Skip to main content
SpringerLink
Log in

Genetic Evaluation for Discrete Polygenic Traits in Animal Breeding

  • Chapter
Advances in Statistical Methods for Genetic Improvement of Livestock

Part of the book series: Advanced Series in Agricultural Sciences ((AGRICULTURAL,volume 18))

Abstract

Linear and non-linear models for the analysis of categorical data in animal breeding are reviewed and discussed on account of recent research made in this area. Only non-linear methods based on the threshold-liability concept introduced by Wright are described. Emphasis is on describing statistical techniques for estimating genetic merit and parameters of genetic and phenotypic variation. For each kind of methodology, the simple case of dichotomous responses is discussed in more detail as it serves as a basis for the presentation. Special consideration also is given to mixed model structures of data involving genetic effects and nuisance environmental parameters as fixed effects, as well as sire transmitting abilities, breeding values or producing abilities as random effects. A linear mixed model approach developed recently is examined in detail and extended to more general situations. For the nonlinear threshold model, it is shown how Bayesian methodology is particularly well suited for estimating location and dispersion parameters in the underlying scale under mixed sources of variation. The generality of the approach is illustrated through a discussion of extensions of the procedure.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Agresti A (1984) Analysis of ordinal categorical data. Wiley, New York

    Google Scholar 

  • Anderson TW (1984) An introduction to multivariate statistical analysis. Wiley, New York

    Google Scholar 

  • Basu D, Pereira CA de B (1982) On the Bayesian analysis of categorical data: the problem of non-response. J Stat Plann Inf 6:345–362

    Article  Google Scholar 

  • Beitler P, Landis JR (1985) A mixed-effects model for categorical data. Biometrics 41:991–1000

    Article  PubMed  CAS  Google Scholar 

  • Benzecri JP (1973) L’analyse des données. I. La taxinomie, II. L’analyse des correspondances. Dunod, Paris

    Google Scholar 

  • Berger JO (1985) Statistical decision theory and Bayesian analysis. 2nd edn. Springer-Verlag, Berlin Heidelberg New York Tokyo

    Google Scholar 

  • Berger PJ, Freeman AE (1978) Prediction of sire merit for calving difficulty. J Dairy Sci 61:1146–1150

    Article  Google Scholar 

  • Bishop YMM, Fienberg SE, Holland PW (1975) Discrete multivariate analysis. MIT Press, Cambridge

    Google Scholar 

  • Bock RD (1975) Multivariate statistical methods in behavioral research. McGraw-Hill, New York

    Google Scholar 

  • Box GEP, Tiao GC (1973) Bayesian inference in statistical analysis. Addison-Wesley, Reading

    Google Scholar 

  • Brier SS (1980) Analysis of contingency tables under cluster sampling. Biometrika 67:591– 596

    Article  Google Scholar 

  • Buhner MG (1980) The mathematical theory of quantitative genetics. Clarendon Press, Oxford

    Google Scholar 

  • Cady RA, Burnside EB (1982) Evaluating dairy bulls for dystocia and mortality of their progeny. 2nd World Congr Genet Appl Livest Prod 7:139–144. Editorial Garsi, Madrid

    Google Scholar 

  • Cox DR, Hinkley DV (1974) Theoretical statistics. Chapman and Hall, London

    Google Scholar 

  • Curnow RN (1972) The multifactorial model for the inheritance of liability to disease and its implication for relatives at risk. Biometrics 28:931–946

    Article  PubMed  CAS  Google Scholar 

  • Danell O (1985) Theoretical aspects in the estimation of breeding values for all-or-none traits. 36th annu meet EAAP, Kallithea, Kassandra, Greece, Sept 30-Oct 3 1985, Mimeo

    Google Scholar 

  • Daudin JJ, Meyniel L (1980) Notice d’utilisation du programme de regression qualitative requin. INA-PG, Dep math, Mimeo

