Bayesian mixture modelling of migration by founder analysis.
PhD thesis, University of Glasgow.
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In this thesis a new method is proposed to estimate major periods of migration from one region into another using phased, non-recombined sequence data from the present. The assumption is made that migration occurs in multiple waves and that during each migration period, a number of sequences, called `founder sequences', migrate into the new region. It is first shown through appropriate simulations based on the structured coalescent that previous inferences based on the idea of founder sequences sufer from the fundamental problem that it is assumed that migration events coincide with the nodes (coalescent events) of the reconstructed tree. It is shown that such an
assumption leads to contradictions with the assumed underlying migration process, and that inferences based on such a method have the potential for bias in the date estimates obtained.
An improved method is proposed which involves `connected star trees', a tree structure that allows the uncertainty in the time of the migration event to be modelled in a probabilistic manner. Useful theoretical results under
this assumption are derived. To model the uncertainty of which founder sequence belongs to which migration period, a Bayesian mixture modelling approach is taken, inferences in which are made by Markov Chain Monte Carlo techniques.
Using the developed model, a reanalysis of a dataset that pertains to the settlement of Europe is undertaken. It is shown that sensible inferences can be made under certain conditions using the new model. However, it is
also shown that questions of major interest cannot be answered, and certain inferences cannot be made due to an inherent lack of information in any dataset composed of sequences from the present day. It is argued that many
of the major questions of interest regarding the migration of modern day humans into Europe cannot be answered without strong prior assumptions being made by the investigator. It is further argued that the same reasons that prohibit certain inferences from being made under the proposed model
would remain in any method which has similar assumptions.
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