Statistical considerations for genomic selection

Abstract

Genomic selection is becoming increasingly important in animal and plant breeding, and is attracting greater attention for human disease risk prediction. This review covers the most commonly used statistical methods and some extensions of them, i.e., ridge regression and genomic best linear unbiased prediction, Bayesian alphabet, and least absolute shrinkage and selection operator. Then it discusses the measurement of the performance of genomic selection and factors affecting the prediction of performance. Among the measurements of prediction performance, the most important and commonly used measurement is prediction accuracy. In simulation studies where true breeding values are available, accuracy of genomic estimated breeding value can be calculated directly. In real or industrial data studies, either training-testing approach or k-fold cross-validation is commonly employed to validate methods. Factors influencing the accuracy of genomic selection include linkage disequilibrium between markers and quantitative trait loci, genetic architecture of the trait, and size and composition of the training population. Genomic selection has been implemented in the breeding programs of dairy cattle, beef cattle, pigs and poultry. Genomic selection in other species has also been intensively researched, and is likely to be implemented in the near future.

Keywords

genomic estimated breeding value / genomic selection / linkage disequilibrium / statistical methods

References

[1] DekkersJ C M, HospitalF. The use of molecular genetics in the improvement of agricultural populations.Nature Reviews Genetics, 2002, 3(1): 22–32

[2] DekkersJ C. Commercial application of marker- and gene-assisted selection in livestock: strategies and lessons.Journal of Animal Science, 2004, 82 E-Suppl: E313–328

[3] MeuwissenT H E, HayesB J, GoddardM E. Prediction of total genetic value using genome-wide dense marker maps.Genetics, 2001, 157(4): 1819–1829

[4] SchaefferL R. Strategy for applying genome-wide selection in dairy cattle.Journal of Animal Breeding and Genetics, 2006, 123(4): 218–223

[5] HoerlA E, KennardR W. Ridge regression- biased estimation for nonorthogonal problems.Technometrics, 1970, 12(1): 55–67

[6] HowardR, CarriquiryA L, BeavisW D. Parametric and nonparametric statistical methods for genomic selection of traits with additive and epistatic genetic architectures.G3: Genes, Genomes, Genetics, 2014, 4(6): 1027–1046

[7] FriedmanJ, HastieT, TibshiraniR. Regularization paths for generalized linear models via coordinate descent.Journal of Statistical Software, 2010, 33(1): 1–22

[8] VanRadenP M. Efficient methods to compute genomic predictions.Journal of Animal Science, 2008, 91(11): 4414–4423

[9] HayesB J, VisscherP M, GoddardM E. Increased accuracy of artificial selection by using the realized relationship matrix.Genetical Research, 2009, 91(1): 47–60

[10] ChristensenO F, MadsenP, NielsenB, OstersenT, SuG. Single-step methods for genomic evaluation in pigs.Animal, 2012, 6(10): 1565–1571

[11] WolcA, ArangoJ, SettarP, FultonJ E, O’SullivanN P, PreisingerR, HabierD, FernandoR, GarrickD J, DekkersJ C M. Persistence of accuracy of genomic estimated breeding values over generations in layer chickens.Genetics, Selection, Evolution, 2011, 43(1): 23

[12] LegarraA, AguilarI, MisztalI. A relationship matrix including full pedigree and genomic information.Journal of Dairy Science, 2009, 92(9): 4656–4663

[13] ChristensenO F, LundM S. Genomic prediction when some animals are not genotyped.Genetics, Selection, Evolution, 2010, 42(1): 2

[14] LegarraA, ChristensenO F, AguilarI, MisztalI. Single step, a general approach for genomic selection.Livestock Science, 2014, 166: 54–65

[15] MisztalI. Inexpensive computation of the inverse of the genomic relationship matrix in populations with small effective population size.Genetics, 2016, 202(2): 401–409

[16] MisztalI, LegarraA, AguilarI. Using recursion to compute the inverse of the genomic relationship matrix.Journal of Dairy Science, 2014, 97(6): 3943–3952

[17] FragomeniB O, LourencoD A L, TsurutaS, MasudaY, AguilarI, LegarraA, LawlorT J, MisztalI. Hot topic: Use of genomic recursions in single-step genomic best linear unbiased predictor (BLUP) with a large number of genotypes.Journal of Dairy Science, 2015, 98(6): 4090–4094