    Google Scholar 

  • Dempfle L (1977) Relation entre BLUP et estimateurs Bayesiens. Ann Genet Sci Anim 9:27– 32

    Google Scholar 

  • Dempster ER, Lerner IM (1950) Heritability of threshold characters. Genetics 35:212–236

    PubMed  CAS  Google Scholar 

  • Dempster AP, Laird NM, Rubin RB (1977) Maximum likelihood estimation from incomplete data via the EM algorithm. J R Stat Soc B 30:1–20

    Google Scholar 

  • Djemali M (1985) The economic importance of dystocia in dairy cattle and the development of an ordered categorical analysis procedure to evaluate sires for calving ease. PhD thesis. Iowa State Univ, Ames, Iowa

    Google Scholar 

  • Djemali M, Berger PJ, Freeman AE, Van Raden PM (1986) Ordered categorical sire evaluation for dystocia in Holsteins. J Dairy Sci 69 suppl 1 (Abstr):125

    Google Scholar 

  • Ducrocq V, Colleau JJ (1986) Interest in quantitative genetics of Dutt’s and Deak’s methods for numerical computation of multivariate normal probability integrals. Genet Sel Evol 18:447–474

    Article  Google Scholar 

  • Edwards JH (1969) Familial predisposition in man. Br Med Bull 24:52–76

    Google Scholar 

  • Elston RC (1977) Estimating heritability of a dichotomous trait. Biometrics 33:232–233

    Google Scholar 

  • Falconer DS (1965) The inheritance of liability to certain diseases estimated from the incidence among relatives. Ann Hum Genet 29:51–76

    Article  Google Scholar 

  • Fernando RL, Gianola D (1984) Optimal properties of the conditional mean as a selection criterion. J Anim Scl 59 suppl 1 (Abstr):177

    Google Scholar 

  • Fienberg SE (1980) The analysis of cross-classified categorical data. 2nd edn. MIT Press, Cambridge

    Google Scholar 

  • Foulley JL, Elsen JM (1987) Posterior probability of the sire’s genotype based on progeny results. 38th ann meet EAAP, Lisbon, Portugal

    Google Scholar 

  • Foulley JL, Gianola D (1984) Estimation of genetic merit from bivariate “all-or-none” responses. Genet Sel Evol 16:285–306

    Article  Google Scholar 

  • Foulley JL, Gianola D (1986) Sire evaluation for multiple binary responses when information is missing on some traits. J Dairy Sci 69:2681–2695

    Article  PubMed  CAS  Google Scholar 

  • Foulley JL, Gianola D, Thompson R (1983) Prediction of genetic merit from data on categorical and quantitative variates with an application to calving difficulty, birth weight and pelvic opening. Genet Sel Evol 15:407–424

    Article  Google Scholar 

  • Foulley JL, Gianola D, Planchenault D (1987a) Sire evaluation with uncertain paternity. Genet Sel Evol 19:83–102

    Article  Google Scholar 

  • Foulley JL, Im S, Gianola D, Hoschele I (1987b) Empirical Bayes estimation of parameters for n polygenic binary traits. Genet Sel Evol 19:197–224

    Article  Google Scholar 

  • Foulley JL, Gianola D, Im S (1987c) Genetic evaluation for traits distributed as Poisson-binomial with reference to reproductive traits. Theor Appl Genet 73:870–877

    Article  Google Scholar 

  • Gianola D (1982) Theory and analysis of threshold characters. J Anim Sci 54:1079–1096

    Google Scholar 

  • Gianola D (1986) On selection criteria and estimation of parameters when the variance is heterogeneous. Theor Appl Genet 72:671–677

    Article  Google Scholar 

  • Gianola D, Fernando RL (1986) Bayesian methods in animal breeding theory. J Anim Sei 63:217–244

    Google Scholar 

  • Gianola D, Foulley JL (1982) Non-linear prediction of latent genetic liability with binary expression: an empirical Bayes approach. 2nd World Congr Genet Appl Livest Prod 7:293–303, Editorial Garsi, Madrid

