The development of Best Linear Unbiased Prediction (BLUP) by Henderson (1973) equipped animal breeders with a tool to evaluate animals for their genetic potential much more efficiently than had been previously possible. However, BLUP requires solving a large system of simultaneous equations (the Mixed Model Equations: MME) which is computationally demanding. It also requires knowledge of the covariances among all random effects. Covariances among additive genetic effects are described by a function of the Numerator Relationship Matrix (A). A simple method to compute its inverse (A⁻¹) was necessary before BLUP could be adopted widely. Such a method was found by Henderson (1975, 1976) whereby A⁻¹ could be written directly from a list of animals, their pedigrees and the inbreeding coefficients of all parents. Now, BLUP is the method of choice for genetic evaluation of livestock and its use is widespread across species and countries. This thesis presents some computer algorithms which reduce the time and memory required to evaluate livestock using BLUP. In six chapters, questions relating to the building of the numerator relationship matrix and its inverse, computing inbreeding coefficients and storing and solving the MME are addressed.

Sewall Wright's Shifting Balance Theory, which postulates that evolution will be most rapid in populations subdivided into numerous small, semi-isolated demes, was evaluated by comparing responses to selection for increased adult bodyweight of 'D. melanoccaster' in three population models. Two were models previously evaluated (sub-lining with crossing of selected sub-lines at intervals, and a circular stepping-stone model), but which had not shown any advantage in subdivision. The third was a new model of Wright's recommended structure, and included excess diffusion from demes with higher phenotypic means to those with lower means every generation. Responses in these models were compared with those obtained by simple mass selection in a single large population. As reported in previous studies, no clear advantages in response were obtained in any of the subdivided models. In one replicate of the new "Wrightian" model however, the pattern of responses suggested the presence of a major non-additive effect producing extremely heavy flies. This effect spread throughout the system of semi-isolated demes comprising this treatment in a manner similar to that described by Wright for the operation of the Shifting Balance Process. The genetic basis of this effect was investigated by offspring-parent regressions with the effect present and absent, by crosses with unselected flies to produce F₁ and F₂ generations, and by attempting to map the gene(s) underlying the effect by chromosomal substitution techniques. However, no clear description of the effect was obtained. In addition to the selection programme, electrophoretic surveys of the experimental populations were conducted. These provided information on levels and partitioning of allozymic variation between and within demes/population units. The description of genetic structuring provided by this data was similar to that based on partitioning the phenotypic variance in bodyweight. Results obtained suggested that models used to evaluate subdivided populations both here and in previous studies, do not produce sufficient genetic differentiation to support inter-deme selection, at least on a simple additive basis. Finally, the relevance of these results to wider understanding of the Shifting Balance Theory is discussed. It is concluded that further evaluation of the Theory should be based upon computer simulation. This approach could be used to define necessary conditions for the operations of the Shifting Balance process, and thus provide a firmer basis for both experimental designs and recommendations regarding structuring of domestic and wild populations.

This thesis describes the characterisation of the β-tubulin gene family in 'Trichostrongylus colubriformis' and the role of a particular β-tubulin locus (tcb-1) in BZ resistance and the subsequent development of a PCR (Polymerase Chain Reaction) based assay that can be used to genotype individual 'T. colubriformis' for a marker associated with a BZ resistance allele. This is the first genotypic assay for the detection of a drug resistance allele in this species of nematode and one of only two (the other detects BZ resistance in Haemonchus contortus) genotypic assays for the detection of a drug resistance gene in parasitic nematodes of sheep. The assay detects a polymorphism in a 13-tubulin allele shown to be involved in BZ resistance in an RFLP analysis. Sequence analysis of this allele revealed striking sequence homology to a β-tubulin allele shown to be involved in BZ resistance in the closely related nematode 'H. contortus' suggesting that these genes have functional homology. Comparison of these sequences with other nematode 13-tubulins suggested that the gene responsible for BZ resistance in these parasitic nematodes was closely related to the ben-1 gene in the free-living nematode 'Caenorhabditis elegans', the product of which has been shown to be responsible for BZ susceptibility in that nematode. When the PCR assay was applied to a BZ naive strain (McMaster susceptible) the resistance allele could be readily detected and the allele frequency of the resistance allele was shown to be in Hardy-Weinberg equilibrium. This suggests that the resistance allele was present in the unselected population as a natural polymorphism and that no deleterious effects were associated with the resistance allele. The assay was also applied successfully to a number of independently selected BZ resistant populations implying that the same allele was selected in each population. Clones for an additional three 'T. colubriformis' β-tubulin genes were obtained. Sequence analysis of the variable 3' ends of these genes showed that the sequence of the loci vary within 'T. colubriformis' but are highly conserved between closely related nematodes species. This degree of homology between species has only been reported for vertebrates and this is the first example of conservation of isotypic classes for β-tubulins in invertebrates.

The aim of this investigation was to study the nature of genetic constraints on life-history evolution in a natural population. To identify possible constraints, estimates of variance and covariance components were obtained in the laboratory for a range of life-history characters in a population of 'Tribolium castaneum' three generations after collection from the wild. Estimates were obtained by means of a diallel analysis. To test predictions about genetic constraints based upon the variance-covariance matrix, selection was conducted for duration of development in both directions for six generations followed by a phenotypic assay of all life-history traits in all lines. After six generations of selection, there were significant differences between selected lines for both males and females for duration of development and growth rate, but no significant correlated responses in other characters. Some correlated responses, such as a decrease in late life egg production in slow developing lines approached significance and, if the selection program had been continued, may have become significant. ... All fecundity indices were positively correlated but genetic correlations of less than unity and the decrease in late life egg production in slow developing lines suggest that the reproductive schedule is amenable to modification by selection. Depression of late life fecundity in slow developing lines was not expected as late life fecundity had no heritable variation, and had low and insignificant positive correlations with duration of development. The depression may have been due to disruption of developmental processes as a result of selection for duration of development. It is possible that patterns of development characteristic of a taxon may restrict the range of future adaptations in that taxon. However, further investigation is needed before conclusions about this depression of fecundity can be drawn. Experimental results do not support theories about the evolution and/or maintenance of senescence by the mechanisms of antagonistic pleiotropy between early and late life history characters or the accumulation of deleterious mutations. Results do support the hypothesis r, that senescence is due to a running out of genetic program for internal repair and maintenance capabilities in organisms. Whilst it is recognised that genetic variation and covariation are dependent upon environment, and thus genetic constraints may differ in different environments, studies which combine a quantitative genetic analysis of a population with a selection program carried out in a single environment are still useful. Firstly, they identify how the genetic variance-covariance matrix affects responses to selection in a specific environment. Secondly, they can help to identify possibly fundamental and universal constraints. Negative genetic correlations reflecting physiological trade-offs may be operational in all "realistic" environments. Studies would need to be repeated in a number of different environments to confirm the identity of these universal genetic constraints.