[18] OstersenT, ChristensenO F, MadsenP, HenryonM. Sparse single-step method for genomic evaluation in pigs.Genetics, Selection, Evolution, 2016, 48(1): 48

[19] StrandénI, MäntysaariE A. Comparison of some equivalent equations to solve single-step GBLUP.In: Proceedings of the 10th World Congress on Genetics Applied to Livestock Production 2014, Vancouver, Canada, 2015

[20] MasudaY, MisztalI, TsurutaS, LegarraA, AguilarI, LourencoD A, FragomeniB O, LawlorT J. Implementation of genomic recursions in single-step genomic best linear unbiased predictor for US Holsteins with a large number of genotyped animals.Journal of Animal Science, 2016, 99(3): 1968–1974

[21] GianolaD, de los CamposG, HillW G, ManfrediE, FernandoR. Additive genetic variability and the Bayesian alphabet.Genetics, 2009, 183(1): 347–363

[22] HabierD, FernandoR L, KizilkayaK, GarrickD J. Extension of the bayesian alphabet for genomic selection.BMC Bioinformatics, 2011, 12(1): 186

[23] FernandoR L, DekkersJ C, GarrickD J. A class of Bayesian methods to combine large numbers of genotyped and non-genotyped animals for whole-genome analyses.Genetics, Selection, Evolution, 2014, 46(1): 50

[24] TibshiraniR. Regression shrinkage and selection via the Lasso.Journal of the Royal Statistical Society. Series B (Methodological), 1996, 58(1): 267–288

[25] EfronB, HastieT, JohnstoneI, TibshiraniR. Least angle regression.Annals of Statistics, 2004, 32(2): 407–451

[26] ParkT, CasellaG. The Bayesian lasso.Journal of the American Statistical Association, 2008, 103(482): 681–686

[27] ZouH, HastieT. Regularization and variable selection via the elastic net.Journal of the Royal Statistical Society. Series B (Statistical Methodology), 2005, 67(2): 301–320

[28] ZouH. The adaptive lasso and its oracle properties.Journal of the American Statistical Association, 2006, 101(476): 1418–1429

[29] ZhangZ, LiuJ, DingX, BijmaP, de KoningD J, ZhangQ. Best linear unbiased prediction of genomic breeding values using a trait-specific marker-derived relationship matrix.PLoS One, 2010, 5(9): e12648

[30] SuG, ChristensenO F, OstersenT, HenryonM, LundM S. Estimating additive and non-additive genetic variances and predicting genetic merits using genome-wide dense single nucleotide polymorphism markers.PLoS One, 2012, 7(9): e45293

[31] KangH, ZhouL, MrodeR, ZhangQ, LiuJ F. Incorporating single-step strategy into random regression model to enhance genomic prediction of longitudinal trait.Heredity, 2016

[32] SunX, QuL, GarrickD J, DekkersJ C M, FernandoR L. A fast EM algorithm for BayesA-like prediction of genomic breeding values.PLoS One, 2012, 7(11): e49157

[33] WellmannR, BennewitzJ. Bayesian models with dominance effects for genomic evaluation of quantitative traits.Genetical Research, 2012, 94(1): 21–37

[34] ErbeM, HayesB J, MatukumalliL K, GoswamiS, BowmanP J, ReichC M, MasonB A, GoddardM E. Improving accuracy of genomic predictions within and between dairy cattle breeds with imputed high-density single nucleotide polymorphism panels.Journal of Dairy Science, 2012, 95(7): 4114–4129

[35] JiangJ, ZhangQ, MaL, LiJ, WangZ, LiuJ F. Joint prediction of multiple quantitative traits using a Bayesian multivariate antedependence model.Heredity, 2015, 115(1): 29–36

[36] GianolaD, FernandoR L, StellaA. Genomic-assisted prediction of genetic value with semiparametric procedures.Genetics, 2006, 173(3): 1761–1776

[37] MaenhoutS, De BaetsB, HaesaertG, Van BockstaeleE. Support vector machine regression for the prediction of maize hybrid performance.Theoretical and Applied Genetics, 2007, 115(7): 1003–1013

[38] GianolaD, OkutH, WeigelK A, RosaG J M. Predicting complex quantitative traits with Bayesian neural networks: a case study with Jersey cows and wheat.BMC Genetics, 2011, 12(1): 87

