Numerical Comparisons of Two Methods of Estimation of Additive × Additive × Additive Interaction of QTL Effects. J. Appl. Genet.
**2022**, 63, 213–221. [Google Scholar] [CrossRef] - Sayed, M.A.; Nassar, S.M.; Moustafa, E.S.; Said, M.T.; Börner, A.; Hamada, A. Genetic Mapping Reveals Novel Exotic and Elite QTL Alleles for Salinity Tolerance in Barley. Agronomy
**2021**, 11, 1774. [Google Scholar] [CrossRef] - Ren, J.; Zhang, X.; Li, Z.; Wu, P. Genetic Analysis of Maternal Haploid Inducibility for In Vivo Haploid Induction in Maize. Agriculture
**2022**, 12, 845. [Google Scholar] [CrossRef] - Bocianowski, J.; Kozak, M.; Liersch, A.; Bartkowiak-Broda, I. A heuristic method of searching for interesting markers in terms of quantitative traits. Euphytica
**2011**, 181, 89–100. [Google Scholar] [CrossRef][Green Version] - Botero-Ramírez, A.; Laperche, A.; Guichard, S.; Jubault, M.; Gravot, A.; Strelkov, S.E.; Manzanares-Dauleux, M.J. Clubroot Symptoms and Resting Spore Production in a Doubled Haploid Population of Oilseed Rape (Brassica napus) Are Controlled by Four Main QTLs. Front. Plant Sci.
**2020**, 11, 604527. [Google Scholar] [CrossRef] - Gacek, K.; Bayer, P.E.; Anderson, R.; Severn-Ellis, A.A.; Wolko, J.; Łopatyńska, A.; Matuszczak, M.; Bocianowski, J.; Edwards, D.; Batley, J. QTL Genetic Mapping Study for Traits Affecting Meal Quality in Winter Oilseed Rape (Brassica Napus L.). Genes
**2021**, 12, 1235. [Google Scholar] [CrossRef] - Kabange, N.R.; Park, S.-Y.; Shin, D.; Lee, S.-M.; Jo, S.-M.; Kwon, Y.; Cha, J.-K.; Song, Y.-C.; Ko, J.-M.; Lee, J.-H. Identification of a Novel QTL for Chlorate Resistance in Rice (Oryza sativa L.). Agriculture
**2020**, 10, 360. [Google Scholar] [CrossRef] - Kwon, Y.-H.; Kabange, N.-R.; Lee, J.-Y.; Lee, S.-M.; Cha, J.-K.; Shin, D.-J.; Cho, J.-H.; Kang, J.-W.; Ko, J.-M.; Lee, J.-H. Novel QTL Associated with Shoot Branching Identified in Doubled Haploid Rice (Oryza sativa L.) under Low Nitrogen Cultivation. Genes
**2021**, 12, 745. [Google Scholar] [CrossRef] - Pegot-Espagnet, P.; Guillaume, O.; Desprez, B.; Devaux, B.; Devaux, P.; Henry, K.; Henry, N.; Willems, G.; Goudemand, E.; Mangin, B. Discovery of interesting new polymorphisms in a sugar beet (elite × exotic) progeny by comparison with an elite panel. Theor. Appl. Genet.
**2019**, 132, 3063–3078. [Google Scholar] [CrossRef][Green Version] - Lephuthing, M.C.; Khumalo, T.P.; Tolmay, V.L.; Dube, E.; Tsilo, T.J. Genetic Mapping of Quantitative Trait Loci Associated with Plant Height and Yield Component Traits in a Wheat (Triticum aestivum L.) Doubled Haploid Population Derived from Tugela-DN × Elands. Agronomy
**2022**, 12, 2283. [Google Scholar] [CrossRef] - Beheshtizadeh, H.; Fakheri, B.A.; Aghnoum, R.; Mahdinezhad, N.; Pourdad, S.S.; Masoudi, B. QTL mapping of grain yield and its components under normal and drought stress conditions in barley (Hordeum vulgare L.). Indian J. Genet. Plant Breed.
**2018**, 78, 69–80. [Google Scholar] [CrossRef] - Ku, L.X.; Sun, Z.H.; Wang, C.L.; Zhang, J.; Zhao, R.F.; Liu, H.Y.; Tai, G.Q.; Chen, Y.H. QTL mapping and epistasis analysis of brace root traits in maize. Mol. Breed.
**2012**, 30, 697–708. [Google Scholar] [CrossRef] - Yusuf, A.O.; Richter, J.