Charles Roy Henderson Explained

Charles Roy Henderson
Birth Date:	1 April 1911
Birth Place:	Coin, Iowa, US
Death Place:	Urbana, Illinois, US
Workplaces:	Cornell University University of Illinois University of Guelph
Alma Mater:	Iowa State University
Doctoral Advisor:	Lenoy Nelson Hazel^[1] Oscar Kempthorne

Charles Roy Henderson (1 April 1911 –) was an American statistician and a pioneer in animal breeding — the application of quantitative methods for the genetic evaluation of domestic livestock. This is critically important because it allows farmers and geneticists to predict whether a crop or animal will have a desired trait, and to what extent the trait will be expressed. He developed mixed model equations to obtain best linear unbiased predictions of breeding values and, in general, any random effect. He invented three methods for the estimation of variance components in unbalanced settings of mixed models, and invented a method for constructing the inverse of Wright's numerator relationship matrix based on a simple list of pedigree information. He, with his Ph.D. student Shayle R. Searle, greatly extended the use of matrix notation in statistics. His methods are widely used by the domestic livestock industry throughout the world and are a cornerstone of linear model theory.

Henderson obtained his B.Sc., M.Sc.(nutrition) and Ph.D.(breeding) degrees at Iowa State University, where he was a student of Professor L. N. Hazel. Henderson joined the faculty of the Department of Animal Science at Cornell University in 1948, and headed the Animal Breeding division for nearly 30 years until he retired in 1976. After retiring from Cornell, he was a visiting professor at the University of Guelph and University of Illinois until his death. He completed his book in 1984 at the University of Guelph.

Honors and awards

1955, Senior Fulbright Research Scholar (New Zealand)
1964, Borden Award, American Dairy Science Association
1964, Animal Breeding and Genetics Award, American Society of Animal Science
1969, Fellow, American Statistical Association
1971, Morrison Award, American Society of Animal Science
1977, National Association of Animal Breeders Award, American Dairy Science Association
1980, Member of the Massey University Wellington
1981, Visiting professor at the University of California, Davis
1981, Hermann-von-Nathusius-Medaille in Gold of the German Society for Animal Production (DGfZ) ^[2]
1981, Fellow, American Society of Animal Science
1982, Jay L. Lush Animal Breeding and Genetics Award, American Dairy Science Association
1984, Henry A. Wallace Award for Service to Agriculture, Iowa State University
1985, Elected to the United States National Academy of Sciences

Selected bibliography

1990s

Book: 1990 . Henderson, CR . Statistical Methods in Animal Improvement: Historical Overview . Advances in Statistical Methods for Genetic Improvement of Livestock . Gianola, Daniel . Hammond, Keith . Springer-Verlag Inc . 2–14 . 978-3-540-50809-0.
Book: 1990 . Henderson, CR . Accounting for Selection and Mating Biases in Genetic Evaluation . Advances in Statistical Methods for Genetic Improvement of Livestock . Gianola, Daniel . Daniel Gianola . Hammond, Keith . Keith Hammond . Springer-Verlag Inc . 413–436 . 978-3-540-50809-0.

