Statistical methodology has played a key role in scientific animal breeding. Approximately one hundred years of statistical developments in animal breeding are reviewed. Some of the scientific foundations of the field are discussed, and many milestones are examined from historical and critical perspectives. The review concludes with a discussion of some future challenges and opportunities arising from the massive amount of data generated by livestock, plant, and human genome projects.


Article metrics loading...

Loading full text...

Full text loading...


Literature Cited

  1. Fernández J, Toro MA. 1999. The use of mathematical programming to control inbreeding in selection schemes. J. Anim. Breed. Genet. 116:447–66 [Google Scholar]
  2. Weigel KA, Lin SW. 2000. Use of computerized mate selection programs to control inbreeding of Holstein and Jersey cattle in the next generation. J. Dairy Sci. 83:822–28 [Google Scholar]
  3. Brown PO, Botstein D. 1999. Exploring the new world of the genome with DNA microarrays. Nat. Genet. 21:33–37 [Google Scholar]
  4. Geisser S. 1993. Predictive Inference: An Introduction New York: Chapman & Hall [Google Scholar]
  5. Gianola D. 2013. Priors in whole-genome regression: the Bayesian alphabet returns. Genetics 194:573–96 [Google Scholar]
  6. Henderson CR. 1948. Estimation of general, specific and maternal combining ability in crosses among inbred lines of swine. PhD Thesis, Iowa State Univ.
  7. Henderson CR. 1953. Estimation of variance and covariance components. Biometrics 9:226–52 [Google Scholar]
  8. Henderson CR. 1963. Selection index and expected genetic advance. Statistical Genetics and Plant Breeding Hanson WD, Robinson HF. 141–63 Publ. 992 Washington, DC: Natl. Acad. Sci. Natl. Res. Counc. [Google Scholar]
  9. Henderson CR. 1973. Sire evaluation and genetic trends. Proceedings of the Animal Breeding and Genetics Symposium in Honor of Dr. Jay L. Lush10–41 Champaign: Am. Soc. Anim. Sci., Am. Dairy Sci. Assoc. [Google Scholar]
  10. Henderson CR. 1975. Best linear unbiased estimation and prediction under a selection model. Biometrics 31:423–49 [Google Scholar]
  11. Henderson CR. 1984. Application of Linear Models in Animal Breeding Guelph, Can.: Univ. Guelph [Google Scholar]
  12. Freeman AE. 1973. Genetic statistics in animal breeding. J. Anim. Sci. 1973:1–9 [Google Scholar]
  13. Gianola D, Hammond K. 1990. Advances in Statistical Methods for Genetic Improvement of Livestock Berlin: Springer-Verlag [Google Scholar]
  14. Gianola D. 2006. Statistics in animal breeding: angels and demons. Proc. 8th World Congr. Genet. Appl. Livest. Prod., CD Paper 00-03. Belo Horizonte, Brazil: Inst. Prociencia
  15. Hill WG. 2014. Applications of population genetics to animal breeding, from Wright, Fisher and Lush to genomic prediction. Genetics 196:1–16 [Google Scholar]
  16. Rosa GJM. 2013. Foundations of animal breeding. Sustainable Food Production Christou P, Savin R, Costa-Pierce B, Misztal I, Whitelaw B. 58–78 New York: Springer [Google Scholar]
  17. Blasco A, Toro MA. 2014. A short critical history of the application of genomics to animal breeding. Livest. Sci. 166:4–9 [Google Scholar]
  18. Galton F. 1886. Regression towards mediocrity in hereditary stature. J. Anthropol. Inst. G.B. Irel. 15:246–63 [Google Scholar]
  19. Lush JL. 1945. Animal Breeding Plans Ames, IA: Coll. Press, 3rd ed.. [Google Scholar]
  20. Hill WG. 1971. Design and efficiency of selection experiments for estimating genetic parameters. Biometrics 27:293–311 [Google Scholar]
  21. Hill WG. 1972. Estimation of realised heritabilities from selection experiments. I. Divergent selection. Biometrics 28:747–65 [Google Scholar]
  22. Wachsmuth AW, Wilkinson L, Dallal GE. 2003. Galton's bend: a previously undiscovered nonlinearity in Galton's family stature regression data. Am. Stat. 57:190–92 [Google Scholar]
  23. Pearson K. 1894. Contributions to the mathematical theory of evolution. Philos. Trans. R. Soc. A 185:71–110 [Google Scholar]
  24. Pearson K. 1903. Mathematical contributions to the theory of evolution. XI. On the influence of natural selection on the variability and correlation of organs. Philos. Trans. R. Soc. A 200:1–66 [Google Scholar]
  25. Bulmer MG. 1971. The effect of selection on genetic variability. Am. Nat. 105:201–11 [Google Scholar]
  26. Bulmer MG. 1980. The Mathematical Theory of Quantitative Genetics Oxford: Oxford Univ. Press [Google Scholar]
  27. Falconer DS, Mackay TFC. 1996. Introduction to Quantitative Genetics Essex, UK: Longman [Google Scholar]
  28. Onaga L. 2010. Toyama Kametaro and Vernon Kellogg: silkworm inheritance experiments in Japan, Siam, and the United States, 1900–1912. J. Hist. Biol. 43:215–64 [Google Scholar]
  29. Yule GO. 1902. Mendel’s laws and their probable relations to intra-racial heredity. New Phytol. 9:193–238 [Google Scholar]
