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RESEARCH ARTICLE

Gene-to-phenotype models and complex trait genetics

Mark Cooper A B , Dean W. Podlich A and Oscar S. Smith A
+ Author Affiliations
- Author Affiliations

A Pioneer Hi-Bred International Inc., 7250 N.W. 62nd Avenue, PO Box 552, Johnston, IA 50131, USA.

B Corresponding author. Email: mark.cooper@pioneer.com

Australian Journal of Agricultural Research 56(9) 895-918 https://doi.org/10.1071/AR05154
Submitted: 9 May 2005  Accepted: 20 June 2005   Published: 28 September 2005

Abstract

The premise that is explored in this paper is that in some cases, in order to make progress in the design of molecular breeding strategies for complex traits, we will need a theoretical framework for quantitative genetics that is grounded in the concept of gene-networks. We seek to develop a gene-to-phenotype (G→P) modelling framework for quantitative genetics that explicitly deals with the context-dependent gene effects that are attributed to genes functioning within networks, i.e. epistasis, gene × environment interactions, and pleiotropy. The E(NK) model is discussed as a starting point for building such a theoretical framework for complex trait genetics. Applying this framework to a combination of theoretical and empirical G→P models, we find that although many of the context-dependent effects of genetic variation on phenotypic variation can reduce the rate of genetic progress from breeding, it is possible to design molecular breeding strategies for complex traits that on average will outperform phenotypic selection. However, to realise these potential advantages, empirical G→P models of the traits will need to take into consideration the context-dependent effects that are a consequence of epistasis, gene × environment interactions, and pleiotropy. Some promising G→P modelling directions are discussed.

Additional keywords: gene-networks, interaction, prediction, validation, complexity.


Acknowledgments

An earlier version of this paper was published in the Proceedings of the 4th International Crop Science Congress, held in Brisbane, 26 September–1 October 2004. We thank the Congress organisers for permission to publish this updated manuscript. Our many colleagues at Pioneer have contributed much to the ideas reviewed in this paper. We thank Stu Kauffman for many stimulating and thought-provoking discussions over the years. Bill Muir provided many valuable comments and suggestions on early and advanced drafts of this manuscript. The innovative research atmosphere that exists at the Santa Fe Institute and the discussions we have had with other researchers via this highly connected intellectual network node have contributed to the ideas reviewed in this paper. We also benefited from the free-ranging discussions with Graeme Hammer, Scott Chapman, Stephen Welch, François Tardieu, Bruce Walsh, and Fred van Eeuwijk, held in Brisbane during the 4th International Crop Science Congress.


References


Baker LH, Curnow RN (1969) Choice of population size and use of variation between replicate populations in plant breeding selection programs. Crop Science 9, 555–560. open url image1

Barabási A-L, Albert R (1999) Emergence of scaling in random networks. Science 286, 509–512.
Crossref | GoogleScholarGoogle Scholar | PubMed | open url image1

Barker T, Campos H, Cooper M, Dolan D, Edmeades G, Habben J, Schussler J, Wright D, Zinselmeier C (2005) Improving drought tolerance in maize. Plant Breeding Reviews 25, 173–253. open url image1

Bouchez A, Hospital F, Causse M, Gallais A, Charcosset A (2002) Marker-assisted introgression of favorable alleles at quantitative trait loci between maize elite lines. Genetics 162, 1945–1959.
PubMed |
open url image1

Brem RB, Kruglyak L (2005) The landscape of genetic complexity across 5,700 gene expression traits in yeast. Proceedings of the National Academy of Sciences of the United States of America 102, 1572–1577.
Crossref | GoogleScholarGoogle Scholar | PubMed | open url image1

Cahill DJ, Schmidt DH (2004) Use of marker assisted selection in a product development breeding program. ‘New directions for a diverse planet: Proceedings of the 4th International Crop Science Congress’. Brisbane, Australia, 26 September to 1 October 2004. (Ed.  T Fischer , N Turner , J Angus , L McIntyre , M Robertson , A Borrell , D Lloyd ) (Online Proceedings)
http://www.cropscience.org.au

Campos H, Cooper M, Habben JH, Edmeades GO, Schussler JR (2004) Improving drought tolerance in maize: a view from industry. Field Crops Research 90, 19–34.
Crossref | GoogleScholarGoogle Scholar | open url image1