-C.; Möllers, C. Genetic variation and QTL analysis of saturated fatty acids in two doubled haploid populations of oilseed rape (Brassica napus L.). Euphytica
**2022**, 218, 88. [Google Scholar] [CrossRef] - Krajewski, P.; Bocianowski, J.; Gawłowska, M.; Kaczmarek, Z.; Pniewski, T.; Święcicki, W.; Wolko, B. QTL for yield componenets and protein content: A multienvironment study of two pea (Pisum sativum L.) populations. Euphytica
**2012**, 183, 323–336. [Google Scholar] [CrossRef][Green Version] - Ali, F.; Chen, W.; Fiaz, S.; Wang, Y.; Wei, X.; Xie, L.; Jiao, G.; Shao, G.; Hu, S.; Tang, S.; et al. QTL Mapping for Grain Appearance Quality Traits Using Doubled Haploid Population of Rice Under Different Environments. Pak. J. Bot.
**2022**, 54, 1265–1275. [Google Scholar] [CrossRef] [PubMed] - Han, Y.; Tan, Y.; Hu, H.; Chang, W.; Dong, L.; Wang, Z.; Zhao, X.; Li, W.; Teng, W. Quantitative trait loci with additive and epistatic effects underlying resistance to two hg types of soybean cyst nematode. Plant Breed.
**2017**, 136, 720–727. [Google Scholar] [CrossRef] - Smeda, J.R.; Schilmiller, A.L.; Anderson, T.; Ben-Mahmoud, S.; Ullman, D.E.; Chappell, T.M.; Kessler, A.; Mutschler, M.A. Combination of Acylglucose QTL reveals additive and epistatic genetic interactions and impacts insect oviposition and virus infection. Mol. Breed.
**2018**, 38, 3. [Google Scholar] [CrossRef] - Dhariwal, R.; Fedak, G.; Dion, Y.; Pozniak, C.; Laroche, A.; Eudes, F.; Randhawa, H.S. High Density Single Nucleotide Polymorphism (SNP) Mapping and Quantitative Trait Loci (QTL) Analysis in a Biparental Spring Triticale Population Localized Major and Minor Effect Fusarium Head Blight Resistance and Associated Traits QTL. Genes
**2018**, 9, 19. [Google Scholar] [CrossRef][Green Version] - Pundir, S.; Sharma, R.; Kumar, D.; Singh, V.K.; Chaturvedi, D.; Kanwar, R.S.; Röder, M.S.; Börner, A.; Ganal, W.M.; Gupta, P.K.; et al. QTL mapping for resistance against cereal cyst nematode (Heterodera avenae Woll.) in wheat (Triticum aestivum L.). Sci. Rep.
**2022**, 12, 9586. [Google Scholar] [CrossRef] - Chase, K.; Adler, F.R.; Lark, K.G. EPISTAT: A computer program for identifying and testing interaction between pairs of quantitative trait loci. Theor. Appl. Genet.
**1997**, 94, 724–730. [Google Scholar] [CrossRef] - Holland, J.B. Computer note. EPISTACY: A SAS program for detecting two-locus epistatic interaction using genetic marker information. J. Hered.
**1998**, 89, 374–375. [Google Scholar] [CrossRef][Green Version] - Kao, C.-H.; Zeng, Z.-B.; Teasdale, R.D. Multiple interval mapping for quantitative trait loci. Genetics
**1999**, 152, 1203–1216. [Google Scholar] [CrossRef] - Zeng, Z.-B.; Kao, C.-H.; Batsen, C.J. Estimating the genetic architecture of quantitative traits. Genet. Res.
**1999**, 74, 279–289. [Google Scholar] [CrossRef] - Carlborg, Ö.; Andersson, L.; Kinghorn, B. The use of a genetic algorithm for simultaneous mapping interacting quantitative trait loci. Genetics
**2000**, 155, 2003–2010. [Google Scholar] [CrossRef] - Sen, S.; Churchill, G.A. A statistical framework for quantitative trait mapping. Genetics
**2001**, 159, 371–387. [Google Scholar] [CrossRef] - Bocianowski, J. The use of weighted multiple linear regression to estimate QTL-by-QTL epistatic effects. Genet. Mol. Biol.
**2012**, 35, 802–809. [Google Scholar] [CrossRef][Green Version] - Bateson, W.; Mendel, G. Mendel’s Principles of Heredity: A Defence, with a Translation of Mendel’s Original Papers on Hybridization; Cambridge University Press: Cambridge, UK, 1902. [Google Scholar] [CrossRef][Green Version]
- Czyczyło-Mysza, I.; Tyrka, M.; Marcinska, I.; Skrzypek, E.; Karbarz, M.; Dziurka, M.; Hura, T.; Dziurka, K.; Quarrie, S.A. Quantitative trait loci for leaf chlorophyll fluorescence parameters, chlorophyll and carotenoid contents in relation to biomass and yield in bread wheat and their chromosome deletion bin assignments. Mol. Breed.
