# Charles Roy Henderson

Charles Roy Henderson ((1911-04-01)April 1, 1911 – (1989-03-14)March 14, 1989) 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)
* 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

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

### 1980s

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

### 1970s

* Henderson, C. R. (1979). "Analysis of covariance in mixed models with unequal subclass numbers". Communications in Statistics - Theory and Methods. 8 (8): 751–787. doi:10.1080/03610927908827798.
* Henderson, CR (1978). "Simulation to examine distributions of estimators of variances and ratios of variances". Journal of Dairy Science. 61 (2): 267–273. doi:10.3168/jds.S0022-0302(78)83590-5.
* Henderson, CR; McAllister, AJ (1978). "The missing subclass problem in two way fixed models". Journal of Animal Science. 46 (4): 1125–1137. doi:10.2527/jas1978.4641125x.
* Henderson, C. R. (1978). "Variance-Covariance Matrix of Estimators of Variances in Unweighted Means ANOVA". Biometrics. 34 (3): 462–468. doi:10.2307/2530609. JSTOR 2530609.
* Henderson, CR (1977). "Best linear unbiased prediction of breeding values not in the model for records". Journal of Dairy Science. 60 (5): 783–787. doi:10.3168/jds.S0022-0302(77)83935-0.
* Henderson, C. R. (1977). "Prediction of the merits of single crosses". Theoretical and Applied Genetics. 49 (6): 273–282. doi:10.1007/BF00275133. PMID 24407416. S2CID 20208156.
* Henderson, CR (1976). "Inverse of a matrix of relationships due to sires and maternal grandsires in an inbred population". Journal of Dairy Science. 59 (9): 1585–1588. doi:10.3168/jds.S0022-0302(76)84409-8.
* Henderson, CR; Quaas, RL (1976). "Multiple trait evaluation using relatives' records". Journal of Animal Science. 43 (6): 1188–1197. doi:10.2527/jas1976.4361188x.
* Henderson, CR (1976). "Multiple trait sire evaluation using the relationship matrix". Journal of Dairy Science. 59 (4): 769–774. doi:10.3168/jds.S0022-0302(76)84274-9.
* Henderson, C. R. (1976). "A Simple Method for Computing the Inverse of a Numerator Relationship Matrix Used in Prediction of Breeding Values". Biometrics. 32 (1): 69–83. doi:10.2307/2529339. JSTOR 2529339.
* Henderson, CR (1975). "Comparison of alternative sire evaluation methods". Journal of Animal Science. 41 (3): 760–770. doi:10.2527/jas1975.413760x.
* Henderson, CR (1975). "Use of relationships among sires to increase accuracy of sire evaluation". Journal of Dairy Science. 58 (11): 1731–1738. doi:10.3168/jds.S0022-0302(75)84777-1.
* Henderson, CR (1975). "Rapid method for computing the inverse of a relationship matrix". Journal of Dairy Science. 58 (11): 1727–1730. doi:10.3168/jds.S0022-0302(75)84776-X.
* Henderson, CR (1975). "Use of all relatives in intraherd prediction of breeding values and producing abilities". Journal of Dairy Science. 58 (12): 1910–1916. doi:10.3168/jds.S0022-0302(75)84808-9.
* Henderson, CR (1975). "Inverse of a matrix of relationships due to sires and maternal grandsires". Journal of Dairy Science. 58 (12): 1917–1921. doi:10.3168/jds.S0022-0302(75)84809-0.
* Henderson, C. R. (1975). "Rapid Method for Computing the Inverse of a Relationship Matrix". Journal of Dairy Science. 58 (11): 1727–1730. doi:10.3168/jds.S0022-0302(75)84776-X.
* Henderson, C. R. (1975). "Best Linear Unbiased Estimation and Prediction under a Selection Model". Biometrics. 31 (2): 423–447. doi:10.2307/2529430. JSTOR 2529430. PMID 1174616.
* Henderson, C. R.; Searle, S. R.; Schaeffer, L. R. (1974). "The Invariance and Calculation of Method 2 for Estimating Variance Components". Biometrics. 30 (4): 583–588. doi:10.2307/2529223. JSTOR 2529223.
* Henderson, C. R. (1973). "Sire Evaluation and Genetic Trends". Journal of Animal Science. 1973: 10–41. doi:10.1093/ansci/1973.Symposium.10.
* Lee, A. J; Henderson, C. R. (1971). "Effect of Cow Culling on Repeatability Estimates". Journal of Animal Science. 32 (2): 167–173. doi:10.2527/jas1971.322167x. ISSN 0021-8812.