  30. Fisher RA. 1918. The correlation between relatives on the supposition of Mendelian inheritance. Trans. R. Soc. Edinb. 52:399–433 [Google Scholar]
  31. Wright S. 1922. Coefficients of inbreeding and relationships. Am. Nat. 56:330–38 [Google Scholar]
  32. Wright S. 1931. Evolution in Mendelian populations. Genetics 16:97–159 [Google Scholar]
  33. Crow JF, Kimura M. 1970. An Introduction to Population Genetics Theory New York: Harper & Row [Google Scholar]
  34. Quaas RL, Pollak EJ. 1980. Mixed model methodology for farm and ranch beef cattle testing programs. J. Anim. Sci. 51:1277–87 [Google Scholar]
  35. Malécot G. 1948. Les Mathématiques de l'hérédité Paris: Masson et Cie [Google Scholar]
  36. Fisher RA. 1930. The Genetical Theory of Natural Selection Oxford: Clarendon [Google Scholar]
  37. Falconer DS. 1960. Introduction to Quantitative Genetics New York: Ronald [Google Scholar]
  38. Edwards AWF. 1977. Foundations of Mathematical Genetics Cambridge: Cambridge Univ. Press [Google Scholar]
  39. Gallais A. 1974. Covariance between arbitrary relatives with linkage and epistasis in the case of linkage disequilibrium. Biometrics 30:429–46 [Google Scholar]
  40. Gianola D, Hospital F, Verrier E. 2013. On the contribution of an additive locus to genetic variance when inheritance is multifactorial with implications on the interpretation of GWAS. Theor. Appl. Genet. 6:1457–72 [Google Scholar]
  41. Meuwissen THE, Hayes BJ, Goddard ME. 2001. Prediction of total genetic value using genome-wide dense marker maps. Genetics 157:1819–29 [Google Scholar]
  42. Lush JL. 1948. The Genetics of Populations Mimeo. Ames: Iowa State Univ. 381 pp. [Google Scholar]
  43. Neiman-Sorensen A, Robertson A. 1961. The association between blood groups and several production characters in three Danish cattle breeds. Acta Agric. Scand. 11:163–96 [Google Scholar]
  44. Manolio TA, Collins FS, Cox NJ, Goldstein DB, Hindorff LA et al. 2009. Finding the missing heritability of complex diseases. Nature 461:747–53 [Google Scholar]
  45. Robertson A. 1980. Selection Experiments in Laboratory and Domestic Animals Oxfordshire, UK: Commonw. Agric. Bur., Farnham R. [Google Scholar]
  46. Robertson A. 1960. A theory of limits in artificial selection. Proc. R. Soc. Lond. B Biol. Sci. 153:234–79 [Google Scholar]
  47. Hill WG, Robertson A. 1966. The effect of linkage on limits to artificial selection. Genet. Res. 8:269–94 [Google Scholar]
  48. Hill WG. 1974. Heritabilities: estimation problems and the present state of information. Proc. First World Congr. Genet. Appl. Livest. Prod. I343–51 Madrid: Graficas Orbe [Google Scholar]
  49. Sorensen DA, Kennedy BW. 1986. Analysis of selection experiments using mixed model methodology. J. Anim. Sci. 63:245–58 [Google Scholar]
  50. Comstock RE, Robinson HF, Harvey PH. 1949. A breeding procedure designed to make maximum use of both general and specific combining ability. Agron. J. 41:360–67 [Google Scholar]
  51. Schaeffer LR. 1985. Model for international evaluation of dairy sires. Livest. Prod. Sci. 12:105–15 [Google Scholar]
  52. Wahba G. 1990. Spline Models for Observational Data Philadelphia: Soc. Ind. Appl. Math. [Google Scholar]
  53. Tibshirani R. 1994. Neural networks: a review from statistical perspective. Stat. Sci. 9:48–49 [Google Scholar]
  54. Wahba G. 2007. Statistical learning in medical data analysis. Tech. Rep. 1136. Dep. Stat., Univ. Wisconsin-Madison
  55. Lush JL. 1931. The number of daughters necessary to prove a sire. J. Dairy Sci. 14:209–20 [Google Scholar]
  56. Lush JL. 1935. Progeny test and individual performance as indicators of an animal's breeding value. J. Dairy Sci. 18:1–19 [Google Scholar]
  57. Kempthorne O. 1967. An Introduction to Genetic Statistics New York: Wiley [Google Scholar]
  58. Eisenhart C. 1947. The assumptions underlying the analysis of variance. Biometrics 3:1–21 [Google Scholar]
  59. Hartley HO, Rao JNK. 1967. Maximum likelihood estimation for the mixed analysis of variance model. Biometrika 54:93–108 [Google Scholar]
  60. Rao CR. 1971. Estimation of variance and covariance components: MINQUE theory. J. Multivar. Anal. 1:257–75 [Google Scholar]
  61. Searle SR. 1971. Topics in variance component estimation. Biometrics 27:1–76 [Google Scholar]
  62. Searle SR. 1974. Prediction, mixed models and variance components. Reliability and Biometry Proschan F, Serfling RJ. Philadelphia: Soc. Ind. Appl. Math. [Google Scholar]
  63. de los Campos G, Sorensen DA, Gianola D. 2014. Genomic heritability: What is it? Proc. 10th World Cong. Genet. Appl. Livest. Prod., Vancouver, Can. https://asas.org/wcgalp-proceedings
  64. Henderson CR. 1976. A simple method for computing the inverse of a numerator relationship matrix used in prediction of breeding values. Biometrics 32:69–83 [Google Scholar]
