Darwin throws dice: modelling stochastic processes of molecular evolution

The availability of protein and DNA sequences in the second half of the 20th century revolutionised evolutionary biology. For the first time, it was possible to quantify genetic variation among individuals and populations. Using molecular data to understand past demography and natural selection became an attainable goal. In the era of whole-genome sequences, application of early theoretical results proved to be challenging. The stochastic nature of evolutionary processes acting on DNA sequences makes it hard to distinguish signal from noise. Although progress has been made, models of molecular evolution are still lagging behind the availability of sequence data. In this thesis I contribute to bridging this gap, even if slightly. My main result is the development of the integrated sequentially Markovian coalescent (iSMC) – a novel framework that jointly models the effects of ancestral demography, recombination heterogeneity (Chapter 1) and mutation heterogeneity (Chapter 2) in shaping genetic diversity along the genome. This principled approach represents a step towards more realistic models of Population Genetics. The consequences of intracellular stochasticity extend beyond DNA sequences, however. Due to randomness in the diffusion of key molecules, isogenic cells differ in their gene expression patterns – hence in their phenotypes – even in homogeneous environments. To avoid chaos, intracellular stochasticity must be tamed by natural selection. In Chapter 3, I leverage single-cell transcriptomics data to disentangle the factors that constrain gene expression noise. Although selection against elevated noise acts at different levels of organisation, I show that it responds primarily to the architecture of molecular networks. This result may impact our understanding of the genotype-phenotype-fitness map.


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