    Google Scholar 

  • Gianola D, Foulley JL (1983a) Sire evaluation for ordered categorical data with a threshold model. Genet Sei Evol 15:201–224

    Article  Google Scholar 

  • Gianola D, Foulley JL (1983b) New techniques of prediction of breeding value for discontinuous traits. Proc 32nd Annu Nat Breed Roundtable. St Louis, Missouri

    Google Scholar 

  • Gianola D, Foulley JL, Fernando RL (1986) Prediction of breeding values when variances are not known. Genet Sel Evol 18:485–498

    Article  Google Scholar 

  • Gill JL (1986) Review of analysis of contingency tables with dichotomous responses. J Anim Breed Genet 103:1–25

    Article  Google Scholar 

  • Gilmour AR (1983) The estimation of genetic parameters from categorical data. PhD thesis. Massey Univ, Palmerston North

    Google Scholar 

  • Gilmour AR, Anderson RD, Rae AL (1985) The analysis of binomial data by a generalized linear mixed model. Biometrika 72:593–599

    Article  Google Scholar 

  • Gilmour AR, Anderson RD, Rae AL (1987) Variance components on an underlying scale for ordered multiple threshold categorical data using a generalized linear model. J Anim Breed Genet 104:149–155

    Article  Google Scholar 

  • Goffinet B, Elsen JM (1984) Critere optimal de selection: quelques resultats generaux. Genet Sel Evol 16:307–318

    Article  Google Scholar 

  • Goux JM (1970) L’héritabilité des caractères à seuil. Sciences agronomiques, Reimes

    Google Scholar 

  • Griffiths DA (1973) Maximum likelihood estimation for the beta binomial distribution and an application to the household distribution of the total number of cases of a disease. Biometrics 29:637–648

    Article  PubMed  CAS  Google Scholar 

  • Grizzle JE, Starmer CF, Koch GG (1969) Analysis of categorical data by linear models. Biometrics 25:489–504

    Article  PubMed  CAS  Google Scholar 

  • Guiard V, Herrendorfer G, Tuchscherer A (1985) Variance component estimation for dichotomous characters and its use for estimating heritability. Biom J 27:653–658

    Article  Google Scholar 

  • Haberman SJ (1978) Analysis of qualitative data. 1. Introductory topics. Academic Press, New York

    Google Scholar 

  • Haberman SJ (1979) Analysis of qualitative data. 2. New developments. Academic Press, New York

    Google Scholar 

  • Harvey WR (1982) Least-squares analysis of discrete data. J Anim Sci 54:1067–1071

    Google Scholar 

  • Harville DA (1974) Bayesian inference for variance components using only error contrasts. Biometrika 61:383–385

    Article  Google Scholar 

  • Harville DA, Mee RW (1984) A mixed model procedure for analyzing ordered categorical data. Biometrics 40:393–408

    Article  Google Scholar 

  • Henderson CR (1973) Sire evaluation and genetic trends. In: Proc Anim Breed Genet Symp in Honor of Dr. J.L. Lush. ASAS and ADSA, Champaign, Illinois pp 10–41

    Google Scholar 

  • Henderson CR (1984) ANOVA, MIVQUE, REML and ML algorithms for estimation of variances and covariances. In: David HA, David HT (eds). Statistics: an appraisal. pp 257–280, Iowa State Univ Press, Ames

    Google Scholar 

  • Henderson CR (1986) Recent developments in variance and covariance estimation. J Anim Sci 63:208–216

    Google Scholar 

  • Henderson CR, Kempthorne O, Searle SR, von Krosigk CN (1959) Estimation of environmental and genetic trends from records subject to culling. Biometrics 1:192– 218

    Article  Google Scholar 

  • Hill WG, Smith C (1977) Estimating heritability of a dichotomous trait. Biometrics 33:231– 236