  65. Harville DA. 1977. Maximum likelihood approaches to variance component estimation and to related problems. J. Am. Stat. Assoc. 72:320–40 [Google Scholar]
  66. Feldman MW, Lewontin RC. 1975. The heritability hang-up. Science 190:1163–68 [Google Scholar]
  67. Kempthorne O. 1978. Logical, epistemological and statistical aspects of nature-nurture data interpretation. Biometrics 34:1–23 [Google Scholar]
  68. Wood PDP. 1967. Algebraic model of the lactation curve in cattle. Nature 216:164–65 [Google Scholar]
  69. White IMS, Thompson R, Brotherstone R. 1999. Genetic and environmental smoothing of lactation curves with cubic splines. J. Dairy Sci. 82:632–38 [Google Scholar]
  70. Taylor St CS. 1980. Genetic size-scaling rules in animal growth. Anim. Prod. 30:161–65 [Google Scholar]
  71. Soller M, Beckmann JS. 1982. Restriction fragment length polymorphisms and genetic improvement. Proc. 2nd World Cong. Genet. Appl. Livest. Prod. 6396–404 Madrid: Editor. Ceuta [Google Scholar]
  72. Soller M, Beckmann JS. 1983. Genetic polymorphism in varietal identification and genetic improvement. Theor. Appl. Genet. 67:25–33 [Google Scholar]
  73. Zhang Q, Boichard D, Hoeschele I, Ernst C, Eggen A et al. 1998. Mapping quantitative trait loci for milk production and health of dairy cattle in a large outbred pedigree. Genetics 149:1959–73 [Google Scholar]
  74. Fernando FL, Grossman M. 1989. Marker assisted selection using best linear unbiased prediction. Genet. Sel. Evol. 21:467–77 [Google Scholar]
  75. Haley CS, Knott SA. 1992. A simple regression method for mapping quantitative trait loci in line crosses using flanking markers. Heredity 69:315–24 [Google Scholar]
  76. Andersson L, Georges M. 2004. Domestic-animal genomics: deciphering the genetics of complex traits. Nat. Rev. Genet. 5:202–12 [Google Scholar]
  77. Qanbari S, Pausch H, Jansen S, Somel M, Strom TM et al. 2014. Classic selective sweeps revealed by massive sequencing in cattle. PLOS Genet. 10:2e1004148 [Google Scholar]
  78. Gowen JW. 1952. Heterosis Ames: Iowa State Coll. Press [Google Scholar]
  79. Smith SP, Mäki-Tanila A. 1990. Genotypic covariance matrices and their inverses for models allowing dominance and inbreeding. Genet. Sel. Evol. 22:65–91 [Google Scholar]
  80. Sun C, VanRaden PM, O’Connell JR, Weigel KA, Gianola D. 2013. Mating programs including genomic relationships and dominance effects. J. Dairy Sci. 96:8014–23 [Google Scholar]
  81. Nishio M, Satoh M. 2014. Including dominance effects in the genomic BLUP method for genomic evaluation. PLOS ONE 9:e85792 [Google Scholar]
  82. Carlborg O, Haley CS. 2004. Epistasis: Too often neglected in complex trait studies?. Nat. Rev. Genet. 5:618–25 [Google Scholar]
  83. Hill WG, Goddard ME, Visscher PM. 2008. Data and theory point to mainly additive genetic variance for complex traits. PLOS Genet. 4:2e1000008 [Google Scholar]
  84. Huang W, Richards S, Carbone MA, Zhu D, Anholt RR et al. 2012. Epistasis dominates the genetic architecture of Drosophila quantitative traits. PNAS 109:15553–59 [Google Scholar]
  85. Mackay TFC. 2014. Epistasis and quantitative traits: using model organisms to study gene–gene interactions. Nat. Rev. Genet. 15:22–33 [Google Scholar]
  86. Taylor MB, Ehrenreich IM. 2014. Genetic interactions involving five or more genes contribute to a complex trait in yeast. PLOS Genet. 10:5e1004324 [Google Scholar]
  87. Cockerham CC. 1954. An extension of the concept of partitioning hereditary variance for the analysis of covariances among relatives when epistasis is present. Genetics 39:859–82 [Google Scholar]
  88. Kempthorne O. 1954. The correlation between relatives in a random mating population. Proc. R. Soc. B 143:103–13 [Google Scholar]
  89. Henderson CR. 1985. Best linear unbiased prediction of nonadditive genetic merits in noninbred populations. J. Anim. Sci. 60:111–17 [Google Scholar]
  90. Henderson CR. 1988. Progress in statistical methods applied to quantitative genetics since 1976. Proceedings of the Second International Conference on Quantitative Genetics Weir BS, Eisen EJ, Goodman MM, Namkoong G. 85–90 Sunderland, MA: Sinauer [Google Scholar]
  91. Willham RL. 1963. The covariance between relatives for characters composed of components contributed by related individuals. Biometrics 19:18–27 [Google Scholar]
  92. Falconer DS. 1965. Maternal effects and selection response. Genetics Today Geerts SJ. 763–74 Oxford: Pergamon [Google Scholar]
  93. Koerkhuis ANM, Thompson R. 1997. Models to estimate maternal effects for juvenile body weight in broiler chickens. Genet. Sel. Evol. 29:225–49 [Google Scholar]
  94. Van Vleck LD. 1993. Selection Index and Introduction to Mixed Model Methods Boca Raton, FL: CRC Press [Google Scholar]
  95. Bijma P. 2006. Estimating maternal genetic effects in livestock. J. Anim. Sci. 84:800–6 [Google Scholar]