[39] FernandesG A, RosaG J M, ValenteB D, CarvalheiroR, BaldiF, GarciaD A, GordoD G M, EspigolanR, TakadaL, TonussiR L, de AndradeW B F, MagalhaesA F B, CharduloL A L, TonhatiH, de AlbuquerqueL G. Genomic prediction of breeding values for carcass traits in Nellore cattle.Genetics, Selection, Evolution, 2016, 48(1): 1–8

[40] LuanT, WoolliamsJ A, LienS, KentM, SvendsenM, MeuwissenT H E. The accuracy of Genomic Selection in Norwegian red cattle assessed by cross-validation.Genetics, 2009, 183(3): 1119–1126

[41] DaetwylerH D, CalusM P L, Pong-WongR, de Los CamposG, HickeyJ M. Genomic prediction in animals and plants: simulation of data, validation, reporting, and benchmarking.Genetics, 2013, 193(2): 347–365

[42] PatryC, DucrocqV. Evidence of biases in genetic evaluations due to genomic preselection in dairy cattle.Journal of Dairy Science, 2011, 94(2): 1011–1020

[43] LiX, WangS, HuangJ, LiL, ZhangQ, DingX. Improving the accuracy of genomic prediction in Chinese Holstein cattle by using one-step blending.Genetics, Selection, Evolution, 2014, 46(1): 66

[44] VanRadenP M, Van TassellC P, WiggansG R, SonstegardT S, SchnabelR D, TaylorJ F, SchenkelF S. Invited review: reliability of genomic predictions for North American Holstein bulls.Journal of Dairy Science, 2009, 92(1): 16–24

[45] HabierD, FernandoR L, DekkersJ C M. The impact of genetic relationship information on genome-assisted breeding values.Genetics, 2007, 177(4): 2389–2397

[46] WientjesY C J, VeerkampR F, CalusM P L. The effect of linkage disequilibrium and family relationships on the reliability of genomic prediction.Genetics, 2013, 193(2): 621–631

[47] LegarraA, Robert-GraniéC, ManfrediE, ElsenJ M. Performance of genomic selection in mice.Genetics, 2008, 180(1): 611–618

[48] SaatchiM, McClureM C, McKayS D, RolfM M, KimJ, DeckerJ E, TaxisT M, ChappleR H, RameyH R, NorthcuttS L, BauckS, WoodwardB, DekkersJ C M, FernandoR L, SchnabelR D, GarrickD J, TaylorJ F. Accuracies of genomic breeding values in American Angus beef cattle using K-means clustering for cross-validation.Genetics, Selection, Evolution, 2011, 43(1): 40

[49] DaetwylerH D, VillanuevaB, WoolliamsJ A. Accuracy of predicting the genetic risk of disease using a genome-wide approach.PLoS One, 2008, 3(10): e3395

[50] DaetwylerH D, Pong-WongR, VillanuevaB, WoolliamsJ A. The impact of genetic architecture on genome-wide evaluation methods.Genetics, 2010, 185(3): 1021–1031

[51] GoddardM. Genomic selection: prediction of accuracy and maximisation of long term response.Genetica, 2009, 136(2): 245–257

[52] GoddardM E, HayesB J, MeuwissenT H E. Using the genomic relationship matrix to predict the accuracy of genomic selection.Journal of Animal Breeding and Genetics, 2011, 128(6): 409–421

[53] MehrbanH, LeeD H, MoradiM H, IlChoC, NaserkheilM, Ibáñez-EscricheN. Predictive performance of genomic selection methods for carcass traits in Hanwoo beef cattle: impacts of the genetic architecture.Genetics, Selection, Evolution, 2017, 49(1): 1

[54] HabierD, FernandoR L, DekkersJ C M. Genomic selection using low-density marker panels.Genetics, 2009, 182(1): 343–353

[55] SolbergT R, SonessonA K, WoolliamsJ A, MeuwissenT H E. Genomic selection using different marker types and densities.Journal of Animal Science, 2008, 86(10): 2447–2454

[56] KhatkarM S, MoserG, HayesB J, RaadsmaH W. Strategies and utility of imputed SNP genotypes for genomic analysis in dairy cattle.BMC Genomics, 2012, 13(1): 538

[57] WengZ, ZhangZ, DingX, FuW, MaP, WangC, ZhangQ. Application of imputation methods to genomic selection in Chinese Holstein cattle.Journal of Animal Science and Biotechnology, 2012, 3(1): 6