1980s

1989 . Henderson . C. R. . Prediction of Merits of Potential Matings from Sire-Maternal Grandsire Models with Nonadditive Genetic Effects . 10.3168/jds.S0022-0302(89)79400-5 . Journal of Dairy Science . 72 . 10 . 2592–2605 . free .
1988 . Henderson, CR . Use of an average numerator relationship matrix for multiple-sire joining . Journal of Animal Science . 66 . 7 . 1614–1621 . 10.2527/jas1988.6671614x .
1988 . Henderson . C. R. . The use of equivalent linear models in mixed model estimation and prediction . 10.1080/03610928808829668 . Communications in Statistics - Theory and Methods . 17 . 4 . 969–982 .
1988 . Henderson . C. R. . Simple Method to Compute Biases and Mean Squared Errors of Linear Estimators and Predictors in a Selection Model Assuming Multivariate Normality . 10.3168/jds.S0022-0302(88)79914-2 . Journal of Dairy Science . 71 . 11 . 3135–3142 . free .
1988 . Henderson . C. R. . Exact Prediction Error Variances for Full Model Computed from Reduced Model . 10.3168/jds.S0022-0302(88)79913-0 . Journal of Dairy Science . 71 . 11 . 3128–3134 . free .
1988 . Henderson . C. R. . A Simple Method to Account for Selected Base Populations . 10.3168/jds.S0022-0302(88)79945-2 . Journal of Dairy Science . 71 . 12 . 3399–3404 . free .
1986 . Sasaki . Yoshiyuki . Henderson . C. R. . Best Linear Unbiased Prediction with the Reduced Animal Model: An Application to Evaluation of Performance-Tested Males . Journal of Animal Science . 63 . 5 . 1384–1388 . 0021-8812 . 10.2527/jas1986.6351384x .
1986 . Henderson . C. R. . Estimation of Variances in Animal Model and Reduced Animal Model for Single Traits and Single Records . 10.3168/jds.S0022-0302(86)80546-X . Journal of Dairy Science . 69 . 5 . 1394–1402 . free .
1986 . Henderson . C. R. . Estimation of Singular Covariance Matrices of Random Effects . 10.3168/jds.S0022-0302(86)80677-4 . Journal of Dairy Science . 69 . 9 . 2379–2385 . free .
1986 . Henderson, CR . Recent Developments in Variance and Covariance Estimation . Journal of Animal Science . 63 . 208–216 . 10.2527/jas1986.631208x .
1985 . Henderson, CR . Best linear unbiased prediction of nonadditive genetic merits in noninbred populations . Journal of Animal Science . 60 . 111–117 . 10.2527/jas1985.601111x .
1985 . Henderson . C. R. . Equivalent Linear Models to Reduce Computations . 10.3168/jds.S0022-0302(85)81099-7 . Journal of Dairy Science . 68 . 9 . 2267–2277 . free .
1985 . Henderson . C. R. . Best Linear Unbiased Prediction Using Relationship Matrices Derived from Selected Base Populations . 10.3168/jds.S0022-0302(85)80843-2 . Journal of Dairy Science . 68 . 2 . 443–448 . free .
1985 . Henderson, CR . MIVQUE and REML Estimation of Additive and Nonadditive Genetic Variances . Journal of Animal Science . 61 . 113–121 . 10.2527/jas1985.611113x .
1984 . Henderson . C. R. . Estimation of Variances and Covariances under Multiple Trait Models . 10.3168/jds.S0022-0302(84)81480-0 . Journal of Dairy Science . 67 . 7 . 1581–1589 . free .
Book: 1984 . Henderson, CR . Applications of Linear Models in Animal Breeding . University of Guelph . Guelph, Ont . 978-0-88955-030-8.
Book: 1984 . Henderson, C.R. . ANOVA, MIVQUE, REML, and ML Algorithms for Estimation of Variances and Covariances . Statistics: An Appraisal . David, H. A. . David, H. T. . Iowa State University . 257–280 . 978-0-8138-1721-7.
Book: 1980 . Henderson, CR . Comparison of Unbiased Estimators and Approximate Tests of Hypothesis in the Unbalanced Mixed Model with Unknown Variances . ASA Proceedings of the Statistical Computing Section . American Statistical Association . 47–51 .

