Mixed-effect model development for functional mapping

Wang Zijian; Ye Meixia; Zhang Han; Wu Rongling

doi:10.12171/j.1000-1522.20220416

Journal of Beijing Forestry University > 2024 > 46(5): 163-172. > DOI: 10.12171/j.1000-1522.20220416

Wang Zijian, Ye Meixia, Zhang Han, Wu Rongling. Mixed-effect model development for functional mapping[J]. Journal of Beijing Forestry University, 2024, 46(5): 163-172. DOI: 10.12171/j.1000-1522.20220416

Citation:

PDF (1843 KB)

Mixed-effect model development for functional mapping

Center of Computational Biology, School of Biological Sciences and Biotechnology, Beijing Forestry University, Beijing 100083, China

More Information

Received Date: October 16, 2022
Revised Date: February 15, 2023
Available Online: April 21, 2024

Graphical Abstract

Abstract

Abstract

Objective
Using the abundance of Escherichia coli strains and functional mapping model as the research foundation, this study explored the impact of mixed effects on the performance of functional mapping model by introducing fixed effects of the population and random effects caused by kinship relationship among individuals into the functional mapping model.
Method
Based on the framework of functional mapping, this study employed the growth data from dynamic cultures of Escherichia coli as a practical case. Subgroups and SNP genotypes were considered as sources of fixed effects, and these fixed effect factors were integrated into the mapping model, leading to the extension of Q-matrix model. While maintaining the use of variance-covariance model for modeling random residuals, the Legendre model was employed to model random effects. A mixed-effect model analysis combining fixed effects with general random effects (model 1) was conducted. Additionally, the restricted maximum likelihood estimation method was utilized to derive variance-covariance parameters, random effects, and fixed effects, enabling the analysis of a mixed model combining fixed effects with random effects arising from kinship relationships (model 2). Finally, the Zwald test method was utilized to derive the calculation method for p-values at each marker locus.
Result
(1) In both models, 95% of the markers exhibited p-values that were consistent with the expected values, resulting in satisfactory upward curvature in the QQ plot. (2) Compared with model 1, model 2 detected a greater number of SNP loci, indicating that model 2 provided a stronger explanation for the random effects caused by kinship relationship. (3) Computer simulation results revealed that when the sample size was small and the heritability was low, the false-positive rate of the model was 4.77%. However, when the sample size reached 800 and the heritability was 1%, the discovery rate of quantitative trait loci (QTL) by the model can exceed 70%. Alternatively, when the sample size was 400 and the heritability exceeded 1.5%, the QTL discovery rate can also exceed 70%.
Conclusion
The mixed model approach proposed in this study, which introduces fixed effects and random effects caused by kinship relationship into the functional mapping model, effectively improves the theory of functional localization. This approach exhibits excellent calibration capabilities for covariate factors in fixed effects and can effectively dissect random effects from remaining residuals. This lays a solid foundation for subsequent improvements in functional localization and the development of software packages for the fixed effects plus kinship (Q + K) model.
- functional mapping,
- association analysis,
- mixed effect,
- restricted maximum likelihood estimation,
- quantitative trait loci (QTL)

FullText(HTML)

References (33)

