Two existing estimators use inferred relationship information on a pair-wise level: regression of the phenotypic similarity of a pair of individuals on an estimate of their relationship and a likelihood procedure that maximises the probability of their genotypic and phenotypic observations. Computer simulation was used to compare the behaviour of these approaches. Bias in estimates of heritability decreased with increasing sample size, decreased heritability, increasing relatedness and increasing sample size. The regression approach showed less bias than the likelihood approach, but much larger sampling variance. A modified form of the likelihood technique, requiring fewer initial assumptions about population parameters was developed, which showed lower bias in its estimates of heritability than the likelihood technique originally proposed. An alternative approach in which marker-information was used to reconstruct sibships through relationship assignment within a single generation using Markov chain Monte Carlo (MCMC) techniques was developed. The reconstructed sibships were assumed correct and analysed using restricted maximum likelihood under an animal model. Simulations to compare the properties of estimates with those made using existing techniques indicated that sibship reconstruction was, in many cases, superior to earlier methods, regaining family-specific weighting lost through pair-wise analysis, having lower mean squared errors and showing only slight downwards bias, provided that there was sufficient marker information. Equations appropriate for MCMC analysis of half-sib, full-sib and hierarchical sib-ship structures are presented. The approaches were extended so that information from other types of marker loci, for example mitochondrial or dominant loci, known maternal information and additional variance parameters can be incorporated into the analysis. Analysis using the technique was made of feral population of Soay sheep, with body weight being used as an example trait. Results indicated that the Soay population has a low level of relatedness and so heritability estimates were not reliable, unless inferred relationship data was used only to augment an existing set of known relationships.

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Lactase, the enzyme responsible for milk digestion, is expressed in the small intestine of nearly all neonate mammals, and normally down-regulates following weaning. This is the ancestral state and in humans is described as lactase non-persistent. However, some people continue to have high expression of the enzyme for life due to a genetically inherited variation known as lactase persistence. A single nucleotide polymorphism, -13910*T was identified as the causal variation in Europeans due to a very tight association with phenotype and evidence of a functional effect in vitro. Subsequently, an apparent disparity was observed between -13910*T frequency and reported lactase persistence frequency in some African populations, raising doubts about the causal nature of the allele. Two possible explanations were proposed either -13910*T is not causal, but in Europeans is tightly linked to the true cause of lactase persistence, or, -13910*T is causal in Europeans, but the trait has evolved independently elsewhere. The primary aim of this thesis was to investigate the causes of lactase persistence in sub-Saharan Africa. The occurrence of only one -13910*T carrier out of 45 lactase persistent people from a cohort of phenotyped Sudanese individuals provided confirmation that the allele is not causal worldwide. Haplotype analysis of a 70kb region spanning the lactase gene in the phenotyped cohort and in non-European pastoralist groups provided no evidence for a shared origin with the European mutation. Resequencing of the -13910 locus led to the identification of a number of candidate SNPs -13915T>G, -13913T>C and -13907C>G, all located within 5bp of the original variant. Despite being clustered within the same OCT1 protein binding site as -13910*T, gel shift experiments revealed that the new alleles did not have a common effect on protein binding. However, -13915*G showed a significant association with lactase persistence. Resequencing of a second phenotyped cohort revealed the presence of many variant alleles at the locus, the occurrence of which is significantly higher in persistent individuals. Nearly every allele associates with an independent haplotype, providing strong evidence that multiple unrelated evolutionary events gave rise to lactase persistence. The frequency and distribution of all newly identified alleles was surveyed in more than 700 individuals from a total of 18 African and Middle Eastern populations, and gives a preliminary indication of the geographic origin of some alleles. The clustering of lactase persistence associated alleles within a single regulatory element implies that they are causal, and possible mechanisms and future approaches are discussed.

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