Charles Roy Henderson

The material presented here is taken from an article by Dr. L. D. Van Vleck, J. Animal Sci. 76:2959-2961.
Please see this article for full details.  Below is a summary of life statistics.

Born: April 1, 1911 in Coin, Iowa, USA (located in Page County, Iowa), raised on a general livestock farm.  He had 3 brothers and one sister.  His parents were Arthur James Henderson and Maud McMichael Henderson.
Died: March 14, 1989 in Champaign, Illinois, USA, from a pulmonary embolism.
Married to Marian M. Martin, December 21, 1940, she died April 16, 1994.  Together they had three children, Charles Jr., James, and Elizabeth.

Iowa State University 1929-1933, B.S. in Animal Husbandry, 1933.

Iowa State University, Graduate Assistant, 1933-1935, M.Sc. in Animal Nutrition, 1935.

Iowa Extension Service, Assistant County Agent, County Agricultural Agent, District Land Use Planning Specialist, 1935-1940.

Ohio Univeristy, Athens, Ohio, 1941-1942, Instructor in animal science, agronomy, and farm management. Was manager of the university farm.

U. S. Army, 1942-1946.  Was a 1st Lieutenant, captain, major in the medical department.  Was assigned to the U. S. Army Medical Nutrition Laboratory and to Fort Knox Armored Forces Research Laboratory where he did teaching and research in military nutrition.  Final assignment was as Commanding Officer of the Medical Nutrition Laboratory.  It was during this time that he became the unofficial statistician of the research group.

Iowa State University, 1946-1948, returned to do a Ph.D. in Genetics and Animal Breeding with Dr. J. L. Lush, with a minor in mathematical statistics, 1948.

Cornell University, 1948-1951, Associate Professor in Animal Science.  In 1951 he became full professor and worked until his retirement in 1976.  He was the head of the animal breeding division and in charge of the graduate program in animal breeding.

Senior Fullbright Research Scholar in New Zealand, 1955-1956, where he met Shayle R. Searle and learned matrix algebra.

Cornell University, Emeritus Professor in 1976 until his death.

He was visiting professor at the University of Wisconsin in the summer of 1978, at the University of Illinois in 1980, was an invited speaker at the World Sheep and Beef Cattle Breeding Congress, New Zealand in November 1980 and was a Massey University Fellow at the same time.  In the early 1980's he visited the University of Guelph numerous times and wrote his book which was published in 1984 (Applications of Linear Models in Animal Breeding)

Honors and Awards
    Borden Award of American Dairy Science Association, 1964
    Eastern AI Cooperative Award of Merit, 1968
    Animal Breeding and Genetics Award of ASAS, 1967
    Fellow of Americal Statistical Association, 1969
    Morrison Award of ASAS, 1971
    National Association of Animal Breeders Award of ADSA, 1977
    Jay L. Lush Award, ADSA 1981?
    National Academy of Sciences, 1985
    Hermann von Nathusius Medal from German Society of Animal Production

The following was most likely prepared by Dale Van Vleck as part of the documentation for Henderson's nomination for the J. L. Lush Award, of which Henderson was the first recipient.  Thanks to Susan Herbert for compiling the list of graduate students of Henderson.