Casti, JL (1997). ‘Reality rules: I. Picturing the world in mathematics, the fundamentals.’ (John Wiley and Sons Inc.: New York)

Casti, JL (1997). ‘Reality rules: II. Picturing the world in mathematics, the frontier.’ (John Wiley and Sons Inc.: New York)

Casti, JL (1997). ‘Would-be worlds: how simulation is changing the frontiers of science.’ (John Wiley and Sons Inc.: New York)

Castro AJ, Chen X, Corey A, Filichkina T, Hayes PM, Mundt C, Richardson K, Sandoval-Islas S, Vivar H (2003) Pyramiding and validation of quantitative trait locus (QTL) alleles determining resistance to barley stripe rust: effects on adult plant resistance. Crop Science 43, 2234–2239. open url image1

Chapman SC, Cooper M, Butler DG, Henzell RG (2000a) Genotype by environment interactions affecting grain sorghum. I. Characteristics that confound interpretation of hybrid yield. Australian Journal of Agricultural Research 51, 197–207.
Crossref | GoogleScholarGoogle Scholar | open url image1

Chapman SC, Cooper M, Hammer GL (2002) Using crop simulation to generate genotype by environment interaction effects for sorghum in water-limited environments. Australian Journal of Agricultural Research 53, 379–389.
Crossref | GoogleScholarGoogle Scholar | open url image1

Chapman SC, Cooper M, Hammer GL, Butler DG (2000b) Genotype by environment interactions affecting grain sorghum. II. Frequencies of different seasonal patterns of drought stress are related to location effects on hybrid yields. Australian Journal of Agricultural Research 51, 209–221.
Crossref | GoogleScholarGoogle Scholar | open url image1

Chapman S, Cooper M, Podlich D, Hammer G (2003) Evaluating plant breeding strategies by simulating gene action and dryland environment effects. Agronomy Journal 95, 99–113. open url image1

Chapman SC, Hammer GL, Butler DG, Cooper M (2000c) Genotype by environment interactions affecting grain sorghum. III. Temporal sequences and spatial patterns in the target population of environments. Australian Journal of Agricultural Research 51, 223–233.
Crossref | GoogleScholarGoogle Scholar | open url image1

Chardon F, Virlon B, Moreau L, Falque M, Joets J, Decousset L, Murigneux A, Charcosset A (2004) Genetic architecture of flowering time in maize as inferred from quantitative trait loci meta-analysis and synteny conservation with the rice genome. Genetics 168, 2169–2185.
Crossref | GoogleScholarGoogle Scholar | PubMed | open url image1

Cheverud JM, Routman EJ (1995) Epistasis and its contribution to genetic variance components. Genetics 139, 1455–1461.
PubMed |
open url image1

Clark AG (2000) Limits to prediction of phenotypes from knowledge of genotypes. Evolutionary Biology 32, 205–224. open url image1

Comstock RE (1977) Quantitative genetics and the design of breeding programs. ‘Proceedings of the International Conference on Quantitative Genetics’. (Ed.  E Pollack , O Kempthorne , TB Bailey ) pp. 705–718. (The Iowa State University Press: Ames, IA)


Cooper M, Chapman SC, Podlich DW, Hammer GL (2002a) The GP problem: quantifying gene-to-phenotype relationships. In Silico Biology 2, 151–164.
PubMed |
open url image1

Cooper, M ,  and  Hammer, GL (Eds) (1996). ‘Plant adaptation and crop improvement.’ (CAB International: Wallingford, UK)

Cooper M, Podlich DW (2002) The E(NK) model: extending the NK model to incorporate gene-by-environment interactions and epistasis for diploid genomes. Complexity 7, 31–47.
Crossref | GoogleScholarGoogle Scholar | open url image1

Cooper M, Podlich DW, Micallef KP, Smith OS, Jensen NM, Chapman SC, Kruger NL (2002) Complexity, quantitative traits and plant breeding: a role for simulation modelling in the genetic improvement of crops. ‘Quantitative genetics, genomics and plant breeding’. (Ed. MS Kang) pp. 143–166. (CABI Publishing: Wallingford, UK)