  96. Skjervold H, Fimland E. 1975. Evidence for a possible influence of the fetus on the milk yield of the dam. Z. Tierz. Zücht. 92:245–51 [Google Scholar]
  97. Van Vleck LD. 1978. A genetic model involving fetal effects on traits of the dam. Biometrics 34:123–27 [Google Scholar]
  98. Kennedy BW, Schaeffer LR. 1990. Reproductive technology and genetic evaluation. Advances in Statistical Methods for Genetic Improvement of Livestock Gianola D, Hammond K. 507–32 Heidelberg: Springer-Verlag [Google Scholar]
  99. Van Vleck LD, Snowder GD, Hanford KJ. 2003. Models with cytoplasmic effects for birth, weaning and fleece weights, and litter size at birth for a population of Targhee sheep. J. Anim. Sci. 81:61–67 [Google Scholar]
  100. Muir WM. 2005. Incorporation of competitive effects in forest tree or animal breeding programs. Genetics 170:1247–59 [Google Scholar]
  101. Bijma P, Muir WM, van Arendonk JA. 2007. Multilevel selection 1: quantitative genetics of inheritance and response to selection. Genetics 175:277–88 [Google Scholar]
  102. Bijma P. 2010. Estimating indirect genetic effects: precision of estimates and optimum designs. Genetics 186:1013–28 [Google Scholar]
  103. Wright S. 1960. The treatment of reciprocal interaction, with or without lag, in path analysis. Biometrics 16:423–45 [Google Scholar]
  104. Haavelmo T. 1943. The statistical implications of a system of simultaneous equations. Econometrica 11:1–12 [Google Scholar]
  105. Hill WG. 1984. On selection among groups with heterogeneous variance. Anim. Prod. 39:473–77 [Google Scholar]
  106. Khatib H. 2012. Livestock Epigenetics New York: Wiley-Blackwell [Google Scholar]
  107. Neugebauer N, Räder I, Schild HJ, Zimmer D, Reinsch N. 2010. Evidence for parent-of-origin effects on genetic variability of beef traits. J. Anim. Sci. 88:523–32 [Google Scholar]
  108. Robertson A. 1955. Prediction equations in quantitative genetics. Biometrics 11:95–98 [Google Scholar]
  109. Dempfle L. 1977. Relation entre BLUP (Best Linear Unbiased Prediction) et estimateurs bayésiens. Ann. Genet. Sel. Anim. 9:27–32 [Google Scholar]
  110. Gianola D, Fernando RL. 1986. Bayesian methods in animal breeding theory. J. Anim. Sci. 63:217–44 [Google Scholar]
  111. Blasco A. 2001. The Bayesian controversy in animal breeding. J. Anim. Sci. 79:2023–46 [Google Scholar]
  112. Grosu H, Schaeffer LR. 2014. History of Genetic Evaluation Methods in Dairy Cattle Bucharest: Publ. House Rom. Acad. [Google Scholar]
  113. Fernando RL, Gianola D. 1986. Optimal properties of the conditional mean as a selection criterion. Theor. Appl. Genet. 72:822–25 [Google Scholar]
  114. Smith FH. 1936. A discriminant function for plant selection. Ann. Eugen. 7:240–50 [Google Scholar]
  115. Hazel LN. 1943. The genetic basis for constructing selection indexes. Genetics 28:476–90 [Google Scholar]
  116. Karam HA, Chapman AB, Pope AL. 1953. Selecting lambs under farm flock conditions. J. Anim. Sci. 12:148–64 [Google Scholar]
  117. Henderson CR, Searle SR, Kempthorne O, von Krosigk M. 1959. Estimation of environmental and genetic trends from records subject to culling. Biometrics 15:192–218 [Google Scholar]
  118. Harvey WR. 1960. Least-squares analysis of data with unequal subclass numbers Bull. 20-8. US Dep. Agric., Agric. Res. Serv., Washington, DC [Google Scholar]
  119. Harvey WR. 1970. Estimation of variance and covariance components in the mixed model. Biometrics 26:485–504 [Google Scholar]
  120. Schaeffer LR, Kennedy BW. 1986. Computing solutions to mixed model equations. Proc. 3rd World Congr. Genet. Appl. Livest. Prod. XII382–93 Lincoln: Agric. Commun., Univ. Neb. [Google Scholar]
  121. Misztal I, Gianola D. 1987. Indirect solution of mixed model equations. J. Dairy Sci. 70:716–23 [Google Scholar]
  122. Patterson HD, Thompson R. 1971. Recovery of inter-block information when block sizes are unequal. Biometrika 58:545–54 [Google Scholar]
  123. Wolfinger R. 1993. Laplace’s approximation for nonlinear mixed models. Biometrika 80:791–95 [Google Scholar]
  124. Lee Y, Nelder JA. 1996. Hierarchical generalized linear models. J. R. Stat. Soc. B 58:619–78 [Google Scholar]
  125. Harville DA, Mee RW. 1984. A mixed model procedure for analyzing ordered categorical data. Biometrics 40:393–408 [Google Scholar]
  126. Gilmour AR, Anderson RD, Rae AL. 1985. The analysis of binomial data by a generalized linear mixed model. Biometrika 72:593–99 [Google Scholar]
  127. Foulley JL, Im S, Gianola D, Höschele I. 1987. Empirical Bayes estimation of parameters for n polygenic binary traits. Genet. Sel. Evol. 19:197–224 [Google Scholar]
  128. Hofer A. 1998. Variance component estimation in animal breeding: a review. J. Anim. Breed. Genet. 115:247–65 [Google Scholar]
  129. Searle SR. 1968. Another look at Henderson's methods of estimating variance components. Biometrics 24:749–78 [Google Scholar]