    The application of the research of Professor C. R. Henderson has resulted in a large increase in milk production with accompanying lower costs of production for dairymen, but more important, the provision of better nutrition at a lower cost to the consumer.  Professor Henderson developed methods of sire evaluation that have been used in the United States and in other countries since 1953.  These included, first, the herdmate method, followed by the sire comparison method, based on best linear unbiased prediction (BLUP).  His discovery of BLUP and its efficient computation by his mixed model methods has provided a remarkably powerful and flexible technique for solving a host of problems in animal breeding as well as in other fields.  This method is rapidly becoming the basis for sire evaluation worldwide.
    Henderson (1953) was the first to publish general methods for estimation of variance components from mixed models with unequal subclass numbers.  These methods have been widely employed by animal breeders to obtain estimates that are essential for design of selection programs.
    Professor Henderson was first to suggest that sampling of young sires in artificial breeding was an effective method for genetic improvement, and he developed methods for determining how many bulls to sample and how many progeny to obtain from each bull.  The New York Artificial Breeders' Cooperative initiated in 1950 a young sire program based on his research.  This later became the model for other artificial breeding organizations and is now used by all studs.
    A recent discovery by Henderson has made possible the realization of a long-time goal of animal breeders to utilize in their selection criteria the information coming from the entire matrix of relationships among relatives.  He found that the needed inverse of the matrix could be obtained extremely rapidly by a simple series of additions.  This discovery is now being used in both sire and cow evaluation around the world, and could be easily incorporated into mixed model methodology.  The major consequence of this development is that young sires can be evaluated more accurately, thereby improving the effectiveness of the young sire sampling program.
    The outstanding achievement of Henderson has been his almost single-handed merger and application of two apparently very different methods to modern animal breeding problems, namely the work of Sewall Wright and J. L. Lush on path coefficient methods and selection index and the pioneering work of Fisher and Yates on unbalanced, fixed linear models.  The techniques of Wright and Lush, which led to the selection index, assumed normally distributed observations jointly distributed with nonobservable breeding values that would logically be used in selection if they could be estimated.  The observations could be adjusted for all fixed environmental influences.  The solution to this adjustment problem motivated animal breeders to utilize least squares to estimate the environmental parameters from the data, often with many missing subclasses.  Since variance and covariances were required for the application of Wright's and Lush's methods, animal breeders became concerned with how to estimate these parameters from unbalanced data.  Statisticians had not developed methods prior to 1946 to handle this problem except for the nested hierarchial design.  This was the status of linear model theory and application when Henderson began his Ph.D. studies at Iowa State.  He had the good fortune to work with J. L. Lush, L. N. Hazel, O. Kempthorne and G. Sprague, all of whom were concerned with these problems.  Henderson chose as his thesis topic the estimation of variances due to general, specific, and maternal combining abilities in single crosses among inbred lines of swine.  Any realistic linear model for these data required a rather complicated linear model with many missing subclasses and with both fixed environmental and random genetic factors.  No techniques then existed for estimating the variances of interest.  This motivated the development of Henderson's Methods 1 and 3.  Method 3 turned out to be particularly powerful since it enabled unbiased estimators of variances to be obtained in the presence of confounding, fixed environmental factors.  Later Henderson's Method 2, a somewhat simpler method for certain mixed models was developed, and all three methods were published in 1953 in Biometrics, which became one of the most frequently cited publications in the scientific literature.  A conference honoring Henderson for his work in the field of variance component estimation and the application of these techniques to animal breeding was held at Cornell University in 1979.
    One clearly original piece of work was Henderson's invention of a method that minimized the contribution of interaction to the bias of estimators in the missing subclass case.  With filled subclasses the method reduced to Yates' weighted squares of means.  The method was incorporated in several computer packages for the analysis of linear models.  Many techniques for linear models were presented in detail in the appendix of his thesis.  For many years these were widely used by animal breeders and the large number who studied at Iowa State.
    In addition to estimation of variances of line cross parameters, Henderson attempted to evaluate the merits of different lines of swine as lines of sires and as lines of dams as well as the merits of specific crosses.  Selection index methods were inadequate to solve these problems in large bodies of data with missing subclasses.  Least squares estimation provided a mechanism, but failed to utilize knowledge that lines and crosses were random samples from a conceptual population as does the selection index.  Accordingly, Henderson developed a technique called regressed least squares to handle this problem.  He estimated breeding values by least squares and then treated these estimates as single observations in selection index evaluation.  Early in his career at Cornell he discovered a much more powerful method that completely integrated the two different approaches, least squares and selection index.  By a simple modification of the normal equations of least squares he was able to obtain a single set of solutions, the best linear unbiased estiamtors (BLUE) of the fixed effects and the selection index criteria for random effects, using records adjusted by the BLUE of the fixed effects.  He later proved that these were BLUP.  BLUP is an extremely flexible statistical procedure and can be used in many industries besides agriculture.
    A very troublesome problem facing animal breeders was the fact that data available for evaluating genetic merit usually came from breeders' herds of from experimental herds in which selection has been practiced.  This selection invalidates the usual random sampling assumptions underlying unbiased estimation methods.  Henderson was able to prove that under a wide range of selection methods and selection intensity the mixed model method yielded unbiased estimators and predictors.  Neither least squares nor selection index possessed these desirable properties.  Accordingly research workers have utilized the mixed model method to study the genetic improvement effected by different programs of selection and to estimate environmental parameters from field data.
    AI of dairy cattle was well underway in New York by the time Henderson began his work at Cornell.  Considerable data on the resulting progeny had accumulated and were studied by him and his students.  The methods of sire evaluation used in the US at that time were of little value in predicting the merit of a sire's progeny resulting from AI.  Differences in environments from herd to herd were a major cause of confusion.  Consequently he developed the herdmate method for dealing with this problem.  He also developed a simple equation based on selection index methods for taking into account the number of progeny for each sire.  The herdmate method was initiated in New York in 1953 and during the 1960s was adopted by the USDA in the national sire evaluation program.  The use of this method in association with AI has been credited with effecting spectacular increases in genetic merit of the US dairy cattle population.  For example, AI dairy cattle in the northeast US have increased in production by 4,815 pounds of milk since 1957 (up to 1979).  Genetic progress has been 43% of the total gain in milk.  This has resulted in additional gross income to northeast dairymen of over 3 billion dollars.  In fact, these increases eventually diminished the value of the herdmate method which was based on the assumption that all sires were mated to a random sample of cows from the same population.  Genetic trends and regional differences in breeding programs seriously invalidated this assumption.  Although it was known that Henderson's mixed model methods could circumvent these difficulties, improvements in computer technology were needed to apply them.  By 1970 the advances in computer technology caught up to Henderson's theory.  The sire comparison method was developed, based on BLUP and applied to the northeastern US dairy cattle population, and soon thereafter applied in Canada to national dairy evaluations (1975) and beef sire evaluations (1974).  Most of the beef cattle associations in the US have adopted these procedures, and the US national dairy program was modified to approximate BLUP.  BLUP appears (in 1979) to be accepted as the standard procedure worldwide.  A major event that hastened this acceptance was a paper presented by Henderson in 1972 at a symposium in honor of his advisor, J. L. Lush.
    Early in his career Henderson became interested in utilizing information from all relatives for the prediction of individual breeding values.  This could be done by incorporating Sewall Wright's numerator relationship matrix in the mixed model equations for BLUP.  Computationally this was very difficult because a rather large matrix first had to be computed and then inverted.  Even the fastest computers of the day were incapable of inverting matrices larger than 300 by 300.  A brilliant discovery in 1975 by Henderson, allowed a very simple method for computing the inverse of this large matrix directly from a list of pedigree information without directly computing the relationship matrix itself.  Given that the matrix was of order n, that is, there are n animals in the system, computation of the relationship matrix would have required n-squared computations and the inverse would require an additional n cubed computations.  Henderson's method only required calculations proportional to n.  Henderson also published details for intra-herd use of this technique which led to the animal model which allowed simultaneous evaluation of sires and cows.
    Another major contribution of Henderson was his pioneering work in the design of a sampling program for testing and selecting young sires for AI.  Based on his work the New York Artificial Breeders Cooperative was the first in the US to embark on a systematic young sire sampling program that has proved to be extremely effective and is now the basis for all AI programs worldwide.
    In addition to his teaching, research, and training of graduate students in animal breeding, Henderson has influenced the developments in other fields through his publications and consulting.  Henderson advised Prof Bronfenbrenner, a social psychologist, widely known for research in child development in cooperation with peers in Israel, Russia, Germany, and the United Kingdom.  Henderson has also done much for his Cornell colleagues to improve the design of animal nutrition and physiology experiments, and the subsequent statistical analyses of those data.  His publication, "Design and Analyses of Animal Science Experiments", has been widely used as a guide.
    In 1984 after his retirement, Henderson finally published his book.  Over 2000 copies were sold in the next 10 years.  There are still many methods in that book that have not been fully assessed by his students or others as to their applicability to present day problems.  With the rise in popularity of molecular genetics and with the passing of time, the  references to Henderson in animal breeding publications has decreased, and eventually his name may disappear from the literature altogether.  Even so, his huge contributions to animal breeding have to be acknowledged as truly outstanding.

