This thesis comprises a collection of 39 research papers
divided into three groups. The first group discusses the
development of statistical methods, especially novel methods of
variance component estimation, with general application. The
second group examines the potential use of statistical methods in
animal breeding studies, ranging from the construction of new
experimental designs to the analysis of non-normal data. The
third group reports on studies on animal breeding data in beef
and dairy cattle.

Group I is entitled "Statistical methods, including
variance component estimation, with general application". The
major theme of this group is the estimation of variance
components. Some previous work based on methods for balanced
data, gave rise to methods that were neither unique nor efficient
and other methods gave results that are inconsistent with the
analysis of variance for balanced data. A method was
introduced, now known as REML (Residual Maximum Likelihood) that
unifies the area. The method was introduced for the analysis of
incomplete block designs with unequal block size but was found to
have important applications in the analysis of groups of similar
trials, time-series and animal breeding. Papers investigating
REML estimation for multivariate data, time-series and detecting
outliers are included. The relationship of REML to other
methods is elucidated, especially for balanced and partially
balanced designs. Computational strategies are discussed.

The last two papers in the group illustrate a method of
analysis of dial lei crosses that involves using multiple copies
of the data. This idea of using multiple copies was shown also
to be useful in the analysis of rectangular lattice designs and
in the interpretation of some recently introduced neighbour
analyses of field trials.

The next group of papers, Group II, report on
"Application of statistical methods to animal breeding studies".
The work on variance components has some application in animal
breeding and I have built on these links. Four papers consider
efficient designs for estimation of genetic parameters, including
designs for estimating heritability from data on two generations
of data, for estimating maternal genetic variances, for
estimating parent-offspri ng regression and for estimating
multivariate genetic parameters. These designs can lead to
substantial reductions in the variances of the estimates of the
parameters, compared with classical designs, halving variances in
some cases. Other papers have shown how to efficiently estimate
heritability from unbalanced data, both from two generations of
data and from more than two generations.

Often in animal breeding experiments animals used as
parents are not selected at random, but selected on phenotypic
measurements, perhaps of relatives. This can cause bias in some
methods of estimation. On the other hand REML estimates can
take account of the selection process. Selection experiments
and the estimation of realised heritability are discussed.

REML estimation has found widespread acceptance by
animal breeders, partly because some quantities arising in the
methods were terms that animal breeders use in evaluating
animals. It was shown how to improve one method of evaluation
and methods of evaluating sires were reviewed

Some work is included on multivariate evaluation. It
is shown how the complex multivariate calculations can be reduced
to simpler univariate calculations using a canonical
transformation, how results on selection indices can be used to
interpret multivariate predictions. A simple interpretation of
quadratic selection indices is given.

Other work considered some parallel problems with
non-normal data. In particular for binary data, estimation of
heritability, optimal designs for estimation of heritability and
prediction of breeding values. It was shown how to estimate
genotype frequencies using generalised linear model methods and
> h?
suggested how to evaluate animals worth and estimate genetic
parameters when the data fits a generalised linear model.

The last group, Group III, is entitled "Experimental
studies". These include reports on a long term study of
evaluation of breeds and cross-breeding in beef cattle in Zambia.
The section also examines the genetic relationship between meat
and milk production in British Friesian cattle. The validity of
models used in dairy sire evaluation are investigated including
the heterogeneity of heritability of milk yield at different
levels of production and the use of a novel model for taking
account of environmental variation within herds.

GROUP I:
STATISTICAL METHODS INCLUDING VARIANCE COMPONENT
ESTIMATE WITH GENERAL APPLICATION

01. R. THOMPSON. 1969. Iterative estimation of variance
components for non-orthogonal data. Biometrics 25,
767-773. ||
02. H.D. PATTERSON and R. THOMPSON. 1971. Recovery of
inter-block information when block sizes are unequal.
Biometrika 58, 545-554. ||
03. H.D. PATTERSON and R. THOMPSON. 1975. Maximum likelihood
estimation of components of variance. Proceedings
of the 8th International Biometric Conference. Ed.
L.C.A. Corsten and T. Postelnicu, 199-207. ||
04. R. THOMPSON. 1980. Maximum likelihood estimation of
variance components. Math. Operationsforsh.
Statist. ljU 545-561. ||
05. R. THOMPSON. 1978. The estimation of variance and
covariance components with an application when
records are subject to culling. Biometrics 29,
527-550. ||
06. L.R. SCHAEFFER, J.W. WILTON and R. THOMPSON. 1978.
Simultaneous estimation of variance and covariance
components from multitrait mixed model equations.
Biometrics 34, 199-208. ||
07. D.M. COOPER and R. THOMPSON. 1977 . A note on the
estimation of the parameters of the
autoregressive-moving average process. Biometrika
64, 625-628. ||
08. R. THOMPSON. 1985. A note on restricted maximum
likelihood estimation with an alternative outlier
model. J.R. Statist. Soc. B 47, 53-55. ||
09. R. THOMPSON. 1975. A note on the W transformation.
Technometrics J7, 511-512. ||
10. R. THOMPSON and K. MEYER. 1986. Estimation of variance
components : what is missing in the EM algorithm? J.
Statist. Comput. Simul. 24 215-230. ||
11. D.L. ROBINSON, R. THOMPSON and P.G.N. DIGBY. REML. 1982.
A program for the analysis of non-orthogonal data by
restricted maximum likelihood. COMPSTAT 1982, II.
Eds. H. Cassinus, P. Ettinger and J.R. Mattieu.
Physica-Verlag, Wien 231-232. ||
12. R. THOMPSON. 1983. Dial lei crosses, partially balanced
incomplete block designs with triangular association
schemes and rectangular lattices. GENSTAT
newsletter JJ3, 16-32. ||
13. R. THOMPSON. 1984. The use of multiple copies of data in
forming and interpreting analysis of variance.
Experimental design, Statistical Methods and Genetic
Statistics. Ed. K. Hinkelmann. Marcel Dekker, New
York, 155-174.