**2013**, 32, 189–210. [Google Scholar] [CrossRef][Green Version] - Singleton, V.L.; Rossi, J.A. Colorimetry of total phenolics with phosphomolybdic-phosphotungstic acid reagents. Am. J. Enol. Viticult.
**1965**, 16, 144–158. [Google Scholar] - Cyplik, A.; Sobiech, A.; Tomkowiak, A.; Bocianowski, J. Genetic Parameters for Selected Traits of Inbred Lines of Maize (Zea mays L.). Appl. Sci.
**2022**, 12, 6961. [Google Scholar] [CrossRef] - Kaczmarek, Z.; Surma, M.; Adamski, T. Epistatic effects in estimation of the number of genes on the basis of doubled haploid lines. Genet. Pol.
**1988**, 29, 353–359. [Google Scholar] - Czyczyło-Mysza, I.M.; Cyganek, K.; Dziurka, K.; Quarrie, S.; Skrzypek, E.; Marcińska, I.; Myśków, B.; Dziurka, M.; Warchoł, M.; Kapłoniak, K.; et al. Genetic Parameters and QTLs for Total Phenolic Content and Yield of Wheat Mapping Population of CSDH Lines under Drought Stress. Int. J. Mol. Sci.
**2019**, 20, 6064. [Google Scholar] [CrossRef][Green Version] - Bocianowski, J.; Krajewski, P. Comparison of the genetic additive effect estimators based on phenotypic observations and on molecular marker data. Euphytica
**2009**, 165, 113–122. [Google Scholar] [CrossRef] - Jansen, R.C.; Stam, P. High resolution of quantitative traits into multiple loci via interval mapping. Genetics
**1994**, 136, 1447–1455. [Google Scholar] [CrossRef] [PubMed] - Province, M.A. 30 Sequential methods of analysis for genome scan. Adv. Genet.
**2001**, 42, 499–514. [Google Scholar] [CrossRef] [PubMed] - Searle, S.R. Matrix Models for Unbalanced Data; John Wiley & Sons, Inc.: New York, NY, USA, 1982; pp. 1–154. [Google Scholar]
- Quarrie, S.A.; Steed, A.; Calestani, C.; Semikhodskii, A.; Lebreton, C.; Chinoy, C.; Steele, N.; Pljevljakusic, D.; Waterman, E.; Weyen, J.; et al. A high-density genetic map of hexaploid wheat (Triticum aestivum L.) from the cross Chinese Spring × SQ1 and its use to compare QTLs for grain yield across a range of environments. Theor. Appl. Genet.
**2005**, 110, 865–880. [Google Scholar] [CrossRef] [PubMed] - Fu, Y.B.; Ritland, K. Marker-Based Inferences About Epistasis for Genes Influencing Inbreeding Depression. Genetics
**1996**, 144, 339–348. [Google Scholar] [CrossRef] - Nap, J.P.; Canner, A.J.; Mlynarova, L.; Stiekema, W.J.; Jansen, R.C. Dissection of a Synthesized Quantitative Trait to Characterize Transgene Interactions. Genetics
**1997**, 147, 315–320. [Google Scholar] [CrossRef] - Routman, E.J.; Cheverud, J.M. Gene effects on a quantitative trait: Two-locus epistatic effects measured at microsatellite markers and at estimated QTL. Evolution
**1997**, 51, 1654–1662. [Google Scholar] [CrossRef] - Bocianowski, J.; Nowosad, K. Mixed linear model approaches in mapping QTLs with epistatic effects by a simulation study. Euphytica
**2015**, 202, 459–467. [Google Scholar] [CrossRef][Green Version] - Slim, L.; Chatelain, C.; Azencott, C.A.; Vert, J.P. Novel methods for epistasis detection in genome-wide association studies. PLoS ONE
**2020**, 15, e0242927. [Google Scholar] [CrossRef] - Rieger, R.; Michaelis, A.; Green, M.M. A Glossary of Genetics and cytogenetics: Classical and Molecular; Springer: New York, NY, USA, 1968; ISBN 9780387076683. [Google Scholar]