Henderson's Advice to Future Scientists
    1. Study the methods of your predecessors
    2. Work hard
    3. Do not fear to try new ideas
    4. Discuss your ideas freely with others
    5. Be quick to admit errors.  Progress comes by correcting mistakes.
    6. Always be optimistic.  Nature is benign.
    7. Enjoy your scientific work.  It can be a great joy.

Henderson's Students
Ackerman, W. A. MSc 1975
Allaire, F. R. PhD 1965
Anderson, R. D. PhD 1978
Blackwell, R. L. PhD 1953
Cummings, E. MSc 1967
Cunningham, E. P. PhD 1962
Davidson, J. G. MSc 1960
Dunbar, R. S. PhD 1952
Elston, R. C. PhD 1959
Evans, D. A. PhD 1979
Freeman, A. E. PhD 1957
Haider, S. M. N. MSc 1959
Hanson, C. MSc 1977
Harville, D. A. MSc/PhD 1964/65
Heidues, T. H. PhD 1961
Hickman, C. G. PhD 1954
Jerome, F. N. PhD 1956
Kennedy, B. W. PhD 1974
Koh, Y. O. PhD 1967
Lee, A. J. PhD 1965
Mao, I. L. PhD 1970
Miller, P. D. MSc/PhD 1966/67
Ngere, L. PhD 1969
Pou, J. W. PhD 1951
Reddy, J. C. MSc 1954
Reed, W. S. MSc 1967
Ronningen, K. MSc 1968
Rothschild, M. F. PhD 1978
Schaeffer, L. R. MSc/PhD 1971/73
Searle, S. R. PhD 1958
Sercan, K. MSc 1973
Slanger, W. D. MSc/PhD 1972/75
Vaccaro, R. PhD 1973
Wearden, S. PhD 1960
Wickham, B. W. PhD 1974