  130. LaMotte LR. 1973. Quadratic estimation of variance components. Biometrics 32:793–804 [Google Scholar]
  131. Fisher RA. 1922. On the mathematical foundations of mathematical statistics. Philos. Trans. R. Soc. A 222:594–604 [Google Scholar]
  132. Harville DA, Callanan TP. 1990. Computational aspects of likelihood-based inference for variance components. Advances in Statistical Methods for Genetic Improvement of Livestock Gianola D, Hammond K. 36–176 Heidelberg: Springer-Verlag [Google Scholar]
  133. Dempster AP, Laird NM, Rubin DB. 1977. Maximum likelihood from incomplete data via the EM algorithm. J. R. Stat. Soc. B 39:1–38 [Google Scholar]
  134. Meyer K, Kirkpatrick M. 2010. Better estimates of genetic covariance matrices by “bending” using penalized maximum likelihood. Genetics 185:1097–110 [Google Scholar]
  135. Harville DA. 1974. Bayesian inference for variance components using only error contrasts. Biometrika 61:383–85 [Google Scholar]
  136. Gianola D, Foulley JL, Fernando RL. 1986. Prediction of breeding values when variances are not known. Proc. 3rd World Congr. Genet. Appl. Livest. Prod. XII356–70 Lincoln: Agric. Commun. Univ. Neb. [Google Scholar]
  137. Harville DA, Carriquiry AL. 1992. Classical and Bayesian prediction as applied to an unbalanced mixed linear model. Biometrics 48:987–1003 [Google Scholar]
  138. James W, Stein C. 1961. Estimation with quadratic loss. Proc. 4th Berkeley Symp. Math. Statist. Prob. 1361–379 Berkeley: Univ. Calif. Press [Google Scholar]
  139. Lindley DV, Smith AFM. 1972. Bayes estimates for the linear model (with discussion). J. R. Stat. Soc. B 34:1–41 [Google Scholar]
  140. Box GEP, Tiao GC. 1973. Bayesian Inference in Statistical Analysis Reading, MA: Addison-Wesley [Google Scholar]
  141. Rönningen K. 1971. Some properties of the selection index derived by Henderson's mixed model method. Z. Tierz. Zuecht. 8:186–93 [Google Scholar]
  142. Sorensen D, Gianola D. 2002. Likelihood, Bayesian and MCMC Methods in Quantitative Genetics New York: Springer [Google Scholar]
  143. Guo SW, Thompson EA. 1991. Monte Carlo estimation of variance component models for large complex pedigrees. Biometrics 48:361–72 [Google Scholar]
  144. Wang CS, Rutledge JJ, Gianola D. 1993. Marginal inference about variance components in a mixed linear model using Gibbs sampling. Genet. Sel. Evol. 25:41–62 [Google Scholar]
  145. Sorensen DA, Wang CS, Jensen J, Gianola D. 1994. Bayesian analysis of genetic change due to selection using Gibbs sampling. Genet. Sel. Evol. 26:333–60 [Google Scholar]
  146. Wang CS, Gianola D, Sorensen DA, Jensen J, Christensen A, Rutledge JJ. 1994. Response to selection for litter size in Danish Landrace pigs: a Bayesian analysis. Theor. Appl. Genet. 88:220–30 [Google Scholar]
  147. Thompson R. 1986. Estimation of realized heritability in a selected population using mixed model methods. Genet. Sel. Evol. 18:475–84 [Google Scholar]
  148. Sorensen DA, Fernando RL, Gianola D. 2001. Inferring the trajectory of genetic variance in the course of artificial selection. Genet. Res. 77:83–94 [Google Scholar]
  149. Wright S. 1926. A frequency curve adapted to variation in percentage occurrence. J. Am. Stat. Assoc. 21:162–78 [Google Scholar]
  150. Wright S. 1934. An analysis of variability in number of digits and in an inbred strain of guinea pigs. Genetics 19:506–36 [Google Scholar]
  151. Dempster ER, Lerner IM. 1950. Heritability of threshold characters. Genetics 35:212–36 [Google Scholar]
  152. Falconer DS. 1965. The inheritance of liability to certain diseases, estimated from the incidence among relatives. Ann. Hum. Genet. 29:51–76 [Google Scholar]
  153. Thompson R. 1979. Sire evaluation. Biometrics 35:339–53 [Google Scholar]
  154. Nelder J, Wedderburn R. 1972. Generalized linear models. J. R. Stat. Soc. A 135:370–84 [Google Scholar]
  155. Gianola D, Foulley JL. 1983. Sire evaluation for ordered categorical data with a threshold model. Genet. Sel. Evol. 15:201–24 [Google Scholar]
  156. Sorensen DA, Andersen S, Gianola D, Korsgaard I. 1995. Bayesian inference in threshold models using Gibbs sampling. Genet. Sel. Evol. 27:229–49 [Google Scholar]
  157. Misztal I, Gianola D, Foulley JL. 1989. Computing aspects of a nonlinear method of sire evaluation for categorical data. J. Dairy Sci. 72:1557–68 [Google Scholar]
  158. 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. 15:407–24 [Google Scholar]
  159. Höschele I, Foulley JL, Colleau JJ, Gianola D. 1984. Genetic evaluation for multiple binary responses. Genet. Sel. Evol. 18:299–320 [Google Scholar]
  160. Foulley JL, Gianola D, Im S. 1987. Genetic evaluation for traits distributed as Poisson-binomial with reference to reproductive traits. Theor. Appl. Genet. 73:870–77 [Google Scholar]
  161. Tempelman RJ, Gianola D. 1996. A mixed effects model for overdispersed count data in animal breeding. Biometrics 52:265–79 [Google Scholar]
