Connectedness in Genetic Evaluation

  • J. L. Foulley
  • J. Bouix
  • B. Goffinet
  • J. M. Elsen
Part of the Advanced Series in Agricultural Sciences book series (AGRICULTURAL, volume 18)

Abstract

The problem of connectedness in genetic evaluation is part of the more general one of “adjusting” for nuisance parameters (e.g., herd x year x season) and of estimating genetic population means (group effects). After a review of approaches to the study of connectedness, its impact is discussed in relation to the type of model used (purely fixed or mixed; with or without genetic group) and to the properties sought from an estimator of genetic merit (unbiasedness vs. mean square error). Consideration of connectedness is especially important in the choice of alternative models. The degree of connectedness is likely to be a factor limiting the effectiveness of adjusting genetic evaluations for sources of bias. A coefficient to assess the degree of connectedness in practice is suggested. This coefficient involves pairs of levels of factors, and it varies between 0 (non-estimability) and 1 (balanced distribution according to the factors involved in disconnectedness). Small numerical examples are given to illustrate theoretical aspects of this problem. Practical applications based on the use of artificial insemination sires to connect herds over space and time are also presented.

Keywords

Covariance Assure Peris 

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References

  1. Bose RC (1947) Presidential address. In: Proc 34th Indian Sci Congr.Google Scholar
  2. Bulmer MG (1980) The mathematical theory of quantitative genetics. Clarendon Press, OxfordGoogle Scholar
  3. Chakrabarti C (1963) On the C matrix in design of experiments. J Indian Stat Assoc 1:8–23Google Scholar
  4. Chatterjee S, Hadi AS (1986) Influential observations, high leverage points and outliers in linear regression. J Stat Sci 1:379–405CrossRefGoogle Scholar
  5. Cochran WG (1951) Improvement by means of selection. In: Neyman J (ed) Proc 2nd Berkeley Symp Math Stat Probab. Univ California Press, Berkeley, pp 449–470Google Scholar
  6. Delattre P (1983) Matrices, determinants, formes quadratiques. Ecole d’automne de biologie theorique, Solignac, 19 Sept-7 Oct 1983, 130 pp MimeoGoogle Scholar
  7. Dempfle L (1977) Relation entre BLUP (Best linear unbiased prediction) et estimateurs bayesiens. Ann Genet Sel Anim 9:27–32Google Scholar
  8. Eccleston JA (1972) On the theory of connected designs. PhD Thesis, Cornell UnivGoogle Scholar
  9. Eccleston JA, Hedayat A (1974) On the theory of connected designs; characterization and optimality. Ann Stat 2:1238–1255CrossRefGoogle Scholar
  10. Eccleston JA, Russell K (1975) Connectedness and orthogonality in multifactor designs. Biometrika 62:341–345CrossRefGoogle Scholar
  11. Fernando RL, Gianola D (1986) Optimal properties of the conditional mean as a selection criterion. Theor Appl Genet 72:822–825Google Scholar
  12. Fernando RL, Gianola D, Grossman M (1983) Identifying all connected subsets in a two-way classification without interaction. J Dairy Sci 66:1399–1402CrossRefGoogle Scholar
  13. Foulley JL, Clerget-Darpoux F (1978) Progeny group size for evaluating natural service bulls using AI reference sires. Ann Genet Sel Anim 10:541–556Google Scholar
  14. Foulley JL, Menissier F (1978) Arguments in favour of an evaluation system for natural service bulls belonging to beef breeds, by taking into account the diffusion of the best AI bulls. XVth World Charolais convention, Sept 16–29, 1978, Charolais 52Google Scholar
  15. Foulley JL, Sapa J (1982) The French evaluation program for natural service beef bulls using AI sire progeny as herd ties. British Cattle Breeders Club, Winter Conference, Cambridge, January 11–12, 1982, Digest 37:64–67Google Scholar
  16. Foulley JL, Schaeffer LR, Song H, Wilton JW (1983) Progeny group size in an organized progeny test program of AI beef bulls using reference sires. Can J Anim Sci 63:17–26CrossRefGoogle Scholar