### 1960s

* Lee, AJ; Henderson, CR (1969). "Components in genetic variance in milk yield". J Dairy Sci. 52 (6): 780–9. doi:10.3168/jds.s0022-0302(69)86648-8. PMID 4907259.
* Cunningham, E. P.; Henderson, C. R. (1968). "An Iterative Procedure for Estimating Fixed Effects and Variance Components in Mixed Model Situations". Biometrics. 24 (1): 13–25. doi:10.2307/2528457. JSTOR 2528457. PMID 5642400.
* Cunningham, E. P.; Henderson, C. R. (1966). "Analytical Techniques for Incomplete Block Experiments". Biometrics. 22 (4): 829–842. doi:10.2307/2528077. JSTOR 2528077.
* Van Vleck, L. D.; Henderson, C.R. (1965). "Statistics in the Design and Analysis of Physiology Experiments". J. Anim. Sci. 24 (2): 559–67. doi:10.2527/jas1965.242559x. PMID 14324385.
* Cunningham, E. P.; Henderson, C. R. (1965). "Repeatability of Weaning Traits in Beef Cattle1". Journal of Animal Science. 24 (1): 188–191. doi:10.2527/jas1965.241188x. ISSN 0021-8812.
* Cunningham, E. P.; Henderson, C. R. (1965). "Estimation of Genetic and Phenotypic Parameters of Weaning Traits in Beef Cattle1". Journal of Animal Science. 24 (1): 182–187. doi:10.2527/jas1965.241182x. ISSN 0021-8812.
* Allaire, F. R.; Henderson, C. R. (1965). "Inbreeding Within an Artificially Bred Dairy Cattle Population". Journal of Dairy Science. 48 (10): 1366–1371. doi:10.3168/jds.S0022-0302(65)88465-X. PMID 5863527.
* VanVleck, L. D.; Henderson, C. R.; Carter, H. W. (1962). "Evaluation of Sires Available through Planned Mating". Journal of Animal Science. 21 (1): 30–32. doi:10.2527/jas1962.21130x. ISSN 0021-8812. S2CID 86233026.
* VanVleck, L. D.; Wadell, L. H.; Henderson, C. R. (1961). "Components of Variance Associated with Milk and Fat Records of Artificially Sired Holstein Daughters". Journal of Animal Science. 20 (4): 812–816. doi:10.2527/jas1961.204812x. ISSN 0021-8812. S2CID 82719432.
* Searle, S. R.; Henderson, C. R. (1961). "Computing Procedures for Estimating Components of Variance in the Two-Way Classification, Mixed Model". Biometrics. 17 (4): 607–616. doi:10.2307/2527859. JSTOR 2527859.
* Heidhues, T; Henderson, C. R. (1961). "Teaching Selection Principles with Herd Records Generated by an Electronic Computer". Journal of Animal Science. 20 (3): 659–664. doi:10.2527/jas1961.203659x. ISSN 0021-8812.
* VanVleck, L. D.; Searle, S. R.; Henderson, C. R. (1960). "The Number of Daughter-Dam Pairs Needed for Estimating Heritability". Journal of Animal Science. 19 (3): 916–920. doi:10.2527/jas1960.193916x. ISSN 0021-8812. S2CID 82532852.

### 1950s

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