[58] WengZ, ZhangZ, ZhangQ, FuW, HeS, DingX. Comparison of different imputation methods from low- to high-density panels using Chinese Holstein cattle.Animal, 2013, 7(5): 729–735

[59] HayesB J, BowmanP J, ChamberlainA C, VerbylaK, GoddardM E. Accuracy of genomic breeding values in multi-breed dairy cattle populations.Genetics, Selection, Evolution, 2009, 41(1): 51

[60] HidalgoA M, BastiaansenJ W M, LopesM S, HarliziusB, GroenenM A M, de KoningD J. Accuracy of predicted genomic breeding values in purebred and crossbred pigs.G3: Genes, Genomes, Genetics, 2015, 5(8): 1575–1583

[61] MoghaddarN, SwanA A, van der WerfJ H J. Comparing genomic prediction accuracy from purebred, crossbred and combined purebred and crossbred reference populations in sheep.Genetics, Selection, Evolution, 2014, 46(1): 58

[62] de RoosA P W, HayesB J, GoddardM E. Reliability of genomic predictions across multiple populations.Genetics, 2009, 183(4): 1545–1553

[63] AkannoE C, SchenkelF S, SargolzaeiM, FriendshipR M, RobinsonJ A B. Persistency of accuracy of genomic breeding values for different simulated pig breeding programs in developing countries.Journal of Animal Breeding and Genetics, 2014, 131(5): 367–378

[64] MuirW M. Comparison of genomic and traditional BLUP-estimated breeding value accuracy and selection response under alternative trait and genomic parameters.Journal of Animal Breeding and Genetics, 2007, 124(6): 342–355

[65] MeuwissenT, GoddardM. Accurate prediction of genetic values for complex traits by whole-genome resequencing.Genetics, 2010, 185(2): 623–631

[66] ClarkS A, HickeyJ M, van der WerfJ H J. Different models of genetic variation and their effect on genomic evaluation.Genetics, Selection, Evolution, 2011, 43(1): 18

[67] IheshiulorO O M, WoolliamsJ A, YuX, WellmannR, MeuwissenT H E. Within- and across-breed genomic prediction using whole-genome sequence and single nucleotide polymorphism panels.Genetics, Selection, Evolution, 2016, 48(1): 15

[68] van BinsbergenR, CalusM P L, BinkM C A M, van EeuwijkF A, SchrootenC, VeerkampR F. Genomic prediction using imputed whole-genome sequence data in Holstein Friesian cattle.Genetics, Selection, Evolution, 2015, 47(1): 71

[69] Pérez-EncisoM, RincónJ C, LegarraA. Sequence- vs. chip-assisted genomic selection: accurate biological information is advised.Genetics, Selection, Evolution, 2015, 47(1): 43

[70] HeidaritabarM, CalusM P L, MegensH J, VereijkenA, GroenenM A M, BastiaansenJ W M. Accuracy of genomic prediction using imputed whole-genome sequence data in white layers.Journal of Animal Breeding and Genetics, 2016, 133(3): 167–179

[71] NiG, CaveroD, FangmannA, ErbeM, SimianerH. Whole-genome sequence-based genomic prediction in laying chickens with different genomic relationship matrices to account for genetic architecture.Genetics, Selection, Evolution, 2017, 49(1): 8

[72] MacLeodI M, HayesB J, GoddardM E. The effects of demography and long-term selection on the accuracy of genomic prediction with sequence data.Genetics, 2014, 198(4): 1671–1684

[73] DaetwylerH D, CapitanA, PauschH, StothardP, van BinsbergenR, BrøndumR F, LiaoX, DjariA, RodriguezS C, GrohsC, EsquerréD, BouchezO, RossignolM N, KloppC, RochaD, FritzS, EggenA, BowmanP J, CooteD, ChamberlainA J, AndersonC, VanTassellC P, HulseggeI, GoddardM E, GuldbrandtsenB, LundM S, VeerkampR F, BoichardD A, FriesR, HayesB J. Whole-genome sequencing of 234 bulls facilitates mapping of monogenic and complex traits in cattle.Nature Genetics, 2014, 46(8): 858–865

[74] DruetT, MacleodI M, HayesB J. Toward genomic prediction from whole-genome sequence data: impact of sequencing design on genotype imputation and accuracy of predictions.Heredity, 2014, 112(1): 39–47