GROUP II:
APPLICATION OF STATISTICAL METHODS TO ANIMAL BREEDING
STUDIES

14. R. THOMPSON. 1976. The estimation of maternal genetic
variances. Biometrics 32 903-917. ||
15. R. THOMPSON. 1976. Design of experiments to estimate
heritability when observations are available on
parents and offspring. Biometrics 32 283-304. ||
16. W.G. HILL and R. THOMPSON. 1977. Design of experiments
to estimate parent-offspring regression using
selected parents. Anim. Prod. 24, 163-168. ||
17. N.D. CAMERON and R. THOMPSON. 1986. Design of
multivariate selection experiments to estimate
genetic parameters. Theor. Appl. Genet. 72, 466-476. ||
18. R. THOMPSON. 1977. The estimation of heritability with
unbalanced data. I. Observations available on
parents and offspring. Biometrics 33, 485-495. ||
19. R. THOMPSON. 1977. The estimation of heritability with
unbalanced data. II. Data available on more than
two generations. Biometrics 33, 495-504. ||
20. R. THOMPSON. 1977. The estimation of heritability with
unbalanced data. III. Unpublished Appendices, 1-17. ||
21. R. THOMPSON. 1976. Estimation of quantitative genetic
parameters. Proceedings of the International
Conference on Quantitative Genetics. Ed. 0.
Kempthorne, E. Pollak and T. Bailey. Iowa State
University press, Ames, Iowa, 639-657.
(vii) ||
22. W.G. HILL and R. THOMPSON. 1978. Probabilities of
non-positive definite between group or genetic
covariance matrices. Biometrics 34, 429-439. ||
23. K. MEYER and R. THOMPSON. 1984. Bias in variance and
covariance component estimators due to selection on a
correlated trait. Z. Tierzucht. Zuchtungsbiol. 101,
33-50. ||
24. R. THOMPSON. 1976. Relationship between the cumulative
different and best linear unbiased predictor methods
of evaluating bulls. Anim. Prod. 23^, 15-24. ||
25. R. THOMPSON. 1979. Sire Evaluation. Biometrics 35,
339-353. ||
26. R. THOMPSON. 1986. Estimation of realised heritability
in a selected population using mixed model methods.
Genet. Sel. Evol . 475-484. ||
27. R. THOMPSON. 1972. The maximum likelihood approach to
the estimate of liability. Anim. Hum. Genet. 36,
221-231. ||
28. R. THOMPSON, B.J. McGUIRK and A.R. GILMOUR. 1985.
Estimating the heritability of all-or-none and
categorical traits by offspring-parent regression.
Z. Tierzucht. Zuchtungsbiol. 102, 342-354. ||
29. J.L. FOULLEY, D. GIANOLA and R. THOMPSON. 1983.
Prediction of genetic merit from data on binary and
quantitative variates with an application to calving
difficulty, birth weight and pelvic opening. Genet.
Sel. Evol. 15, 401-424. ||
30. R. THOMPSON and R.J. BAKER. 1981. Composite link
functions in generalised linear models. J.R.
Statist. Soc. B. 30, 125-131. ||
31. R. THOMPSON. 1980. A note on the estimation of economic
values for selection indices. Anim. Prod. 31,
115-117.

GROUP III:
EXPERIMENTAL STUDIES

32. W. THORPE, D.K.R. CRUICKSHANK and R. THOMPSON. 1980.
Genetic and evironmental influences on beef cattle
production in Zambia. Factors affecting weaner
production from Angoni, Barotse and Boran dams.
Anim. Prod. 30, 217-234. ||
33. W. THORPE, D.K.R. CRUICKSHANK and R. THOMPSON. 1980.
Genetic and environmental influences on beef cattle
production in Zambia. 2. Sire weights for age of
purebred and reciprocally crossbred progeny. Anim.
Prod. 30, 235-243. ||
34. W. THORPE, D.K.R. CRUICKSHANK and R. THOMPSON. 1980.
Genetic and environmental influences on beef cattle
production in Zambia. 3. Carcass characteristics of
purebred and reciprocally crossbred progeny. Anim.
Prod. 30, 245-252. ||
35. W. THORPE, D.C.K. CRUICKSHANK and R. THOMPSON. 1982.
Genetic and environmental influences on beef cattle
in Zambia. 4. Weaner production from purebred and
reciprocally crossbred progeny. Anim. Prod. 33,
165-177. ||
36. W. THORPE, D.K.R. CRUICKSHANK and R. THOMPSON. 1979. The
growth and carcass character!- sti cs of crosses of
Hereford and Friesian with Angoni, Barotse and Boran
cattle in Zambia. J. Agric. Sci., Camb. 93,
423-430. ||
37. I.L. MASON, V.E. VIAL and R. THOMPSON. 1972. Genetic
parameters of beef characteristics and the genetic
relationship between meat and milk production in
British Friesian cattle. Anim. Prod. 135-148. ||
38. W.G. HILL, M.R. EDWARDS, M-K A. AHMED and R. THOMPSON.
1983. Heritability of milk yield and composition at
different levels and variability of production.
Anim. Prod. 36, 59-68. ||
39. V.P.S. CHAUHAN and R. THOMPSON. 1986. Dairy sire
evaluation using a "rolling months" model. Z.
Tierzucht. Zuchtungsbiol 103, 321-333.