  162. Tempelman RJ, Gianola D. 1999. Genetic analysis of fertility in dairy cattle using negative binomial mixed models. J. Dairy Sci. 82:1834–47 [Google Scholar]
  163. Smith SP, Allaire FR. 1986. Analysis of failure times measured on dairy sows: theoretical considerations in animal breeding. J. Dairy Sci. 69:217–27 [Google Scholar]
  164. Ducrocq V, Casella G. 1996. Bayesian analysis of mixed survival models. Genet. Sel. Evol. 28:505–29 [Google Scholar]
  165. Famula TR. 1981. Exponential stayability model with censoring and covariates. J. Dairy Sci. 64:538–45 [Google Scholar]
  166. Damgaard LH, Korsgaard IR. 2006. A bivariate quantitative genetic model for a linear Gaussian trait and a survival trait. Genet. Sel. Evol. 38:45–64 [Google Scholar]
  167. Ducrocq V, Sölkner J. 1998. The Survival Kit: a Fortran package for the analysis of survival data. Proc. 6th World Congr. Genet. Appl. Livest. Prod. 2251–52 Armidale, UK: Anim. Genet. Breed. Unit [Google Scholar]
  168. Lush JL, Shrode RR. 1950. Changes in milk production with age and milking frequency. J. Dairy Sci. 33:338–57 [Google Scholar]
  169. Brody S. 1945. Bioenergetics and Growth New York: Reinhold Publ. Corp. [Google Scholar]
  170. Schaeffer LR, Dekkers JCM. 1994. Random regressions in animal models for test-day production in dairy cattle. Proc. World Cong. Genet. Appl. Livest. Prod. 18443–46 Guelph, Can.: Univ. Guelph [Google Scholar]
  171. Kirkpatrick M, Lofsvold D. 1989. The evolution of growth trajectories and other complex quantitative characters. Genome 31:778–83 [Google Scholar]
  172. Meyer K. 1998. Modeling repeated records: covariance functions and random regression models to analyse animal breeding data. Proc. 6th World Congr. Genet. Appl. Livest. Prod. 25517–20 Armidale, UK: Anim. Genet. Breed. Unit [Google Scholar]
  173. Strandén I, Gianola D. 1999. Mixed effects linear models with t-distributions for quantitative genetic analysis: a Bayesian approach. Genet. Sel. Evol. 31:25–42 [Google Scholar]
  174. Rosa GJM, Padovani CR, Gianola D. 2003. Robust linear mixed models with normal/independent distributions and Bayesian MCMC implementation. Biom. J. 45:573–90 [Google Scholar]
  175. Rosa GJM, Gianola D, Padovani CR. 2004. Bayesian longitudinal data analysis with mixed models and thick-tailed distributions using MCMC. J. Appl. Stat. 31:855–73 [Google Scholar]
  176. Kizilkaya K, Tempelman RJ. 2005. A general approach to mixed effects modeling of residual variances in generalized linear mixed models. Genet. Sel. Evol. 37:31–56 [Google Scholar]
  177. Kizilkaya K, Fernando RL, Garrick DJ. 2014. Reduction in accuracy of genomic prediction for ordered categorical data compared to continuous observations. Genet. Sel. Evol. 46:37 [Google Scholar]
  178. Reber DL, Stern HS, Berger PJ. 2000. Bayesian inference for the mixed linear model with application to selection in animal breeding. J. Agric. Biol. Environ. Stat. 5:240–56 [Google Scholar]
  179. Gianola D, Heringstad B, Ødegård J. 2006. On the quantitative genetics of mixture characters. Genetics 173:2247–55 [Google Scholar]
  180. Detilleux J, Leroy PL. 2000. Application of a mixed normal mixture model to the estimation of mastitis-related parameters. J. Dairy Sci. 83:2341–49 [Google Scholar]
  181. Ødegård J, Jensen J, Madsen P, Gianola D, Klemetsdal G et al. 2003. Mixture models for detection of mastitis in dairy cattle using test-day somatic cell scores: a Bayesian approach via Gibbs sampling. J. Dairy Sci. 86:3694–703 [Google Scholar]
  182. Ødegård J, Jensen J, Madsen P, Gianola D, Klemetsdal G. 2005. A Bayesian liability-normal mixture model for analysis of a continuous mastitis-related trait. J. Dairy Sci. 88:2652–59 [Google Scholar]
  183. Boettcher PJ, Moroni P, Pisoni G, Gianola D. 2005. Application of a finite mixture model to somatic cell scores of Italian goats. J. Dairy Sci. 88:2209–16 [Google Scholar]
  184. Rodrigues-Motta M, Gianola D, Chang YM, Heringstad B. 2006. A zero-inflated Poisson model for genetic analysis of number of mastitis cases in Norwegian red cows. Proc. 8th World Congr. Genet. Appl. Livest. Prod. CD Pap. 26-05. Belo Horizonte, Brazil: Inst. Prociencia [Google Scholar]
  185. Celeux G, Hurn M, Robert C. 2000. Computational and inferential difficulties with mixture posterior distributions. J. Am. Stat. Assoc. 95:957–79 [Google Scholar]
  186. Meyer K. 1991. Estimating variances and covariances for multivariate animal models by restricted maximum likelihood. Genet. Sel. Evol. 23:67–83 [Google Scholar]
  187. Kriese LA, Boldman KG, Van Vleck LD, Kachman SD. 1994. A flexible set of programs to estimate (co)variances for messy multiple trait animal models using derivative free REML and sparse matrix techniques. Proc. 5th World Congr. Genet. Appl. Livest. Prod. 2243–44 Guelph, Can.: Univ. Guelph [Google Scholar]