**Table 1.**Minimal and maximal values of average for lines, means for all doubled haploid lines for total phenolic content, coefficient of variation, phenotypic estimates of the total additive×additive×additive effect (aaa

_{p}) and the number of genes (the number of effective factors).

Year | 2010 | 2011 | 2012 | |||
---|---|---|---|---|---|---|

Stress | Control | Severe Drought | Control | Severe Drought | Control | Severe Drought |

Minimal | 7.104 | 6.499 | 7.164 | 6.231 | 7.645 | 4.626 |

Maximal | 14.414 | 12.682 | 16.321 | 15.070 | 13.781 | 13.023 |

Mean | 10.450 | 9.435 | 11.993 | 10.214 | 10.736 | 8.204 |

Coefficient of variation | 18.06 | 18.72 | 15.39 | 15.51 | 14.34 | 23.63 |

aaa_{p} | 0.309 * | 0.156 * | −0.250 * | 0.437 ** | −0.023 | 0.620 *** |

The number of genes (the number of effective factors) | 4.617 | 3.824 | 5.050 | 6.021 | 4.164 | 4.846 |

**Table 2.**Genotypic estimates of the total additive×additive×additive effects estimated based on unweighted (aaa

_{gu}) and weighted (aaa

_{gw}) multiple linear regression.

Year | 2010 | 2011 | 2012 | |||||
---|---|---|---|---|---|---|---|---|

Stress | Control | Severe Drought | Control | Severe Drought | Control | Severe Drought | ||

Unweighted | QTLs number | 6 | 5 | 4 | 6 | 7 | 6 | |

Number of aaa_{gu} | 8 | 1 | 0 | 2 | 14 | 8 | ||

aaa_{gu} effects | Min. | −0.288 | 0.350 | −0.489 | −0.410 | −0.138 | ||

Max. | 0.533 | 0.350 | 0.569 | 0.538 | 0.409 | |||

Total | −0.043 | 0.350 | 0.110 | 0.170 | 0.688 | |||

R^{2} [in %] | 32.4 | 42.0 | 36.3 | 39.1 | 44.5 | |||

Weighted | QTLs number | 16 | 15 | 20 | 14 | 26 | 14 | |

Number of aaa_{gw} | 3 | 5 | 9 | 5 | 6 | 6 | ||

aaa_{gw} effects | Min. | −0.659 | −0.494 | −0.607 | −0.499 | −0.526 | −1.124 | |

Max. | 0.598 | 0.612 | 0.548 | 0.368 | 0.557 | 1.182 | ||

Total | 0.443 | −0.265 | 1.178 | −1.302 | −0.184 | −0.228 | ||

R^{2} [in %] | 46.2 | 61.4 | 95.0 | 58.8 | 78.9 | 58.5 |

**Table 3.**Genotypic estimates of the additive×additive×additive interaction effects for the particular QTL×QTL×QTL threes based on unweighted (aaa

_{gu}) and weighted (aaa

_{gw}) multiple linear regression.

Year | 2010 | 2011 | 2012 | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Stress | Control | Severe Drought | Control | Severe Drought | Control | Severe Drought | ||||||||

QTL1 (LG) | QTL2 (LG) | QTL3 (LG) | aaa_{gu} | aaa_{gw} | aaa_{gu} | aaa_{gw} | aaa_{gu} | aaa_{gw} | aaa_{gu} | aaa_{gw} | aaa_{gu} | aaa_{gw} | aaa_{gu} | aaa_{gw} |

