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One of the fundamental properties of the immune system is its capacity to avoid autoimmune diseases. The mechanism underlying this process, known as self-tolerance, is hitherto unresolved but seems to involve the control of clonal expansion of autoreactive lymphocytes. This article reviews mathematical modeling of self-tolerance, addressing two specific(More)
The promoter regions of many genes contain multiple binding sites for the same transcription factor (TF). One possibility is that this multiplicity evolved through transitional forms showing redundant cis-regulation. To evaluate this hypothesis, we must disentangle the relative contributions of different evolutionary mechanisms to the evolution of binding(More)
Gene expression from both parental alleles is beneficial by masking the effects of deleterious recessive mutations and by reducing the noise in gene expression in diploid organisms. However, a class of genes are expressed preferentially or strictly from a single allele. The selective advantage of avoiding biallelic expression is clear for allelic-excluded(More)
Evolutionary algorithms (EAs) form a popular optimisation paradigm inspired by natural evolution. In recent years the field of evolutionary computation has developed a rigorous analytical theory to analyse their runtime on many illustrative problems. Here we apply this theory to a simple model of natural evolution. In the Strong Selection Weak Mutation(More)
The Dobzhansky–Muller model posits that incompatibilities between alleles at different loci cause speciation. However, it is known that if the alleles involved in a Dobzhansky–Muller incompatibility (DMI) between two loci are neutral, the resulting reproductive isolation cannot be maintained in the presence of either mutation or gene flow. Here we show that(More)
Even though both population and quantitative genetics, and evolutionary computation, deal with the same questions, they have developed largely independently of each other. I review key results from each field, emphasising those that apply independently of the (usually unknown) relation between genotype and phenotype. The infinitesimal model provides a(More)
The theory of population genetics and evolutionary computation have been evolving separately for nearly 30 years. Many results have been independently obtained in both fields and many others are unique to its respective field. We aim to bridge this gap by developing a unifying framework for evolutionary processes that allows both evolutionary algorithms and(More)
The role of gene interactions in the evolutionary process has long been controversial. Although some argue that they are not of importance, because most variation is additive, others claim that their effect in the long term can be substantial. Here, we focus on the long-term effects of genetic interactions under directional selection assuming no mutation or(More)
The behaviour of gene regulatory networks (GRNs) is typically analysed using simulation-based statistical testing-like methods. In this paper, we demonstrate that we can replace this approach by a formal verification-like method that gives higher assurance and scalability. We focus on Wagner's weighted GRN model with varying weights, which is used in(More)
Evolution of gene regulation is crucial for our understanding of the phenotypic differences between species, populations and individuals. Sequence-specific binding of transcription factors to the regulatory regions on the DNA is a key regulatory mechanism that determines gene expression and hence heritable phenotypic variation. We use a biophysical model(More)