    Article  Google Scholar 

  • Hoschele I (1986) Estimation of breeding values and variance components with quasi-continuous data. Doctoral Thesis, Univ Hohenheim, Stuttgart

    Google Scholar 

  • Hoschele I, Gianola D, Foulley JL (1987) Estimation of variance components with quasi-continuous data using Bayesian methods. J Anim Breed Genet 104:334–349

    Article  Google Scholar 

  • Im S (1982) Contribution a l’etude des tables de contingence a parametres aleatoires: utilisation en biometrie. Doctoral Thesis. Univ Paul Sabatier

    Google Scholar 

  • Im S (1986) Mutual independence in a mixed effects model. Biometrics 42:997

    PubMed  CAS  Google Scholar 

  • James JW, McGuirk BJ (1982) Regression of offspring on parent for all-or-none traits. Z Tïerz Züchtungsbiol 99:308–314

    Article  Google Scholar 

  • Jensen J (1986) Sire evaluation for type traits with linear and non-linear procedures. Livest Prod Sci 15:165–171

    Article  Google Scholar 

  • Judge GG, Griffiths WE, Carter Hill R, Lutkepohl H, Lee TC (1985) The theory and practice of econometrics. 2nd edn. Wiley, New York

    Google Scholar 

  • Kackar RN, Harville DA (1981) Unbiasedness of two-stage estimation and prediction procedures for mixed linear models. Commun Stat Theor Meth A 10:1249–1261

    Article  Google Scholar 

  • Kakwani NC (1967) The unbiasedness of Zellner’s seemingly unrelated regression equations estimators. J Am Stat Assoc 82:141–142

    Article  Google Scholar 

  • Kendall MG, Stuart A (1961) The advanced theory of statistics. Vol 2. Hafher, New York

    Google Scholar 

  • Koch GG, Imrey PB, Reinfurt DW (1972) Linear model analysis of categorical data with incomplete response vectors. Biometrics 28:633–692

    Google Scholar 

  • Kolakowski D, Bock RD (1981) A multivariate generalization of probit analysis. Biometrics 37:541–551

    Article  Google Scholar 

  • Laird NM, Lange N, Stram D (1987) Maximum likelihood computation with repeated measures: application to the EM algorithm. J Am Stat Assoc 82:97–105

    Article  Google Scholar 

  • Lalouel JM, Rao DC, Morton NE, Elston RC (1983) A unified model for complex segregation analysis. J Hum Genet 35:816–826

    CAS  Google Scholar 

  • Landis JR, Koch GG (1977) A one-way components of variance model for categorical data. Biometrics 33:671–679

    Article  Google Scholar 

  • Lavergne C (1984) Contribution a l’etude des modeles a effets aleatoires dans l’analyse des donnees qualitatives. Doctoral Thesis. Univ Paul Sabatier, Toulouse

    Google Scholar 

  • Lefort G (1980) Le modele de base de la selection: justifications et limites. In: Legay JM et al. (eds) Biometrie et Genetique 4:1–14, Societe Francaise de Biometrie, INRA, Dep biometrie

    Google Scholar 

  • Lush JL, Lamoreux WF, Hazel LN (1948) The heritability of resistance to death in the fowl. Poult Sci 27:375–388

    Google Scholar 

  • Malecot G (1947) Les criteres statistiques et la subjectivite de la connaissance scientifique. Ann Univ Lyon 10:43–74

    Google Scholar 

  • McCullagh P (1980) Regression models for ordinal data. J R Stat Soc Ser B 42:109–142

    Google Scholar 

  • McCullagh P (1986) Testing in industrial experiments with ordered categorical data. Technometrics 28:307

    Article  Google Scholar 

  • McCullagh P, Neider JA (1983) Generalized linear models. Chapman and Hall, London

    Google Scholar 

  • Meijering A, Gianola D (1985a) Linear versus nonlinear methods of sire evaluation for categorical traits: a simulation study. Genet Sel Evol 17:115–132