dupw004b (1A) | wPt-3094 (3A) | wmc1 (3B) | 0.471 | |||||||||||

dupw004b (1A) | wPt-668160 (1A) | gwm635b (7A) | 0.612 | |||||||||||

wPt-3094 (3A) | gwm165.3 (4A) | wPt-0391 (4B) | 0.350 | |||||||||||

wPt-3094 (3A) | gwm635b (7A) | wPt-671748 (7D) | −0.494 | |||||||||||

cfa2262 (3A) | dupw004a (4A) | blt101.t7 (4D) | −0.499 | |||||||||||

blt4.1 (3B) | wPt-4048 (3B) | gwm269.2 (4A) | −0.138 | |||||||||||

blt4.1 (3B) | gwm269.2 (4A) | gwm165.3 (4A) | 0.049 | |||||||||||

wPt-6239 (3B) | blt101.t7 (4D) | wPt-2697 (5A) | −0.337 | |||||||||||

wPt-6239 (3B) | blt101.t7 (4D) | wmc83 (7A) | −0.348 | |||||||||||

rPt-8896 (3B) | wmc1 (3B) | gwm52 (3D) | −0.376 | |||||||||||

wPt-0021 (3B) | gwm52 (3D) | barc60 (4B) | −0.659 | |||||||||||

gwm269.2 (4A) | gwm165.3 (4A) | gwm205 (5D) | 0.008 | |||||||||||

gwm269.2 (4A) | gwm165.3 (4A) | barc44 (5D) | −0.152 | |||||||||||

gwm269.2 (4A) | gwm165.3 (4A) | m69p78.1 (7A) | −0.100 | |||||||||||

gwm269.2 (4A) | gwm205 (5D) | barc44 (5D) | 0.063 | |||||||||||

gwm269.2 (4A) | gwm205 (5D) | m69p78.1 (7A) | −0.263 | |||||||||||

gwm269.2 (4A) | barc44 (5D) | wPt-9834 (5A) | 0.533 | |||||||||||

gwm165.3 (4A) | gwm165.3 (4A) | wPt-667091 (7D) | 0.158 | |||||||||||

gwm165.3 (4A) | wPt-0391 (4B) | wPt-3883 (7A) | 0.026 | |||||||||||

gwm165.3 (4A) | wPt-0391 (4B) | wPt-667091 (7D) | −0.179 | |||||||||||

gwm165.3 (4A) | wPt-0391 (4B) | wmc243b (7D) | 0.247 | |||||||||||

gwm165.3 (4A) | gwm205 (5D) | m69p78.1 (7A) | 0.156 | |||||||||||

gwm165.3 (4A) | barc44 (5D) | m69p78.1 (7A) | −0.288 | |||||||||||

gwm165.3 (4A) | gwm174 (5D) | wPt-3883 (7A) | 0.026 | |||||||||||

gwm165.3 (4A) | gwm174 (5D) | wPt-667091 (7D) | 0.031 | |||||||||||

gwm165.3 (4A) | gwm174 (5D) | wmc243b (7D) | −0.161 | |||||||||||

gwm165.3 (4A) | wPt-3883 (7A) | wmc243b (7D) | −0.008 | |||||||||||

wPt-0391 (4B) | wPt-0391 (4B) | wPt-667091 (7D) | −0.410 | |||||||||||

wPt-0391 (4B) | gwm174 (5D) | wPt-3883 (7A) | 0.128 | |||||||||||

wPt-0391 (4B) | gwm174 (5D) | wmc243b (7D) | 0.538 | |||||||||||

wPt-0391 (4B) | wPt-3883 (7A) | wPt-667091 (7D) | −0.151 | |||||||||||

barc152 (1B) | wPt-6239 (3B) | gwm191b (3D) | −0.400 | |||||||||||

barc152 (1B) | m65p64.8_4B (4B) | wPt-8149 (7A) | −0.526 | |||||||||||

barc152 (1B) | m92p78.10 (2A) | m60p64.13_3B (3B) | 0.557 | |||||||||||

barc152 (1B) | wPt-8072 (2B) | gwm165.3 (4A) | −0.493 | |||||||||||

m65p64.8a (5B) | gwm271 (5B) | m69p78.1 (7A) | 0.504 | |||||||||||

gwm174 (5D) | wPt-3883 (7A) | wPt-667091 (7D) | −0.130 | |||||||||||

gwm174 (5D) | wPt-3883 (7A) | wmc243b (7D) | 0.055 | |||||||||||

psr648_1B (1B) | wmc181 (2A) | gwm285 (3B) | 0.598 | |||||||||||

m17p65.1 (1B) | cfd73 (2D) | wmc468 (4A) | −0.478 | |||||||||||

wmc432 (1D) | wPt-3738 (1D) | psp2151.3 (2A) | −0.640 | |||||||||||

