# Your search: "author:"Nielsen, Rasmus""

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## Scholarly Works (66 results)

The concept of relatedness is fundamental is many areas of genetic studies, such as disease association studies, conservation genetics, and inferences about the demographic history and social structure of a population. Related individuals show signatures of shared ancestry in their genomes, which can then be analyzed to infer the relationship. In this thesis, we present statistical methods for estimating the relationship between individuals at varying time scales and the population parameters that produced such structure. In particular, we develop methods for analyzing genetic markers to estimate the pedigrees of close relatives and the mating parameters, such as the effective population size, that govern the population. Using simulations, we find that our method can infer pedigrees and the effective population size better than existing methods. We also discuss a method to infer regions of Neanderthal ancestry in human genomes, which can then be used to study the distant relationship between Neanderthals and humans. We apply the method on a sample of ancient humans to estimate the date of admixture between Neanderthals and humans.

The rising availability of genome-scale data for a large number of species has allowed for more in-depth studies of the genetics between species using increasingly sophisticated methods. The accumulation of pairwise differences between individuals are indicative of how diverged they are in time. The multi-species coalescent (MSC) has been the most popular framework with which to model the dynamics of the coalescent process in the presence of species barriers, such as a tree structure. Modelling using the MSC in the presence of increasing amounts of data (loci and species) while maintaining feasible computational times is the main focus of many emerging methods.

In this dissertation, I explore the use of the MSC in 3 different ways, using classical and novel statistical analysis to provide insight into species divergence parameters. I begin by constructing a novel statistical method for inferring species tree divergence times and population size parameters for any given tree topology from sequence data. The program COAL-PHYRE, presented here, makes use of the MSC marginally between individuals, as I demonstrate that pairwise information within the MSC is sufficient to learn times and population sizes on a tree. My focus then shifts to the derivation of the covariance between pairs of coalescence times and its application to studying average pairwise differences and the commonly used statistic, Fst. I confirm that estimates of Fst are biased, and quantify the effect of not accounting for this bias in different applications. I conclude by continuing to study the covariance between coalescence times and its use in inferring species tree topologies. I define a metric based on these statistics which, when paired with the minimum spanning tree algorithm, provides estimates of species tree topologies. I provide partial proofs of statistical consistency of the approach.

Improvements in sequencing technologies and the resulting increased availability of genetic data call for new and more sophisticated analysis methods. Particularly in ecological genetics and evolutionary biology, questions that can be addressed are often limited by the availability of analysis tools and statistical inference procedures. Non-equilibrium models in particular have been relatively poorly studied, mainly because analytical approaches are challenging and many useful and well-known results make equilibrium assumptions. However, using heuristic methods and strongly simplified models, we can make progress and arrive at procedures that help us gaining new insights from population genetic data. After an introductionary first chapter, in the second chapter, I develop an Approximate Bayesian Computation procedure to distinguish selection from standing variation from selection on a \textit{de novo} mutation. This method is applied to human genetic data where we identify two genes, ASPM and PSCA, that are most likely affected by selection on standing variation. In the third chapter, I develop an inference procedure to infer the origin of a range expansion, introducing the directionality index statistic psi. Applying this method to human data, we find a most likely origin of humanity in southern Africa, and evidence of the main expansion routes into Asia, finding evidence for a Southern route. In the fourth chapter, I extend the work on range expansions by developing an analytical model based on branching processes, which gives a biological interpretation to psi, and allows us to measure the decay of genetic diversity with distance. An application to *Arabidopsis thaliana* reveals that we are able to infer both recent expansions in the Americas, as well as expansions from the last glacial maximum in Europe. Between these three chapters, I use different approximation procedures to introduce inference procedures for models where direct likelihood calculations are not available.

Adaptation is a fundamental process in evolution, which leads populations to better survive and reproduce in changing environments. A key insight of population genetics has been that present-day genetic variation is affected by past, and even ongoing, adaptations. Recent expansion of DNA sequencing has afforded us access to genetic variation from now up to nearly millions of individuals. In this dissertation, I develop modeling and inference for DNA sequence variation in order to identify the genetic bases of adaptations, with a focus on evolution of complex traits in humans. First, I review population genetics approaches for detecting natural selection, and argue that these approaches have been hamstrung by the intractability of the so-called ‘full likelihood’ of selection (Chapter 1); I then develop a method to tractably compute this likelihood via importance sampling of the ancestral recombination graph (ARG), enabling us to find targets of selection too subtle to detect with previous methods (Chapter 2); I extend this likelihood method to jointly model DNA sequence variation and complex trait variation (via summary statistics from genome-wide association study, aka GWAS) to quantify the amount of selection acting on a complex trait, and to account for pleiotropy/correlated response in these estimates (Chapter 3); Finally, I present a method to detect polygenic adaptations in the presence of population structure, which explicit accounts for uncorrected stratification and other sources of error in the GWAS via an approach similar to LD score regression (Chapter 4).