10.00-11.00 Room A1.01 Robert C. Griffiths FRS (Statistics, University of Oxford)
Population Genetics Stochastic Process Models Forward and Backward in Time
Classical stochastic process models in population genetics describe how a population of genes evolves forward in time under random drift, mutation, selection and recombination. Examples are the Wright-Fisher diffusion process; Moran models, which are birth and death processes; and Cannings models, where parents have an exchangeable offspring distribution. Coalescent models, which are random trees or graphs, describe the ancestral lineages of samples of genes back in time. These backwards and forwards models belong together technically as dual stochastic processes. This talk will briefly discuss examples of forwards and backwards in time models. Forwards the models are the Wright-Fisher diffusion process; Fleming-Viot diffusion process describing DNA sequence evolution; and Moran models with multiple offspring and selection. The backwards models describing ancestral lineage history are respectively the Kingman coalescent process; Gene trees, which are perfect phylogenies constructed from mutation patterns on DNA sequences; and branching coalescing lineage graphs.
11:00-12:00 Room A1.01 Jochen Blath (Institut für Mathematik, TU Berlin)
An Ancestral Recombination Graph for Diploid Populations with Skewed Offspring Distributions
(joint work with Matthias Birkner (Mainz), Bjarki Eldon (Oxford))
We consider a diploid biparental multilocus population model of Moran type, in which randomly chosen pairs of diploid individuals contribute offspring to the population. The number of offspring can be large, in particular relative to the total population size. Such 'heavily skewed' reproduction mechanisms have been considered by various authors recently, cf. e.g. Eldon and Wakeley (2008), and reviewed by Hedgecock and Pudovkin (2011). The chromosomes of each diploid offspring are derived from two distinct individuals, resulting in a separation of timescales phenomenon: ancestral lineages can only coalesce when in distinct individuals. We extend a result of Möhle (1998) to obtain convergence of the ancestral process to an ancestral recombination graph. Due to diploidy and large offspring numbers, novel effects appear. For example, the marginal genealogy at each locus is given by a ξ-coalescent necessarily involving simultaneous quadrifold multiple mergers, and different loci remain substantially correlated even as the recombination rate grows large. We compute correlations of coalescence times for two loci and discuss our findings for simulated data.
12:00-14:00 Lunch in the Mathematics Institute Common Room
14:00-15:00 Room B3.02 Garrett Hellenthal (UCL Genetics Institute)
Inferrring Human Admixture History and Relatedness Using DNA
Humans have a very complex history, shaped in part by major migrations to new geographic regions and interactions among different groups at various time periods. These events have influenced the genetic make-up of present-day populations, for example leading to discernible (though subtle) differences in the DNA of individuals sampled from different geographic regions. Recent world-wide collections of genome-wide DNA allow an unprecedented opportunity to exploit these differences to learn about human history. Here I present a novel statistical approach to describe how present-day populations relate to one another genetically, for example clustering individuals with similar genetic profiles. I furthermore describe a new method that uses DNA to identify "admixture events" where two or more ancestral populations met and exchanged DNA at some point in the past (for example due to an invasion or re-settlement). In particular, this new methodology infers precisely when such events occurred, which groups were involved, and how much DNA was exchanged. Such details allow the confirmation or rejection of hypotheses based on archaeological records, as well as unearthing previously unknown historical interactions. These analyses showcase the utility of DNA for reconstructing human history in unprecedented detail.
15:00-15:30 Tea/Coffee in the Mathematics Institute Common Room