wPt-3738 (1D) | tPt-0202 (3A) | gwm269.2 (4A) | −1.124 | |||||||||||

wPt-3738 (1D) | tPt-0202 (3A) | dupw004a (4A) | 1.182 | |||||||||||

wPt-3738 (1D) | gwm513 (4B) | wmc157 (7D) | 0.387 | |||||||||||

wPt-3738 (1D) | wmc429 (1D) | tPt-0202 (3A) | 0.354 | |||||||||||

wmc429 (1D) | cfd11 (2D) | wPt-10291 (3D) | −0.505 | |||||||||||

wmc429 (1D) | gwm30.1 (2D) | tPt-0202 (3A) | 0.481 | |||||||||||

wmc429 (1D) | wPt-7466 (2D) | wPt-9749 (2D) | −0.607 | |||||||||||

wmc429 (1D) | gwm269.2 (4A) | dupw004a (4A) | −0.387 | |||||||||||

wmc429 (1D) | wPt-6316 (1D) | wPt-7466 (2D) | 0.548 | |||||||||||

wmc429 (1D) | wPt-6316 (1D) | wPt-10291 (3D) | 0.436 | |||||||||||

wmc429 (1D) | wPt-6316 (1D) | gwm161 (3D) | 0.493 | |||||||||||

wmc429 (1D) | wPt-6316 (1D) | gwm165.3 (4A) | −0.511 | |||||||||||

wmc429 (1D) | wPt-6316 (1D) | gwm639.2 (5B) | 0.419 | |||||||||||

wmc429 (1D) | wPt-732556 (1D) | gwm30.1 (2D) | 0.424 | |||||||||||

m92p78.10 (2A) | wPt-6239 (3B) | gwm161 (3D) | 0.360 | |||||||||||

m92p78.10 (2A) | wPt-6239 (3B) | wPt-8149 (7A) | 0.317 | |||||||||||

wmc453a (2A) | wPt-3883 (7A) | wPt-8919 (7B) | 0.569 | |||||||||||

wmc453a (2A) | wmc283.1 (7A) | wPt-8919 (7B) | −0.459 | |||||||||||

psp2151.3 (2A) | blt4.1 (3B) | wPt-4048 (3B) | 0.201 | |||||||||||

psp2151.3 (2A) | blt4.1 (3B) | gwm269.2 (4A) | 0.136 | |||||||||||

psp2151.3 (2A) | blt4.1 (3B) | gwm165.3 (4A) | −0.095 | |||||||||||

psp2151.3 (2A) | wPt-4048 (3B) | gwm269.2 (4A) | 0.409 | |||||||||||

psp2151.3 (2A) | wPt-4048 (3B) | gwm165.3 (4A) | 0.091 | |||||||||||

psp2151.3 (2A) | gwm269.2 (4A) | gwm165.3 (4A) | 0.035 | |||||||||||

wPt-3949 (2B) | wmc257 (2B) | gwm165.3 (4A) | 0.368 | |||||||||||

wmc257 (2B) | wPt-2697 (5A) | gwm292_5D (5D) | −0.485 |

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |

© 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Cyplik, A.; Czyczyło-Mysza, I.M.; Jankowicz-Cieslak, J.; Bocianowski, J. QTL×QTL×QTL Interaction Effects for Total Phenolic Content of Wheat Mapping Population of CSDH Lines under Drought Stress by Weighted Multiple Linear Regression. *Agriculture* **2023**, *13*, 850.
https://doi.org/10.3390/agriculture13040850

**AMA Style**

Cyplik A, Czyczyło-Mysza IM, Jankowicz-Cieslak J, Bocianowski J. QTL×QTL×QTL Interaction Effects for Total Phenolic Content of Wheat Mapping Population of CSDH Lines under Drought Stress by Weighted Multiple Linear Regression. *Agriculture*. 2023; 13(4):850.
https://doi.org/10.3390/agriculture13040850

**Chicago/Turabian Style**

Cyplik, Adrian, Ilona Mieczysława Czyczyło-Mysza, Joanna Jankowicz-Cieslak, and Jan Bocianowski. 2023. "QTL×QTL×QTL Interaction Effects for Total Phenolic Content of Wheat Mapping Population of CSDH Lines under Drought Stress by Weighted Multiple Linear Regression" *Agriculture* 13, no. 4: 850.
https://doi.org/10.3390/agriculture13040850