Cooper M, Smith OS, Graham G, Arthur WL, Feng L, Podlich DW (2004) Genomics, genetics and plant breeding: a private sector perspective. Crop Science 44, 1907–1913. open url image1

Coors JG (1999) Selection methodology and heterosis. ‘The genetics and exploitation of heterosis in crops’. (Eds JG Coors, S Pandey, TB Bailey, L McIntyre, M Robertson, A Borrell, D Lloyd) pp. 225–245. (ASA-CSSA-SSSA: Madison, WI)

Crutchfield JP (2003) When evolution is revolution—origins of innovation. ‘Evolutionary dynamics: exploring the interplay of selection, accident, neutrality, and function’. (Eds JP Crutchfield, P Schuster) pp. 101–133. (Oxford University Press: Oxford, UK)

Crutchfield JP, Schuster P (2003) Preface: dynamics of evolutionary processes. In ‘Evolutionary dynamics: exploring the interplay of selection, accident, neutrality, and function’. (Eds JP Crutchfield, P Schuster) (Oxford University Press: Oxford, UK)

Davidson EH, Rast JP, Oliveri P, Ransick A, Calestani C , et al. (2002) A genomic regulatory network for development. Science 295, 1669–1678.
Crossref | GoogleScholarGoogle Scholar | PubMed | open url image1

Dorogovtsev, SN ,  and  Mendes, JFF (2003). ‘Evolution of networks: from biological nets to the Internet and WWW.’ (Oxford University Press: Oxford, UK)

Duvick DN, Smith JSC, Cooper M (2004) Long-term selection in a commercial hybrid maize breeding program. Plant Breeding Reviews 24, 109–151. open url image1

van Eeuwijk FA, Cooper M, DeLacy IH, Ceccarelli S, Grando S (2001) Some vocabulary and grammar for the analysis of multi-environment trials, as applied to the analysis of FPB and PPB trials. Euphytica 122, 477–490.
Crossref | GoogleScholarGoogle Scholar | open url image1

van Eeuwijk FA, Malosetti M, Yin X, Struik PC, Stam P (2005) Statistical models for genotype by environment data: from conventional ANOVA models to eco-physiological QTL models. Australian Journal of Agricultural Research 56, 883–894. open url image1

Falconer, DS ,  and  Mackay, TFC (1996). ‘Introduction to quantitative genetics.’ 4th edn . (Longman: Essex, UK)

Fehr, WR (Ed.) (1984). ‘Genetic contributions to yield gains of five major crop plants.’ (ASA and CSSA: Madison, WI)

Fisher RA (1918) The correlation between relatives on the supposition of Mendelian inheritance. Transactions of the Royal Society of Edinburgh 52, 399–433. open url image1

Fraser, A ,  and  Burnell, D (1970). ‘Computer models in genetics.’ (McGraw Hill Book Company: New York)

Gavrilets, S (2004). ‘Fitness landscapes and the origin of species.’ (Princeton University Press: Princeton, NJ)

Goldman IL (2000) Prediction in plant breeding. Plant Breeding Reviews 19, 15–40. open url image1

Goodnight CJ (1999) Epistasis and heterosis. ‘The genetics and exploitation of heterosis in crops’. (Eds JG Coors, S Pandey, TB Bailey, L McIntyre, M Robertson, A Borrell, D Lloyd) pp. 59–68. (ASA-CSSA-SSSA: Madison, WI)

Gould, SJ (1989). ‘Wonderful life: the Burgess Shale and the nature of history.’ (W.W. Norton & Company: New York)

Grigorov MG (2005) Global properties of biological networks. Drug Discovery Today 10, 365–372.
Crossref | GoogleScholarGoogle Scholar | PubMed | open url image1

Hallauer, AR ,  and  Miranda Fo, JB (1988). ‘Quantitative genetics in maize breeding.’ 2nd edn . (Iowa State University Press: Ames, IA)

Hammer GL, Chapman S, van Oosterom E, Podlich DW (2005) Trait physiology and crop modelling as a framework to link phenotypic complexity to underlying genetic systems. Australian Journal of Agricultural Research 56, 947–960. open url image1

Harris SE, Sawhill BK, Wuensche A, Kauffman S (2002) A model of transcriptional regulatory networks based on biases in the observed regulation rules. Complexity 7, 23–40.
Crossref | GoogleScholarGoogle Scholar | open url image1