1970s

1979 . Henderson . C. R. . 10.1080/03610927908827798 . Analysis of covariance in mixed models with unequal subclass numbers . Communications in Statistics - Theory and Methods . 8 . 8 . 751–787 .
1978 . Henderson, CR . Simulation to examine distributions of estimators of variances and ratios of variances . . 61 . 2 . 267–273 . 10.3168/jds.S0022-0302(78)83590-5 . free .
1978 . Henderson, CR . McAllister, AJ . The missing subclass problem in two way fixed models . Journal of Animal Science . 46 . 4 . 1125–1137 . 10.2527/jas1978.4641125x .
1978 . Henderson . C. R. . Variance-Covariance Matrix of Estimators of Variances in Unweighted Means ANOVA . Biometrics . 34 . 3 . 462–468 . 10.2307/2530609 . 2530609 .
1977 . Henderson, CR . Best linear unbiased prediction of breeding values not in the model for records . . 60 . 5 . 783–787 . 10.3168/jds.S0022-0302(77)83935-0 . free .
1977 . Henderson . C. R. . Prediction of the merits of single crosses . 10.1007/BF00275133 . Theoretical and Applied Genetics . 49 . 6 . 273–282 . 24407416. 20208156 .
1976 . Henderson, CR . Inverse of a matrix of relationships due to sires and maternal grandsires in an inbred population . . 59 . 9 . 1585–1588 . 10.3168/jds.S0022-0302(76)84409-8 . free .
1976 . Henderson, CR . Quaas, RL . Multiple trait evaluation using relatives' records . Journal of Animal Science . 43 . 6 . 1188–1197 . 10.2527/jas1976.4361188x .
1976 . Henderson, CR . Multiple trait sire evaluation using the relationship matrix . . 59 . 4 . 769–774 . 10.3168/jds.S0022-0302(76)84274-9 . free .
1976 . Henderson . C. R. . A Simple Method for Computing the Inverse of a Numerator Relationship Matrix Used in Prediction of Breeding Values . Biometrics . 32 . 1 . 69–83 . 10.2307/2529339 . 2529339 .
1975 . Henderson, CR . Comparison of alternative sire evaluation methods . Journal of Animal Science . 41 . 3 . 760–770 . 10.2527/jas1975.413760x .
1975 . Henderson, CR . Use of relationships among sires to increase accuracy of sire evaluation . . 58 . 11 . 1731–1738 . 10.3168/jds.S0022-0302(75)84777-1 . free .
1975 . Henderson, CR . Rapid method for computing the inverse of a relationship matrix . . 58 . 11 . 1727–1730 . 10.3168/jds.S0022-0302(75)84776-X . free .
1975 . Henderson, CR . Use of all relatives in intraherd prediction of breeding values and producing abilities . . 58 . 12 . 1910–1916 . 10.3168/jds.S0022-0302(75)84808-9 . free .
1975 . Henderson, CR . Inverse of a matrix of relationships due to sires and maternal grandsires . . 58 . 12 . 1917–1921 . 10.3168/jds.S0022-0302(75)84809-0 . free .
1975 . Henderson . C. R. . Rapid Method for Computing the Inverse of a Relationship Matrix . 10.3168/jds.S0022-0302(75)84776-X . Journal of Dairy Science . 58 . 11 . 1727–1730 . free .
1975 . Henderson . C. R. . Best Linear Unbiased Estimation and Prediction under a Selection Model . Biometrics . 31 . 2 . 423–447 . 10.2307/2529430 . 1174616. 2529430 .
1974 . Henderson . C. R. . Searle . S. R. . Schaeffer . L. R. . The Invariance and Calculation of Method 2 for Estimating Variance Components . Biometrics . 30 . 4 . 583–588 . 10.2307/2529223 . 2529223 .
1973 . Henderson . C. R. . Sire Evaluation and Genetic Trends . Journal of Animal Science . 1973. 10–41 . 10.1093/ansci/1973.Symposium.10 .
1971 . Lee . A. J . Henderson . C. R. . Effect of Cow Culling on Repeatability Estimates . Journal of Animal Science . 32 . 2 . 167–173 . 0021-8812 . 10.2527/jas1971.322167x .

1960s

1969 . Lee . AJ . Henderson . CR . Components in genetic variance in milk yield . J Dairy Sci . 52 . 6 . 780–9 . 10.3168/jds.s0022-0302(69)86648-8 . 4907259 . free .
1968 . Cunningham . E. P. . Henderson . C. R. . An Iterative Procedure for Estimating Fixed Effects and Variance Components in Mixed Model Situations . Biometrics . 24 . 1 . 13–25 . 10.2307/2528457 . 5642400. 2528457 .
1966 . Cunningham . E. P. . Henderson . C. R. . Analytical Techniques for Incomplete Block Experiments . Biometrics . 22 . 4 . 829–842 . 10.2307/2528077 . 2528077 .
1965 . Van Vleck . L. D. . Henderson . C.R. . Statistics in the Design and Analysis of Physiology Experiments . J. Anim. Sci. . 24 . 2 . 559–67 . 14324385 . 10.2527/jas1965.242559x .
1965 . Cunningham . E. P. . Henderson . C. R. . Repeatability of Weaning Traits in Beef Cattle1 . Journal of Animal Science . 24 . 1 . 188–191 . 0021-8812 . 10.2527/jas1965.241188x .
1965 . Cunningham . E. P. . Henderson . C. R. . Estimation of Genetic and Phenotypic Parameters of Weaning Traits in Beef Cattle1 . Journal of Animal Science . 24 . 1 . 182–187 . 0021-8812 . 10.2527/jas1965.241182x .
1965 . Allaire . F. R. . Henderson . C. R. . 10.3168/jds.S0022-0302(65)88465-X . Inbreeding Within an Artificially Bred Dairy Cattle Population . Journal of Dairy Science . 48 . 10 . 1366–1371 . 5863527. free .
1962 . VanVleck . L. D. . Henderson . C. R. . Carter . H. W. . Evaluation of Sires Available through Planned Mating . Journal of Animal Science . 21 . 1 . 30–32 . 0021-8812 . 10.2527/jas1962.21130x . 86233026 .
1961 . VanVleck . L. D. . Wadell . L. H. . Henderson . C. R. . Components of Variance Associated with Milk and Fat Records of Artificially Sired Holstein Daughters . Journal of Animal Science . 20 . 4 . 812–816 . 0021-8812 . 10.2527/jas1961.204812x . 82719432 .
1961 . Searle . S. R. . Henderson . C. R. . Computing Procedures for Estimating Components of Variance in the Two-Way Classification, Mixed Model . Biometrics . 17 . 4 . 607–616 . 10.2307/2527859 . 2527859 .
1961 . Heidhues . T . Henderson . C. R. . Teaching Selection Principles with Herd Records Generated by an Electronic Computer . Journal of Animal Science . 20 . 3 . 659–664 . 0021-8812 . 10.2527/jas1961.203659x .
1960 . VanVleck . L. D. . Searle . S. R. . Henderson . C. R. . The Number of Daughter-Dam Pairs Needed for Estimating Heritability . Journal of Animal Science . 19 . 3 . 916–920 . 0021-8812 . 10.2527/jas1960.193916x . 82532852 .