    Article  Google Scholar 

  • Meijering A, Gianola D (1985b) Observations on sire evaluation with categorical data using heteroscedastic mixed linear models. J Dairy Sci 68:1126–1232

    Article  Google Scholar 

  • Millier C (1977) Codage de variables qualitatives: une application a des notations de tavelure sur des varietes de poires. INRA. Mimeo 15pp

    Google Scholar 

  • Morton NE, MacLean CJ (1974) Analysis of family resemblance. III Complex segregation of quantitative traits. Am J Hum Genet 26:489–503

    PubMed  CAS  Google Scholar 

  • Nair VN (1986) Testing in industrial experiments with ordered categorical data. Technometrics 28:283–311

    Article  Google Scholar 

  • Plackett RL (1981) The analysis of categorical data. 2nd edn. Griffin, London

    Google Scholar 

  • Pollak EJ, Freeman AE (1976) Parameter estimation and sire evaluation for dystocia and calf size in Holsteins. J Dairy Sci 59:1817–1824

    Article  Google Scholar 

  • Quaas RL, Van Vleck LD (1980) Categorical trait sire evaluation by best linear unbiased prediction of future progeny categories frequencies. Biometrics 36:117–122

    Article  Google Scholar 

  • Quaas RL, Zhao Y, Pollak EJ (1988) Describing interactions in dystocia scores with a threshold model. J Anim Sci 66:396–399

    PubMed  CAS  Google Scholar 

  • Razungles J (1977) Héritabilité des caractères discrets: étude bibliographique critique. Ann Genet Sel Anim 9:43–61

    Google Scholar 

  • Robertson A, Lerner IM (1949) The heritability of all-or-none traits: viability of poultry. Genetics 34:395–411

    Google Scholar 

  • Ronningen K (1971) Some properties of the selection index derived by “Henderson’s mixed model method” Z Tierz Züchtungsbiol 88:186–193

    Article  Google Scholar 

  • Rutledge JJ, Gunsett FC (1982) Analysis of categorical data in the animal sciences. J Anim Sci 54:1072–1078

    Google Scholar 

  • Schaeffer LR (1979) Estimation of variance and covariance components for average daily gain and backfat thickness in swine. In: Searle SR, Van Vleck LD (eds.). Variance components and animal breeding. Proc conf in Honor of CR Henderson. pp 123–137, Cornell Univ, Ithaca

    Google Scholar 

  • Schaeffer LR, Wilton JW (1976) Methods of sire evaluation for calving ease. J Dairy Sci 59:544–551

    Article  Google Scholar 

  • Schmidt P (1976) Econometrics. Dekker, New York

    Google Scholar 

  • Searle SR (1971) Linear models. Wiley, New York

    Google Scholar 

  • Searle SR, Speed FM, Henderson HV (1981) Some computational and model equivalences in analyses of variance of unequal subclass numbers data. Am Stat 35:16–33

    Article  Google Scholar 

  • Shah AK, Claypool PL (1984) Analysis of binary data for the balanced one-way classification. Commun Stat Theor Meth 13:1375–1390

    Article  Google Scholar 

  • Smith C (1970) Heritability of liability and concordance in monozygous twins. Ann Hum Genet 34:85–91

    Article  PubMed  CAS  Google Scholar 

  • Smith SP, Allaire FR (1986) Analysis of failure times measures on dairy cows: theoretical considerations in animal breeding. J Dairy Sci 69:217–227

    Article  Google Scholar 

  • Smith SP, Graser H-U (1986) Estimating variance components in a class of mixed models by restricted maximum likelihood. J Dairy Sci 60:1156–1165

    Article  Google Scholar 

  • Stiratelli R, Laird N, Ware JH (1984) Random effects models for serial observations with binary response. Biometrics 40:961–971