Hill WG (2005) A century of corn selection. Science 307, 683–684.
Crossref | GoogleScholarGoogle Scholar | PubMed | open url image1

Holland JB (2001) Epistasis and plant breeding. Plant Breeding Reviews 21, 27–92. open url image1

Hoogenboom G, White JW, Messina CD (2004) From genome to crop: integration through simulation modeling. Field Crops Research 90, 145–163.
Crossref | GoogleScholarGoogle Scholar | open url image1

Ideker T (2004) Systems biology 101—what you need to know. Nature Biotechnology 22, 473–475.
Crossref | GoogleScholarGoogle Scholar | PubMed | open url image1

Ideker T, Thorsson V, Ranish JA, Christmas R, Buhler J, Eng JK, Bumgarner R, Goodlett DR, Aebersold R, Hood L (2001) Integrated genomic and proteomic analyses of a systematically perturbed metabolic network. Science 292, 929–934.
Crossref | GoogleScholarGoogle Scholar | PubMed | open url image1

Jackson P, Robertson M, Cooper M, Hammer G (1996) The role of physiological understanding in plant breeding; from a breeding perspective. Field Crops Research 49, 11–37.
Crossref | GoogleScholarGoogle Scholar | open url image1

Janick, J (Ed.) (2004). ‘Plant breeding reviews 24, Part 1: Long-term selection: maize.’ (John Wiley and Sons, Inc.: Hoboken, NJ)

Janick, J (Ed.) (2004). ‘Plant breeding reviews 24, Part 2: Long-term selection: crops, animals, and bacteria.’ (John Wiley and Sons, Inc.: Hoboken, NJ)

Jeong H, Tombor B, Albert R, Oltvai ZN, Barabási A-L (2000) The large-scale organization of metabolic networks. Nature 407, 651–654.
Crossref | GoogleScholarGoogle Scholar | PubMed | open url image1

Karp PD (2001) Pathway databases: a case study in computational symbolic theories. Science 293, 2040–2044.
Crossref | GoogleScholarGoogle Scholar | PubMed | open url image1

Kauffman, SA (1993). ‘The origins of order: self-organization and selection in evolution.’ (Oxford University Press: New York)

Kauffman S, Peterson C, Samuelsson B, Troein C (2003) Random Boolean network models and the yeast transcriptional network. Proceedings of the National Academy of Sciences of the United States of America 100, 14796–14799.
Crossref | GoogleScholarGoogle Scholar | PubMed | open url image1

Kauffman S, Peterson C, Samuelsson B, Troein C (2004) Genetic networks with canalyzing Boolean rules are always stable. Proceedings of the National Academy of Sciences of the United States of America 101, 17102–17107.
Crossref | GoogleScholarGoogle Scholar | PubMed | open url image1

Keller M, Karutz C, Schmid JE, Stamp P, Winzeler M, Keller B, Messmer MM (1999) Quantitative trait loci for lodging resistance in a segregating wheat × spelt population. Theoretical and Applied Genetics 98, 1171–1182.
Crossref | GoogleScholarGoogle Scholar | open url image1

Kempthorne O (1988) An overview of the field of quantitative genetics. ‘Proceedings of the 2nd International Conference on Quantitative Genetics’. (Ed.  BS Weir , EJ Eisen , MM Goodman , G Namkoong , M Robertson , A Borrell , D Lloyd ) pp. 47–56. (Sinauer Associates, Inc.: Sunderland, MA)


Kitano H (2002) Looking beyond the details: a rise in system-oriented approaches in genetics and molecular biology. Current Genetics 41, 1–10.
Crossref | GoogleScholarGoogle Scholar | PubMed | open url image1

Kitano H (2004) Biological robustness. Nature Reviews Genetics 5, 826–837.
Crossref | GoogleScholarGoogle Scholar | PubMed | open url image1

Laurie CC, Chasalow SD, LeDeaux JR, McCarroll R, Bush D, Hauge B, Lai C, Clark D, Rocheford TR, Dudley JW (2004) The genetic architecture of response to long-term artificial selection for oil concentration in the maize kernel. Genetics 168, 2141–2155.
Crossref | GoogleScholarGoogle Scholar | PubMed | open url image1