  188. Groeneveld E. 1994. VCE: a multivariate multimodel REML (co)variance component estimation package. Proc. 5th World Congr. Genet. Appl. Livest. Prod. 2247–48 Guelph, Can.: Univ. Guelph [Google Scholar]
  189. Gilmour AR, Thompson R, Cullis BR. 1995. AI, an efficient algorithm for REML estimation in linear mixed models. Biometrics 51:1440–50 [Google Scholar]
  190. Van Tassel CP, Van Vleck LD. 1996. Multiple-trait Gibbs sampler for animal models: flexible programs for Bayesian and likelihood based (co)variance component inference. J. Anim. Sci. 74:2586–97 [Google Scholar]
  191. Groeneveld E, Garcia Cortes LA. 1998. VCE 4.0: a (co)variance component package for frequentists and Bayesians. Proc. 6th World Congr. Genet. Appl. Livest. Prod. 27455–56 Armidale, UK: Anim. Genet. Breed. Unit [Google Scholar]
  192. Curnow RN. 1961. The estimation of repeatability and heritability from records subject to culling. Biometrics 17:553–66 [Google Scholar]
  193. Im S, Fernando RL, Gianola D. 1989. Likelihood inferences in animal breeding under selection: a missing data theory viewpoint. Genet. Sel. Evol. 21:399–414 [Google Scholar]
  194. Weller JI. 1986. Maximum likelihood techniques for the mapping and analysis of quantitative trait loci with the aid of genetic markers. Biometrics 42:627–41 [Google Scholar]
  195. Lander ES, Botstein D. 1989. Mapping Mendelian factors underlying quantitative traits using RFLP linkage maps. Genetics 121:185–99 [Google Scholar]
  196. Lande R, Thompson R. 1990. Efficiency of marker-assisted selection in the improvement of quantitative traits. Genetics 124:743–56 [Google Scholar]
  197. Gianola D, de los Campos G, Hill WG, Manfredi E, Fernando RL. 2009. Additive genetic variability and the Bayesian alphabet. Genetics 187:347–63 [Google Scholar]
  198. Schaeffer LR. 2006. Strategy for applying genome-wide selection in dairy cattle. J. Anim. Breed. Genet. 123:218–23 [Google Scholar]
  199. Van Raden PM, Van Tassell CP, Wiggans GR, Sonstegard TS, Schnabel RD et al. 2009. Reliability of genomic predictions for North American Holstein bulls. J. Dairy Sci. 92:16–24 [Google Scholar]
  200. Hayes BJ, Bowman PJ, Chamberlain AJ, Goddard ME. 2009. Genomic selection in dairy cattle: progress and challenges. J. Dairy Sci. 92:433–43 [Google Scholar]
  201. Habier D, Fernando RL, Dekkers JCM. 2007. The impact of genetic relationship information on genome-assisted breeding values. Genetics 177:2389–97 [Google Scholar]
  202. Van Raden PM. 2008. Efficient methods to compute genomic predictions. J. Dairy Sci. 91:4414–23 [Google Scholar]
  203. Goddard ME. 2009. Genomic selection: prediction of accuracy and maximisation of long term response. Genetica 136:245–57 [Google Scholar]
  204. de los Campos G, Naya H, Gianola D, Crossa J, Legarra A et al. 2009. Predicting quantitative traits with regression models for dense molecular markers and pedigree. Genetics 182:375–85 [Google Scholar]
  205. Habier D, Fernando RL, Kizilkaya K, Garrick DJ. 2011. Extension of the Bayesian alphabet for genomic selection. BMC Bioinform. 12:186 [Google Scholar]
  206. Erbe M, Hayes BJ, Matukumali LK, Goswami S, Bowman PJ et al. 2012. Improving accuracy of genomic predictions within and between dairy cattle breeds with imputed high-density single nucleotide polymorphism panels. J. Dairy Sci. 95:4114–29 [Google Scholar]
  207. de los Campos G, Hickey JM, Pong-Wong R, Daetwyler HD, Calus MPL. 2013. Whole-genome regression and prediction methods applied to plant and animal breeding. Genetics 193:327–45 [Google Scholar]
  208. Heslot N, Yang HP, Sorrells ME, Jannink JL. 2012. Genomic selection in plant breeding: a comparison of models. Crop Sci. 52:146–60 [Google Scholar]
  209. Gianola D, Perez-Enciso M, Toro M. 2003. On marker-assisted prediction of genetic value: beyond the ridge. Genetics 163:347–65 [Google Scholar]
  210. Yang W, Tempelman RJ. 2012. A Bayesian ante-dependence model for whole genome prediction. Genetics 4:1491–501 [Google Scholar]
  211. Wimmer V, Lehermeier C, Albrecht T, Auinger HJ, Wang Y, Schön CC. 2013. Genome-wide prediction of traits with different genetic architecture through efficient variable selection. Genetics 195:573–87 [Google Scholar]
  212. Lehermeier C, Wimmer V, Albrecht T, Auinger HJ, Gianola D et al. 2013. Sensitivity to prior specification in Bayesian genome-based prediction models. Stat. Appl. Genet. Mol. Biol. 12:1–17 [Google Scholar]
  213. González-Recio O, Gianola D, Rosa GJM, Weige KA, Kranis A. 2009. Genome-assisted prediction of a quantitative trait measured in parents and progeny: application to food conversion rate in chickens. Genet. Sel. Evol. 41:3–13 [Google Scholar]
  214. Erbe M, Pimentel ECG, Sharifi AR, Simianer H. 2010. Assessment of cross-validation strategies for genomic prediction in cattle. Proc. 9th World Congr. Genet. Appl. Livest. Prod., Abstr. 129.
