Gene-flow has been studied in this research from an analytical, theoretical, and practical angle. While simple models of restricted gene-flow are tractable analytically and can produce very accurate predictions when compared with the results of computer simulations, models of discrete populations with geographical structure and models of continuous populations need further research. In particular, models of isolation by distance in a continuum are very difficult to relate to concepts familiar to the population geneticist since the basic concept linking continuous populations to discrete ones, the neighbourhood size, is shown to be flawed. Inferring gene-flow from indirect methods implies obtaining unbiased estimators of quantities such as F-statistics. The framework for estimation presented in this research can be used to derive unbiased estimators in different situations, and can also help to clarify the underlying assumptions made when making these estimates. In particular the conditions are specified under which Nei and Chesser's (1983) and Weir and Cockerham's (1984) estimators are most appropriate. While analytical treatment of geographically structured populations is difficult, F-statistics can be used to unravel levels of genetic structuring in these populations. Methods are presented which yield ways of discriminating between samples taken within and among breeding units, a necessary distinction if levels of gene-flow are to be inferred. Calculations of pairwise Fat, even in continuous populations, provide a picture of the geography of gene-flow in the population investigated. The methods are applied to data sets of three species, Brassica oleracea ssp. oleracea, Beta vulgaris ssp. maritima and Nucella lapillus and lead to new insights in the population biology of these species.

<p>cDNA microarrays is one of the first high-throughput gene expression technologies that has emerged within molecular biology for the purpose of functional genomics. cDNA microarrays compare the gene expression levels between cell samples, for thousands of genes simultaneously. </p><p>The microarray technology offers new challenges when it comes to data analysis, since the thousands of genes are examined in parallel, but with very few replicates, yielding noisy estimation of gene effects and variances. Although careful image analyses and normalisation of the data is applied, traditional methods for inference like the Student <i>t</i> or Fisher’s <i>F</i>-statistic fail to work.</p><p>In this thesis, four papers on the topics of empirical Bayes and full Bayesian methods for two-channel microarray data (as e.g. cDNA) are presented. These contribute to proving that empirical Bayes methods are useful to overcome the specific data problems. The sample distributions of all the genes involved in a microarray experiment are summarized into prior distributions and improves the inference of each single gene.</p><p>The first part of the thesis includes biological and statistical background of cDNA microarrays, with an overview of the different steps of two-channel microarray analysis, including experimental design, image analysis, normalisation, cluster analysis, discrimination and hypothesis testing. The second part of the thesis consists of the four papers. Paper I presents the empirical Bayes statistic <i>B</i>, which corresponds to a <i>t</i>-statistic. Paper II is based on a version of <i>B</i> that is extended for linear model effects. Paper III assesses the performance of empirical Bayes models by comparisons with full Bayes methods. Paper IV provides extensions of <i>B</i> to what corresponds to <i>F</i>-statistics.</p>

cDNA microarrays is one of the first high-throughput gene expression technologies that has emerged within molecular biology for the purpose of functional genomics. cDNA microarrays compare the gene expression levels between cell samples, for thousands of genes simultaneously. The microarray technology offers new challenges when it comes to data analysis, since the thousands of genes are examined in parallel, but with very few replicates, yielding noisy estimation of gene effects and variances. Although careful image analyses and normalisation of the data is applied, traditional methods for inference like the Student t or Fisher’s F-statistic fail to work. In this thesis, four papers on the topics of empirical Bayes and full Bayesian methods for two-channel microarray data (as e.g. cDNA) are presented. These contribute to proving that empirical Bayes methods are useful to overcome the specific data problems. The sample distributions of all the genes involved in a microarray experiment are summarized into prior distributions and improves the inference of each single gene. The first part of the thesis includes biological and statistical background of cDNA microarrays, with an overview of the different steps of two-channel microarray analysis, including experimental design, image analysis, normalisation, cluster analysis, discrimination and hypothesis testing. The second part of the thesis consists of the four papers. Paper I presents the empirical Bayes statistic B, which corresponds to a t-statistic. Paper II is based on a version of B that is extended for linear model effects. Paper III assesses the performance of empirical Bayes models by comparisons with full Bayes methods. Paper IV provides extensions of B to what corresponds to F-statistics.