Lee TI, Rinaldi NJ, Robert F, Odom DT, Bar-Joseph Z , et al. (2002) Transcriptional regulatory networks in Saccharomyces cerevisiae. Science 298, 799–804.
Crossref | GoogleScholarGoogle Scholar | PubMed | open url image1

Löffler C, Wei J, Fast T, Gogerty J, Langton S, Bergman M, Merrill B, Cooper M (2005) Classification of maize environments using crop simulation and geographic information systems. Crop Science 45, 1708–1716.
Crossref |
open url image1

Lynch, M ,  and  Walsh, B (1998). ‘Genetics and analysis of quantitative traits.’ (Sinauer Associates, Inc.: Sunderland, MA)

Mackay TFC (2004a) The genetic architecture of quantitative traits: lessons from Drosophila. Current Opinions in Genetics and Development 14, 1–5.
Crossref | GoogleScholarGoogle Scholar | open url image1

Mackay TFC (2004b) Complementing complexity. Nature Genetics 36, 1145–1147.
Crossref | GoogleScholarGoogle Scholar | PubMed | open url image1

Moreau L, Charcosset A, Gallais A (2004a) Experimental evaluation of several cycles of marker-assisted selection in maize. Euphytica 137, 111–118.
Crossref | GoogleScholarGoogle Scholar | open url image1

Moreau L, Charcosset A, Gallais A (2004b) Use of trial clustering to study QTL × environment effects for grain yield and related traits in maize. Theoretical and Applied Genetics 110, 92–105.
Crossref | GoogleScholarGoogle Scholar | PubMed | open url image1

Mueller LA, Zhang P, Rhee SY (2003) AraCyc: a biochemical pathway database for Arabidopsis. Plant Physiology 132, 453–460.
Crossref | GoogleScholarGoogle Scholar | PubMed | open url image1

Namkoong G, Lewontin RC, Yanchuk AD (2005) Plant genetic resource management: the next investments in quantitative and qualitative genetics. Genetic Resources and Crop Evolution 51, 853–862.
Crossref | GoogleScholarGoogle Scholar | open url image1

Nelson MR, Kardia SLR, Ferrell RE, Sing CF (2001) A combinatorial partitioning method to identify multilocus genotypic partitions that predict quantitative trait variation. Genome Research 11, 458–470.
Crossref | GoogleScholarGoogle Scholar | PubMed | open url image1

Nguyen, HT ,  and  Blum, A (Eds) (2004). ‘Physiology and biotechnology integration for plant breeding.’ (Marcel Dekker, Inc.: New York)

Niebur WS, Rafalski JA, Smith OS, Cooper M (2004) Applications of genomics technologies to enhance rate of genetic progress for yield of maize within a commercial breeding program. ‘New directions for a diverse planet: Proceedings of the 4th International Crop Science Congress’. Brisbane, Australia, 26 September to 1 October 2004. (Ed.  T Fischer , N Turner , J Angus , L McIntyre , M Robertson , A Borrell , D Lloyd ) (Online Proceedings)
www.cropscience.org.au

Nyquist WE (1991) Estimation of heritability and prediction of selection response in plant populations. Critical Reviews in Plant Sciences 10, 235–322. open url image1

Oltvai ZN, Barabási A-L (2002) Life’s complexity pyramid. Science 298, 763–764.
Crossref | GoogleScholarGoogle Scholar | PubMed | open url image1

Openshaw SJ, Frascaroli E (1997) QTL detection and marker-assisted selection for complex traits in maize. In ‘Proceedings of the 52nd Annual Corn and Sorghum Research Conference’. (American Seed Trade Association: Washington, DC)


Patil KR, Nielsen J (2005) Uncovering transcriptional regulation of metabolism by using metabolic network topology. Proceedings of the National Academy of Sciences of the United States of America 102, 2685–2689.
Crossref | GoogleScholarGoogle Scholar | PubMed | open url image1

Peccoud J, Vander Velden K, Podlich DW, Winkler C, Arthur L, Cooper M (2004) The selective values of alleles in a molecular network model are context-dependent. Genetics 166, 1715–1725.
Crossref | GoogleScholarGoogle Scholar | PubMed | open url image1