1950s

1959 . Henderson . C. R. . Kempthorne . O. . Searle . S. R. . Von Krosigk . C. M. . The Estimation of Environmental and Genetic Trends from Records Subject to Culling . Biometrics . 15 . 2 . 10.2307/2527669 . 192–218 . 2527669 .
1955 . Blackwell . R. L. . Henderson . C. R. . Variation in Fleece Weight, Weaning Weight and Birth Weight of Sheep under Farm Conditions . Journal of Animal Science . 14 . 3 . 831–843 . 0021-8812 . 10.1093/ansci/14.3.831 .
1953 . Henderson . C. R. . Estimation of Variance and Covariance Components . Biometrics . 9 . 2 . 226–252 . 10.2307/3001853 . 3001853 .

References

1980 . Anon . Henderson, CR: Estimation of variance and covariance components . Current Contents/Agriculture Biology & Environmental Sciences . 24 . 10 .
Van Vleck . L. D. . Charles Roy Henderson, 1911-1989: A brief biography . Journal of Animal Science . 76 . 12 . 2959–2961 . 1998 . 9928597 . 10.2527/1998.76122959x.
Freeman . A. E. . C. R. Henderson: Contributions to the Dairy Industry . 10.3168/jds.S0022-0302(91)78600-1 . Journal of Dairy Science . 74 . 11 . 4045–4051 . 1991 . 1757642. free .
Kennedy . B. W. . C. R. Henderson: The Unfinished Legacy . 10.3168/jds.S0022-0302(91)78602-5 . Journal of Dairy Science . 74 . 11 . 4067–4081 . 1991 . 1757644. free .
Schaeffer . L. R. . C. R. Henderson: Contributions to Predicting Genetic Merit . 10.3168/jds.S0022-0302(91)78601-3 . Journal of Dairy Science . 74 . 11 . 4052–4066 . 1991 . 1757643. free .
Searle . S. R. . C. R. Henderson, the Statistician; and His Contributions to Variance Components Estimation . 10.3168/jds.S0022-0302(91)78599-8 . Journal of Dairy Science . 74 . 11 . 4035–4044 . 1991 . 1757641. 1813/31657 . free .
Van Vleck . L. D. . C. R. Henderson: Farm Boy, Athlete, and Scientist . 10.3168/jds.S0022-0302(91)78603-7 . Journal of Dairy Science . 74 . 11 . 4082–4096 . 1991 . 1757645. free .
News: Charles Henderson, Statistician, Dies at 77. The New York Times. 10. March 18, 1989.
Book: Charles Roy Henderson, April 1, 1911 – March 14, 1989 . L. Dale Van Vleck . . 1998.
Book: Summary of Oral Interviews Created as Part of an Artificial Insemination Documentation Project . Robert H. Foote . Cornell University . Ithaca, NY . August 2002 . 9780889550308 . 64074423 .

Notes and References

http://www.ans.iastate.edu/history/faculty/hazel/hazel.html Lanoy Nelson Hazel 1911-1992
http://www.dgfz-bonn.de/hermann_von_nathusius.html List of people honored with the Herman-von-Nathusius-Medaille