[75] GuoG, LundM S, ZhangY, SuG. Comparison between genomic predictions using daughter yield deviation and conventional estimated breeding value as response variables.Journal of Animal Breeding and Genetics, 2010, 127(6): 423–432

[76] YangJ, BenyaminB, McEvoyB P, GordonS, HendersA K, NyholtD R, MaddenP A, HeathA C, MartinN G, MontgomeryG W, GoddardM E, VisscherP M. Common SNPs explain a large proportion of the heritability for human height.Nature Genetics, 2010, 42(7): 565–569

[77] WientjesY C J, CalusM P L, GoddardM E, HayesB J. Impact of QTL properties on the accuracy of multi-breed genomic prediction.Genetics, Selection, Evolution, 2015, 47(1): 42

[78] UemotoY, SasakiS, KojimaT, SugimotoY, WatanabeT. Impact of QTL minor allele frequency on genomic evaluation using real genotype data and simulated phenotypes in Japanese Black cattle.BMC Genetics, 2015, 16(1): 134

[79] SunC, VanRadenP M, ColeJ B, O’ConnellJ R. Improvement of prediction ability for genomic selection of dairy cattle by including dominance effects.PLoS One, 2014, 9(8): e103934

[80] GuoX, ChristensenO F, OstersenT, WangY, LundM S, SuG. Genomic prediction using models with dominance and imprinting effects for backfat thickness and average daily gain in Danish Duroc pigs.Genetics, Selection, Evolution, 2016, 48(1): 67

[81] NishioM, SatohM. Including dominance effects in the genomic BLUP method for genomic evaluation.PLoS One, 2014, 9(1): e85792

[82] SantosV S, Martins FilhoS, ResendeM D, AzevedoC F, LopesP S, GuimarãesS E, SilvaF F. Genomic prediction for additive and dominance effects of censored traits in pigs.Genetics and Molecular Research, 2016, 15(4)

[83] ErtlJ, LegarraA, VitezicaZ G, VaronaL, EdelC, EmmerlingR, GötzK U. Genomic analysis of dominance effects on milk production and conformation traits in Fleckvieh cattle.Genetics, Selection, Evolution, 2014, 46(1): 40

[84] XuS. An empirical Bayes method for estimating epistatic effects of quantitative trait loci.Biometrics, 2007, 63(2): 513–521

[85] WangD, Salah El-BasyoniI, Stephen BaenzigerP, CrossaJ, EskridgeK M, DweikatI. Prediction of genetic values of quantitative traits with epistatic effects in plant breeding populations.Heredity, 2012, 109(5): 313–319

[86] CaiX, HuangA, XuS. Fast empirical Bayesian LASSO for multiple quantitative trait locus mapping.BMC Bioinformatics, 2011, 12(1): 211

[87] HuZ, LiY, SongX, HanY, CaiX, XuS, LiW. Genomic value prediction for quantitative traits under the epistatic model.BMC Genetics, 2011, 12(1): 15

[88] LorenzanaR E, BernardoR. Accuracy of genotypic value predictions for marker-based selection in biparental plant populations.Theoretical and Applied Genetics, 2009, 120(1): 151–161

[89] JiangY, ReifJ C. Modeling epistasis in genomic selection.Genetics, 2015, 201(2): 759–768

[90] CosterA, BastiaansenJ W M, CalusM P L, van ArendonkJ A M, BovenhuisH. Sensitivity of methods for estimating breeding values using genetic markers to the number of QTL and distribution of QTL variance.Genetics, Selection, Evolution, 2010, 42(1): 9

[91] ZhongS, DekkersJ C M, FernandoR L, JanninkJ L. Factors affecting accuracy from genomic selection in populations derived from multiple inbred lines: a Barley case study.Genetics, 2009, 182(1): 355–364

[92] PszczolaM, StrabelT, MulderH A, CalusM P L. Reliability of direct genomic values for animals with different relationships within and to the reference population.Journal of Dairy Science, 2012, 95(1): 389–400

[93] RincentR, LaloëD, NicolasS, AltmannT, BrunelD, RevillaP, RodríguezV M, Moreno-GonzalezJ, MelchingerA, BauerE, SchoenC C, MeyerN, GiauffretC, BaulandC, JaminP, LabordeJ, MonodH, FlamentP, CharcossetA, MoreauL. Maximizing the reliability of genomic selection by optimizing the calibration set of reference individuals: comparison of methods in two diverse groups of maize inbreds (Zea mays L.).Genetics, 2012, 192(2): 715–728