Podlich DW, Cooper M (1998) QU-GENE: a platform for quantitative analysis of genetic models. Bioinformatics 14, 632–653.
Crossref | GoogleScholarGoogle Scholar | PubMed | open url image1

Podlich DW, Cooper M (1999) Modelling plant breeding programs as search strategies on a complex response surface. Lecture Notes in Computer Science 1585, 171–178. open url image1

Podlich DW, Cooper M, Basford KE (1999) Computer simulation of a selection strategy to accommodate genotype. Plant Breeding 118, 17–28.
Crossref | GoogleScholarGoogle Scholar | open url image1

Podlich DW, Winkler CR, Cooper M (2004) Mapping as You Go: an effective approach for marker-assisted selection of complex traits. Crop Science 44, 1560–1571. open url image1

Ravasz E, Somera AL, Mongru DA, Oltvai ZN, Barabási A-L (2002) Hierarchical organization of modularity in metabolic networks. Science 297, 1551–1555.
Crossref | GoogleScholarGoogle Scholar | PubMed | open url image1

Reymond M, Muller B, Leonardi A, Charcosset A, Tardieu F (2003) Combining quantitative trait loci analysis and an ecophysiological model to analyze the genetic variability of the responses of maize leaf growth to temperature and water deficit. Plant Physiology 131, 664–675.
Crossref | GoogleScholarGoogle Scholar | PubMed | open url image1

Ribaut J-M, Hoisington D, Bänziger M, Setter TL, Edmeades GO (2004) Genetic dissection of drought tolerance in maize: a case study. ‘Physiology and biotechnology integration for plant breeding’. (Eds HT Nguyen, A Blum) pp. 571–609. (Marcel Dekker, Inc.: New York)

Schlosser, G ,  and  Wagner, GP (Eds) (2004). ‘Modularity in development and evolution.’ (The University of Chicago Press: Chicago, IL)

Schön CC, Utz HF, Groh S, Truberg B, Openshaw S, Melchinger AE (2004) Quantitative trait locus mapping based on resampling in a vast maize testcross experiment and its relevance to quantitative genetics for complex traits. Genetics 167, 485–498.
Crossref | GoogleScholarGoogle Scholar | PubMed | open url image1

Schrage, M (2000). ‘Serious play: how the world’s best companies simulate to innovate.’ (Harvard Business School Press: Boston, MA)

Schuster P (2004) Chemical reaction kinetics is back: Attempts to deal with complexity in biology. Complexity 10, 14–16.
Crossref | GoogleScholarGoogle Scholar | open url image1

Segrè D, DeLuna A, Church GM, Kishony R (2004) Modular epistasis in yeast metabolism. Nature Genetics 37, 77–83.
PubMed |
open url image1

Sing CF, Stengård JH, Kardia SLR (2003) Genes, environment, and cardiovascular disease. Arteriosclerosis, Thrombosis, and Vascular Biology 23, 1190–1196.
Crossref | GoogleScholarGoogle Scholar | PubMed | open url image1

Somerville C, Dangl J (2000) Plant biology in 2010. Science 290, 2077–2078.
Crossref | GoogleScholarGoogle Scholar | PubMed | open url image1

Strogatz SH (2001) Exploring complex networks. Nature 410, 268–276.
Crossref | GoogleScholarGoogle Scholar | PubMed | open url image1

Tardieu F (2003) Virtual plants: modeling as a tool for the genomics of tolerance to water deficit. Trends in Plant Science 8, 9–14.
Crossref | GoogleScholarGoogle Scholar | PubMed | open url image1

Tardieu F, Reymond M, Muller B, Granier C, Simonneau T, Sadok W, Welcker C (2005) Linking physiological and genetic analyses of the control of leaf growth under fluctuating environmental conditions. Australian Journal of Agricultural Research 56, 937–946. open url image1

The Complex Trait Consortium (2004) The collaborative cross, a community resource for the genetic analysis of complex traits. Nature Genetics 36, 1133–1137.
Crossref | GoogleScholarGoogle Scholar | PubMed | open url image1

Wade MJ (2001) Epistasis, complex traits, and mapping genes. Genetica 112–113, 59–69.
Crossref | GoogleScholarGoogle Scholar | PubMed | open url image1

