**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 |