  215. Daetwyler HD, Villanueva B, Woolliams JA. 2008. Accuracy of predicting the genetic risk of disease using a genome-wide approach. PLOS ONE 3:10e3395 [Google Scholar]
  216. Aguilar I, Misztal I, Johnson DL, Legarra A, Tsuruta S, Lawlor TJ. 2010. A unified approach to utilize phenotypic, full pedigree, and genomic information for genetic evaluation of Holstein final score. J. Dairy Sci. 93:743–52 [Google Scholar]
  217. Dekkers JCM, Hospital F. 2002. The use of molecular genetics in the improvement of agricultural populations. Nat. Rev. Genet. 3:22–32 [Google Scholar]
  218. Gianola D, Fernando RL, Stella A. 2006. Genomic assisted prediction of genetic value with semi-parametric procedures. Genetics 173:1761–76 [Google Scholar]
  219. Gianola D, Van Kaam JT. 2008. Reproducing kernel Hilbert spaces regression methods for genomic assisted prediction of quantitative traits. Genetics 178:2289–303 [Google Scholar]
  220. Gianola D, Okut H, Weigel KA, Rosa GJM. 2011. Predicting complex quantitative traits with Bayesian neural networks: a case study with Jersey cows and wheat. BMC Genet. 12:87 [Google Scholar]
  221. Pérez-Rodríguez P, Gianola D, Weigel KA, Rosa GJ, Crossa J. 2013. An R package for fitting Bayesian regularized neural networks with applications in animal breeding. J. Anim. Sci. 91:3522–31 [Google Scholar]
  222. González-Recio O, Gianola D, Long L, Weigel KA, Rosa GJM, Avendaño S. 2008. Non-parametric methods for incorporating genomic information into genetic evaluations: an application to mortality in broilers. Genetics 178:2305–13 [Google Scholar]
  223. Jarquín D, Crossa J, Lacaze X, Du Cheyron P, Daucourt J et al. 2014. A reaction norm model for genomic selection using high-dimensional genomic and environmental data. Theor. Appl. Genet. 127:595–607 [Google Scholar]
  224. Tusell L, Pérez-Rodríguez P, Forni S, Wu XL, Gianola D. 2013. Genome-enabled methods for predicting litter size in pigs: a comparison. Animal 7:1739–49 [Google Scholar]
  225. Ornella L, Pérez P, Tapia E, González-Camacho JM, Burgueño J et al. 2014. Genomic-enabled prediction with classification algorithms. Heredity 112:616–26 [Google Scholar]
  226. Wheeler HE, Aquino-Michaels K, Gamazon ER, Trubetskoy VV, Dolan ME et al. 2014. Poly-omic prediction of complex traits: OmicKriging. Genet. Epidemiol. 38:412–15 [Google Scholar]
  227. Breiman L. 1996. Bagging predictors. Mach. Learn. 24:123–40 [Google Scholar]
  228. Gianola D, Sorensen D. 2004. Quantitative genetic models for describing simultaneous and recursive relationships between phenotypes. Genetics 176:1407–24 [Google Scholar]
  229. Rosa GJM, Valente BD, de los Campos G, Wu XL, Gianola D, Silva MA. 2011. Inferring causal phenotype networks using structural equation models. Genet. Sel. Evol. 43:6 [Google Scholar]
  230. Valente BD, Rosa GJM, Gianola D, Wu XL, Weigel KA. 2013. Is structural equation modeling advantageous for the genetic improvement of multiple traits?. Genetics 194:561–72 [Google Scholar]
  231. Civelek M, Lusis AJ. 2014. Systems genetics approaches to understand complex traits. Nat. Rev. Genet. 15:34–48 [Google Scholar]
  232. Cartwright TC, Fitzhugh HA, Long CR. 1975. Systems analysis of sources of genetic and environmental variation in efficiency of beef production: mating plans. J. Anim. Sci. 40:433–43 [Google Scholar]
  • Article Type: Review Article
This is a required field
Please enter a valid email address
Approval was a Success
Invalid data
An Error Occurred
Approval was partially successful, following selected items could not be processed due to error