  17. Foulley JL, Bouix J, Goffinet B, Elsen JM (1984) Comparaison de peres et connexions. In: Elsen JM, Foulley JL (eds) Insemination artificielle et amelioration genetique: bilan et perspectives critiques. Colloques de l’INRA 29:131–176, INRA Service des publication, VersaillesGoogle Scholar
  18. Gianola D (1986) On selection criteria and estimation of parameters when the variance is heterogeneous. Theor Appl Genet 72:671–677CrossRefGoogle Scholar
  19. Gianola D, Fernando RL (1986) Bayesian methods in animal breeding theory. J Anim Sci 63:217–244Google Scholar
  20. Goffinet B (1983) Selection on selected records. Genet Sel Evol 15:91–98CrossRefGoogle Scholar
  21. Goffinet B, Elsen JM (1984) Critere optimal de selection quelques resultats generaux. Genet Sel Evol 16:307–317CrossRefGoogle Scholar
  22. 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 10–41Google Scholar
  23. Kennedy BW (1981) Bias and mean square error from ignoring genetic groups in mixed model sire evaluation. J Dairy Sci 62:689–697CrossRefGoogle Scholar
  24. Kullback S (1968) Information theory and statistics. Dover Publications, New YorkGoogle Scholar
  25. McClintock AE, Taylor JF (1982) Developments in the use of BLUP for estimating genetic merit. In: Barker JSF, McClintock AE (eds) Future developments in the genetic improvement of animals. Academic Press, Aust, pp 157–178Google Scholar
  26. Petersen PH (1978) A test for connectedness fitted for the two-way BLUP sire evaluation. Acta Agric Scand 28:360–362CrossRefGoogle Scholar
  27. Pollak EJ, Quaas RL (1982) A comparison of sire evaluations when sires are nonrandomly used across herds. J Dairy Sci suppl 1 (Abstr) 65:102–103Google Scholar
  28. Quaas RL, Pollak EJ (1981) Modified equations for sire models with groups. J Dairy Sci 64:1868–1870CrossRefGoogle Scholar
  29. Quaas RL, Pollak EJ (1982) Thompson’s accumulated group model for sire evaluation. J Anim Sci 55 suppl 1 (Abstr): 160Google Scholar
  30. Raghavarao D, Federer WT (1975) On connectedness in two-way elimination of heterogeneity designs. Ann Stat 3:730–735Google Scholar
  31. Rao CR (1952) Advanced statistical methods in biometric research. Wiley, New YorkGoogle Scholar
  32. Sapa J, Menissier F (1986) Beef sire evaluation for natural service in France. II. On-farm progeny-testing. 37th annu meet EAAP, Budapest, Hungary, Sept 1–4, 1986. Mimeo, 11 ppGoogle Scholar
  33. Searle, SR (1971) Linear models. Wiley, New YorkGoogle Scholar
  34. Shah KR, Yadolah D (1977) On the connectedness of designs. Sankhya 39:284–287Google Scholar
  35. Spike PL, Freeman AE (1977) Effect of genetic differences among herds on accuracy of selection and expected genetic change. J Dairy Sci 60:967–974CrossRefGoogle Scholar
  36. Thompson R (1979) Sire evaluation. Biometrics 35:339–353CrossRefGoogle Scholar
  37. Tong AKW, Kennedy BW, Moxley JE (1980) Potential errors in sire evaluation from regional genetic differences. J Dairy Sci 63:627–633CrossRefGoogle Scholar
  38. Ufford GE, Henderson CR, Keown JF, Van Vleck LD (1979) Accuracy of first lactation versus all lactations sire evaluations by best linear unbiased prediction. J Dairy Sci 63:603–612CrossRefGoogle Scholar
  39. Weeks DL, Williams DR (1964) A note on the determination of connectedness in an N-way cross-classification. Technometrics 6:319–324CrossRefGoogle Scholar
  40. Westell RA (1984) Simultaneous evaluation of sires and cows for a large population. PhD Thesis, Cornell Univ, Ithaca, NYGoogle Scholar
  41. Wilkinson JH (1965) The algebraic eigenvalue problem. Clarendon Press, OxfordGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1990

Authors and Affiliations

  • J. L. Foulley
    • 1
  • J. Bouix
    • 2
  • B. Goffinet
    • 3
  • J. M. Elsen
    • 2
  1. 1.Station de Génétique Quantitative et AppliquéeInstitut National de la Recherche Agronomique (INRA)Jouy-en-JosasFrance
  2. 2.Station d’Amélioration Génétique des AnimauxINRAToulouseFrance
  3. 3.INRA Laboratoire de BiométrieCastanet-Tolosan CedexFrance

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