Wade MJ (2002) A gene’s eye view of epistasis, selection, and speciation. Journal of Evolutionary Biology 15, 337–346.
Crossref | GoogleScholarGoogle Scholar | open url image1

Wagner A (2002) Estimating coarse gene network structure from large-scale gene perturbation data. Genome Research 12, 309–315.
Crossref | GoogleScholarGoogle Scholar | PubMed | open url image1

Walsh B (2005) The struggle to exploit non-additive variation. Australian Journal of Agricultural Research 56, 873–881. open url image1

Wang J, van Ginkel M, Podlich D, Ye G, Trethowan R, Pfeiffer W, DeLacy IH, Cooper M, Rajaram S (2003) Comparison of two breeding strategies by computer simulation. Crop Science 43, 1764–1773. open url image1

Wang J, van Ginkel M, Trethowan R, Ye G, DeLacy I, Podlich D, Cooper M (2004) Simulating the effects of dominance and epistasis on selection response in the CIMMYT wheat breeding program using QuCim. Crop Science 44, 2006–2018. open url image1

Watts DJ, Strogatz SH (1998) Collective dynamics of ‘small-world’ networks. Nature 393, 440–442.
Crossref | GoogleScholarGoogle Scholar | PubMed | open url image1

Weinberger ED (1991) Local properties of Kauffman’s NK model, a tuneably rugged energy landscape. Physical Review A 44, 6399–6413.
Crossref | GoogleScholarGoogle Scholar | PubMed | open url image1

Weir BS, Cockerham CC (1977) Two-locus theory in quantitative genetics. In ‘Proceedings of the International Conference on Quantitative Genetics’. (Ed.  E Pollack , O Kempthorne , TB Bailey ) pp. 247–269. (The Iowa State University Press: Ames, IA)


Welch SM, Dong Z, Roe JL, Das S (2005) Flowering time control: gene network modelling and the link to quantitative genetics. Australian Journal of Agricultural Research 56, 919–936. open url image1

Winzeler EA, Shoemaker DD, Astromoff A, Liang H, Anderson K , et al. (1999) Functional characterization of the S. cerevisiae genome by gene deletion and parallel analysis. Science 285, 901–906.
Crossref | GoogleScholarGoogle Scholar | PubMed | open url image1

Wolfram, S (2002). ‘A new kind of science.’ (Wolfram Media, Inc.: Champaign, IL)

Wright S (1932) The roles of mutation, inbreeding, crossbreeding and selection in evolution. In ‘Proceedings of the 6th International Congress of Genetics’. Ithaca, New York. (Brooklyn Botanic Garden: Menasha, WI)


Wright S (1963) Plant and animal improvement in the presence of multiple selective peaks. In ‘Statistical genetics and plant breeding’. Publication 982 (Eds WD Hanson, HF Robinson) pp. 116–122. (National Academy of Sciences–National Research Council: Washington, DC)

Wright S (1977) Shifting balance theories of evolution. In ‘Evolution and the genetics of populations, a treatise in four volumes, Vol. 3. Experimental results and evolutionary deductions’. pp. 441–473. (The University of Chicago Press: Chigaco, IL)

Wright S (1978) The relation of livestock breeding to theories of evolution. Journal of Animal Science 46, 1192–1200. open url image1

Xu W, Subudhi PK, Crasta OR, Rosenow DT, Mullet JE, Nguyen HT (2000) Molecular mapping of QTLs conferring stay-green in grain sorghum (Sorghum bicolor L. Moench). Genome 43, 461–469.
Crossref | GoogleScholarGoogle Scholar | PubMed | open url image1

Yin X, Struik PC, Kropff MJ (2004) Role of crop physiology in predicting gene-to-phenotype relationships. Trends in Plant Science 9, 426–432.
Crossref | GoogleScholarGoogle Scholar | PubMed | open url image1

Zhu H, Glichrist L, Hayes P, Kleinhofs A, Kudrna D, Liu Z, Prom L, Steffenson B, Toojinda T, Vivar H (1999) Does function follow form? Principal QTLs for Fusarium head blight (FHB) resistance are coincident with QTLs for inflorescence traits and plant height in a doubled-haploid population of barley. Theoretical and Applied Genetics 99, 1221–1232.
Crossref | GoogleScholarGoogle Scholar | open url image1