References

[1]	Das K, Li J, Fu G, et al. Dynamic semiparametric Bayesian models for genetic mapping of complex trait with irregular longitudinal data[J]. Statistics in Medicine, 2013, 32(3): 509−523. doi: 10.1002/sim.5535
[2]	Sun L D, Wu R L. Mapping complex traits as a dynamic system[J]. Physics of Life Reviews, 2015, 13: 155−185. doi: 10.1016/j.plrev.2015.02.007
[3]	Ma C X, Casella G, Wu R. Functional mapping of quantitative trait loci underlying the character process: a theoretical framework[J]. Genetics, 2002, 161(4): 1751−1762. doi: 10.1093/genetics/161.4.1751
[4]	甘静雯. 基于随机微分方程的复杂性状功能作图模型构建[D]. 北京: 北京林业大学, 2021. Gan J W. Construction of functional mapping model for complex traits based on stochastic differential equations[D]. Beijing: Beijing Forestry University, 2021.
[5]	Lou X, Yang M, Wu R L, et al. A general statistical framework for unifying interval and linkage disequilibrium mapping: towards highresolution mapping of quantitative traits[J]. Journal of the American Statistical Association, 2005, 100: 158−171.
[6]	Wu R L, Ma C X, Lin M, et al. A general framework for analyzing the genetic architecture of developmental characteristics[J]. Genetics, 2004, 166(3): 1541−1551. doi: 10.1534/genetics.166.3.1541
[7]	Wu R L, Lin M. Functional mapping: how to map and study the genetic architecture of dynamic complex traits[J]. Nature Reviews Genetics, 2006, 7(3): 229−237. doi: 10.1038/nrg1804
[8]	Chitwood D H, Topp C N. Revealing plant cryptotypes: defining meaningful phenotypes among infinite traits[J]. Current Opinion in Plant Biology, 2015, 24: 54−60. doi: 10.1016/j.pbi.2015.01.009
[9]	Li Z, Sillanpaa M J. Dynamic quantitative trait locus analysis of plant phenomic data[J]. Trends in Plant Science, 2015, 20(12): 822−833. doi: 10.1016/j.tplants.2015.08.012
[10]	Ye M X, Jiang L B, Mao K, et al. Functional mapping of seasonal transition in perennial plants[J]. Briefings in Bioinformatics, 2015, 16(3): 526−535. doi: 10.1093/bib/bbu025
[11]	Zhao W, Hou W, Littell R C, et al. Structured antedependence models for functional mapping of multiple longitudinal traits[J]. Statistical Applications in Genetics and Molecular Biology, 2005, 4: e33.
[12]	Wu R L, Ma C X, Littell R C, et al. A logistic mixture model for characterizing genetic determinants causing differentiation in growth trajectories[J]. Genetics Resesearch, 2002, 79(3): 235−245. doi: 10.1017/S0016672302005633
[13]	Hou W, Li H, Zhang B, et al. A nonlinear mixed-effect mixture model for functional mapping of dynamic traits[J]. Heredity (Edinb), 2008, 101(4): 321−328. doi: 10.1038/hdy.2008.53
[14]	Zhu H, Lee S. Analysis of generalized linear mixed models via a stochastic approximation algorithm with Markov chain Monte-Carlo method[J]. Statistics and Computing, 2002, 12(2): 175−183.
[15]	Stoica P, Moses R, Friedlander B, et al. Maximum likelihood estimation of the parameters of multiple sinusoids from noisy measurements[J]. IEEE Transactions on Acoustics, Speech, and Signal Processing, 1989, 37(3): 379−392.
[16]	Yu J, Pressoir G, Briggs W H, et al. A unified mixed-model method for association mapping that accounts for multiple levels of relatedness[J]. Nature Genetics, 2006, 38(2): 203−208. doi: 10.1038/ng1702
[17]	Meyer K. WOMBAT: a tool for mixed model analyses in quantitative genetics by restricted maximum likelihood (REML)[J]. Journal of Zhejiang University-Science B, 2007, 8(11): 815−821. doi: 10.1631/jzus.2007.B0815
[18]	Hauck W W, Donner A. Corrigenda: “Wald’s test as applied to hypotheses in logit analysis”[J]. Journal of the American Statistical Association, 1980(370): 482.
[19]	Marchelan F, Osilenker B P. Estimates for Legendre-Sobolev polynomials that are orthogonal with respect to the scalar product[J]. Journal of Inequalities and Applications, 1997(6): 871−880.
[20]	Zhao W, Chen Y Q, Casella G, et al. A non-stationary model for functional mapping of complex traits[J]. Bioinformatics, 2005, 21(10): 2469−2477. doi: 10.1093/bioinformatics/bti382
[21]	Nelder J A, Mead R. A simplex method for function minimization[J]. Computer Science, 1965, 7: 308−313.
[22]	Lindstrom M J, Bates D M. Correction to: “Newton-Raphson and EM algorithms for linear mixed-effects models for repeated measures-data”[J]. Journal of the American Statistical Association, 1994(428): 1572.
[23]	Laird N M, Ware J H. Random-effects models for longitudinal data[J]. Biometrics, 1982, 38(4): 963−974. doi: 10.2307/2529876
[24]	Vanraden P M. Efficient methods to compute genomic predictions[J]. Journal of Dairy Science, 2008, 91(11): 4414−4423. doi: 10.3168/jds.2007-0980
[25]	Yang D, Jin Y, He X, et al. Inferring multilayer interactome networks shaping phenotypic plasticity and evolution[J]. Nature Communications, 2021, 12(1): 5304. doi: 10.1038/s41467-021-25086-5
[26]	Jiang L, He X, Jin Y, et al. A mapping framework of competition-cooperation QTLs that drive community dynamics[J]. Nature Communications, 2018, 9(1): 3010. doi: 10.1038/s41467-018-05416-w
[27]	Raj A, Stephens M, Pritchard J K. fastSTRUCTURE: variational inference of population structure in large SNP data sets[J]. Genetics, 2014, 197(2): 573−589. doi: 10.1534/genetics.114.164350
[28]	Jiang L, Clavijo J A, Sun L, et al. Plastic expression of heterochrony quantitative trait loci (hQTLs) for leaf growth in the common bean (Phaseolus vulgaris)[J]. New Phytologist, 2015, 207(3): 872−882. doi: 10.1111/nph.13386
[29]	Lander E S, Botstein D. Mapping mendelian factors underlying quantitative traits using RFLP linkage maps[J]. Genetics, 1989, 121(1): 185−199. doi: 10.1093/genetics/121.1.185
[30]	Kang H M, Zaitlen N A, Wade C M, et al. Efficient control of population structure in model organism association mapping[J]. Genetics, 2008, 178(3): 1709−1723. doi: 10.1534/genetics.107.080101
[31]	Zhang Z, Ersoz E, Lai C Q, et al. Mixed linear model approach adapted for genome-wide association studies[J]. Nature Genetics, 2010, 42(4): 355−360. doi: 10.1038/ng.546
[32]	Lippert C, Listgarten J, Liu Y, et al. Fast linear mixed models for genome-wide association studies[J]. Nature Methods, 2011, 8(10): 833−835. doi: 10.1038/nmeth.1681
[33]	Ning C, Wang D, Zhou L, et al. Efficient multivariate analysis algorithms for longitudinal genome-wide association studies[J]. Bioinformatics, 2019, 35(23): 4879−4885. doi: 10.1093/bioinformatics/btz304

Cited By

Cited by

Periodical cited type(2)

1.	李明清，过双飞，郑凯. 耦合价值与风险评价的矿产资源型城市生态安全格局构建：以马鞍山市为例. 湖南城市学院学报(自然科学版). 2025(01): 43-52 .
2.	智烈慧，马田田，高原，李晓文，邵冬冬，郭卫华，崔保山. 围垦开发下滨海湿地格局演变的自然-人为复合驱动过程. 生态学报. 2024(21): 9626-9635 .

Other cited types(0)

Get Citation

PDF

XML

Article views (378) PDF downloads (35) Cited by(2)

Turn off MathJax

Article Contents

Abstract

References

Mixed-effect model development for functional mapping

Abstract

References

Cited by

Periodical cited type(2)

Other cited types(0)

Catalog

Export File

Citation

Format

Content