    Article  PubMed  CAS  Google Scholar 

  • Tallis GM (1962) The maximum likelihood estimation of correlation from contingency tables. Biometrics 18:342–353

    Article  Google Scholar 

  • Thompson R (1972) The maximum likelihood approach to the estimate of liability. Ann Hum Genet 36:221–231

    Article  PubMed  CAS  Google Scholar 

  • Thompson R (1979) Sire evaluation. Biometrics 35:339–353

    Article  Google Scholar 

  • Thompson R, Cameron ND (1986) Estimation of genetic parameters. In: Dickerson GE, Johnson RK (eds) 3rd World Congr Genet Appl Livest Prod. Agric Commun, Univ Nebraska, Lincoln, Nebraska, XII:371–381

    Google Scholar 

  • Thompson R, McGuirk BJ, Gilmour AR (1985) Estimating the heritability of all-or-none and categorical traits by offspring-parent regression. Z Tierz Züchtungsbiol 102:342–354

    Google Scholar 

  • Tukey J (1962) The future of data analysis. Ann Math Stat 33:1–67

    Article  Google Scholar 

  • Van Raden PM, Freeman AE (1986) Computing restricted maximum likelihood estimates of variances and covariances. J Dairy Sci 69 suppl 1:208

    Google Scholar 

  • Van Vleck LD, Karner PJ (1980) Sire evaluation by best linear unbiased prediction for categorically scored type traits. J Dairy Sci 63:1328–1333

    Article  Google Scholar 

  • Van Vleck LD, Edlin KM (1984) Multiple trait evaluation of bulls for calving ease. J Dairy Sci 67:3025–3033

    Article  Google Scholar 

  • Williams DA (1975) The analysis of binary responses from toxicological experiments involving reproduction and teratogenicity. Biometrics 31:949–952

    Article  PubMed  CAS  Google Scholar 

  • Woolson RF, Clarke WR (1984) Analysis of categorical incomplete longitudinal data. J R Stat Soc Ser A 147:87–99

    Article  Google Scholar 

  • Wright S (1934a) An analysis of variability in number of digits in an inbred strain of guinea pig. Genetics 19:506–536

    PubMed  CAS  Google Scholar 

  • Wright S (1934b) The results of crosses between inbred strains of guinea pigs differing in number of digits. Genetics 19:537–551

    PubMed  CAS  Google Scholar 

  • Wright S (1968) Evolution and the genetics of populations. 1. Genetic and biometric foundations. Univ Chicago Press, Chicago

    Google Scholar 

  • Zellner A, Rossi PE (1984) Bayesian analysis of dichotomous quantal response models. J Econometrics 25:365–393

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Station de Génétique Quantitative et Appliquée, INRA, Jouy-en-Josas, France

    J. L. Foulley

  2. Department of Animal Sciences, University of Illinois, Urbana, Illinois, USA

    D. Gianola

  3. Laboratoire de Biometrie, INRA, 31326, Castanet-Tolosan, France

    S. Im

Authors
  1. J. L. Foulley
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. D. Gianola
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. S. Im
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Animal Sciences 126 Animal Sciences Laboratory, University of Illinois, 1207 West Gregory Drive, Urbana, Illinois, 61801, USA

    Daniel Gianola

  2. Animal Genetics and Breeding Unit (AGBU), University of New England and NSW Agriculture and Fisheries, Armidale, New South Wales, 2351, Australia

    Keith Hammond

Rights and permissions

Reprints and permissions

Copyright information

© 1990 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Foulley, J.L., Gianola, D., Im, S. (1990). Genetic Evaluation for Discrete Polygenic Traits in Animal Breeding. In: Gianola, D., Hammond, K. (eds) Advances in Statistical Methods for Genetic Improvement of Livestock. Advanced Series in Agricultural Sciences, vol 18. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-74487-7_17

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-74487-7_17

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-74489-1

  • Online ISBN: 978-3-642-74487-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation