Approaches For Inferring Past Population Size Changes From Genome-wide Genetic Data.

The history of populations or species is of fundamental importance in a variety of areas. Gaining details about demographic, cultural, climatic or political aspects of the past may provide insights that improve the understanding of how populations have evolved over time and how they may evolve in future. Different types of resources can be informative about different periods of time. One especially important resource is genetic data, either from a single individual or a group of organisms. Environmental conditions and circumstances can directly affect the existence and success of a group of individuals. Since genetic material gets passed on from generation to generation, traces of past events can still be detected in today\''s genetic data. For many decades scientists have tried to understand the principles of how external influences can directly affect the appearance and features of populations, leading to theoretical models that can interpret modern day genetic variation in the light of past events. Among other influencing factors like migration, natural selection etc., population size changes can have a great impact on the genetic diversity of a group of organisms. For example, in the field of conservation biology, gaining insights into how the size of a population evolves may assist in detecting past or ongoing temporal reductions of population size. This seems crucial since the reduction in size also correlates with a reduction in genetic diversity which in turn might negatively affect the evolutionary potential of a population. Using computational and population genetics methods, sequences from whole genomes can be scanned for traces of such events and therefore assist in new interpretations of historical details of populations or groups of interest. This thesis focuses on the detection and interpretation of past population size changes. Two approaches to infer particular parameters from underlying demographic models are described. The first part of this thesis introduces two summary statistics which were designed to detect fluctuations in size from genome-wide Single Nucleotide Polymorphism (SNP) data. Demographic inferences from such data are inherently complicated due to recombination and ascertainment bias. Hence, two new statistics are introduced: allele frequency-identity by descent (AF-IBD) and allele frequency-identity by state (AF-IBS). Both make use of linkage disequilibrium information and exhibit defined relationships to the time of the underlying mathematical process. A fast and efficient Approximate Bayesian Computation framework based on AF-IBD and AF-IBS is constructed that can accurately estimate demographic parameters. These two statistics were tested for the biasing effects of hidden recombination events, ascertainment bias and phasing errors. The statistics were found to be robust to a variety of these tested biases. The inference approach was then applied to genome-wide SNP data to infer the demographic histories of two human populations: (i) Yoruba from Africa and (ii) French from Europe. Results suggest, that AF-IBD and AF-IBS are able to capture sufficient amounts of information from underlying data sets in order to accurately infer parameters of interest, such as the beginning, end and strength of periods of varying size. Additionally the results from empirical data suggest a rather stable ancestral population size with a mild recent expansion for Yoruba, whereas the French apparently experienced a rather long-lasting strong bottleneck followed by a drastic population growth. The second part of this thesis introduces a new way of summarizing information from the site frequency spectrum. Commonly applied site frequency spectrum based inference methods make use of allele frequency information from individual segregating sites. Our newly developed method, the 2 point spectrum, summarizes allele frequency information from all possible pairs of segregating sites, thereby increasing the number of potentially informative values from the same underlying data set. These additional information are then incorporated into a Markov Chain Monte Carlo framework. This allows for a high degree of flexibility and implements an efficient method to infer population size trajectories over time. We tested the method on a variety of different simulated data sets from underlying demographic models. Furthermore, we compared the performance and accuracy of our method to already established methods like PSMC and diCal. Results indicate that this non-parametric 2 point spectrum method can accurately infer the extent and times of past population size changes and therefore correctly estimates the history of temporal size fluctuations. Furthermore, the initial results suggest that the amount of required data and the accuracy of the final results are comparable with other publicly available non-parametric methods. An easy to use command line program was implemented and will be made publicly available. In summary, we introduced three highly sensitive summary statistics and proposed different approaches to infer parameters from demographic models of interest. Both methods provide powerful frameworks for accurate parameter inference from genome-wide genetic data. They were tested for a variety of demographic models and provide highly accurate results. They may be used in the settings as described above or incorporated into already existing inference frameworks. Nevertheless, the statistics should prove useful for new insights into populations, especially those with complex demographic histories