[94] HabierD, FernandoR L, GarrickD J. Genomic BLUP decoded: a look into the black box of genomic prediction.Genetics, 2013, 194(3): 597–607

[95] ClarkS A, HickeyJ M, DaetwylerH D, van der WerfJ H J. The importance of information on relatives for the prediction of genomic breeding values and the implications for the makeup of reference data sets in livestock breeding schemes.Genetics, Selection, Evolution, 2012, 44(1): 4

[96] García-RuizA, ColeJ B, VanRadenP M, WiggansG R, Ruiz-LópezF J, Van TassellC P. Changes in genetic selection differentials and generation intervals in US Holstein dairy cattle as a result of genomic selection.Proceedings of the National Academy of Sciences of the United States of America, 2016, 113(28): E3995–E4004

[97] TaylorJ F, TaylorK H, DeckerJ E. Holsteins are the genomic selection poster cows.Proceedings of the National Academy of Sciences of the United States of America, 2016, 113(28): 7690–7692

[98] RomanosJ, RosénA, KumarV, TrynkaG, FrankeL, SzperlA, Gutierrez-AchuryJ, van DiemenC C, KanningaR, JankipersadsingS A, SteckA, EisenbarthG, van HeelD A, CukrowskaB, BrunoV, MazzilliM C, NúñezC, BilbaoJ R, MearinM L, BarisaniD, RewersM, NorrisJ M, IvarssonA, BoezenH M, LiuE, WijmengaC, PreventC D G. Improving coeliac disease risk prediction by testing non-HLA variants additional to HLA variants.Gut, 2014, 63(3): 415–422

[99] AbrahamG, Tye-DinJ A, BhalalaO G, KowalczykA, ZobelJ, InouyeM. Accurate and robust genomic prediction of celiac disease using statistical learning.PLoS Genetics, 2014, 10(2): e1004137

[100] WeiZ, WangK, QuH Q, ZhangH, BradfieldJ, KimC, FrackletonE, HouC, GlessnerJ T, ChiavacciR, StanleyC, MonosD, GrantS F, PolychronakosC, HakonarsonH. From disease association to risk assessment: an optimistic view from genome-wide association studies on type 1 diabetes.PLoS Genetics, 2009, 5(10): e1000678

[101] AbrahamG, HavulinnaA S, BhalalaO G, ByarsS G, De LiveraA M, YetukuriL, TikkanenE, PerolaM, SchunkertH, SijbrandsE J, PalotieA, SamaniN J, SalomaaV, RipattiS, InouyeM. Genomic prediction of coronary heart disease.European Heart Journal, 2016, 37(43): 3267–3278

[102] VazquezA I, VeturiY, BehringM, ShresthaS, KirstM, ResendeM F Jr, de Los CamposG. Increased proportion of variance explained and prediction accuracy of survival of breast cancer patients with use of whole-genome multiomic profiles.Genetics, 2016, 203(3): 1425–1438

[103] de MaturanaE L, ChanokS J, PicornellA C, RothmanN, HerranzJ, CalleM L, García-ClosasM, MarenneG, BrandA, TardónA, CarratoA, SilvermanD T, KogevinasM, GianolaD, RealF X, MalatsN. Whole genome prediction of bladder cancer risk with the Bayesian LASSO.Genetic Epidemiology, 2014, 38(5): 467–476

[104] VazquezA I, de los CamposG, KlimentidisY C, RosaG J, GianolaD, YiN, AllisonD B. A comprehensive genetic approach for improving prediction of skin cancer risk in humans.Genetics, 2012, 192(4): 1493–1502

[105] VisscherP M. Human complex trait genetics in the 21st century.Genetics, 2016, 202(2): 377–379

Acknowledgements

This work was supported by the National Natural Science Foundations of China (31272419, 31661143013), the National High Technology Research and Development Program of China (2013AA102503), China Agriculture Research System (CARS-36), and the Program for Changjiang Scholar and Innovation Research Team in University (IRT_15R62).

Compliance with ethics guidelines

Huimin Kang, Lei Zhou, and Jianfeng Liu declare that they have no conflicts of interest or financial conflicts to disclose.

This article is a review and does not contain any studies with human or animal subjects performed by any of the authors.

RIGHTS & PERMISSIONS

The Author(s) 2017. Published by Higher Education Press. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0)