Genetic differences are a critical driver of disease risk and healthy variation, across the tree of life. Mutations arise and spread in our distant, genealogical ancestors, and so genetic variation data can provide a window into our evolutionary past, allowing us to understand processes such as population size changes, admixture, natural selection, and even evolution of the mutation and recombination processes that generate the variation itself. It has long been recognised that knowledge of genealogical relationships among individuals would allow us to capture almost all the information available from such data. However, only in recent years has it become computationally feasible to infer such genealogies, genome-wide, from variation patterns. One such method, Relate, developed in our lab, allows approximate inference of genealogical trees under coalescent-like models, for up to tens of thousands of samples. Here, we will show that a powerful approach for inference is to identify and characterise departures from the relatively simple models used to build these trees. By defining a 'population' as a set of coalescence rates between labelled individuals backwards in time, we can uncover variability in these rates, and use a single collection of trees to identify ancient mixing events among populations - including 'ghost' groups we have never sampled - natural selection favouring the descendents of particular branches of the genealogy, and departures from mathematical expectations under clock-like behaviour, indicating disruption of recombination or mutation.[-]

Consider two ancestral lineages sampled from a system of two-dimensional branching random walks with logistic regulation in the stationary regime. We study the asymptotics of their coalescence time for large initial separation and find that it agrees with well known results for a suitably scaled two-dimensional stepping stone model and also with Malécot's continuous-space approximation for the probability of identity by descent as a function of sampling distance.
This can be viewed as a justification for the replacement of locally fluctuating population sizes by fixed effective sizes. Our main tool is a joint regeneration construction for the spatial embeddings of the two ancestral lineages.[-]

We consider a population model in which the season alternates between winter and summer, and individuals can acquire mutations either that are advantageous in the summer and disadvantageous in the winter, or vice versa. Also, we assume that individuals in the population can either be active or dormant, and that individuals can move between these two states. Dormant individuals do not reproduce but do not experience selective pressures. We show that, under certain conditions, over time we see two waves of adaptation. Some individuals repeatedly acquire mutations that are beneficial in the summer, while others repeatedly acquire mutations that are beneficial in the winter. Individuals can survive the season during which they are less fit by entering a dormant state. This result suggests that, for populations in fluctuating environments, dormancy may have the potential to induce speciation. This is joint work with Fernando Cordero and Adrian Gonzalez Casanova.[-]

In this presentation, we shall discuss the reconstruction of demographic parameters based on the genetic variability observed within a sample of individual DNA. In the family of models that we consider, the statistics describing this genetic diversity (number of mutations, distribution of the mutations amongst individuals in the sample) depend on a more or less coarse ‘resolution of (i.e., level of information on) the hidden genealogical tree that relates the sampled individuals. Considering the optimal resolution thus allows to greatly improve the exploration of the space of possible genealogies when computing the likelihood of demographic parameters, compared to classical methods based on full labelled trees such as Kingmans coalescent. We shall focus on two examples, based on works with Raazesh Sainudiin (Uppsala Univ.) and with Julia Palacios (Stanford Univ.), Sohini Ramachandran (Brown Univ.) and John Wakeley (Harvard Univ.).[-]

In the infinitesimal model, one or several quantitative traits are described as the sum of a genetic and a non-genetic component, the first being distributed within families as a normal random variable centred at the average of the parental genetic components, and with a variance independent of the parental traits. The idea behind the normal distribution of the genetic component is that the genetic part of the trait of interest is the sum of the ‘infinitesimal' contributions of the allelic states at a very large number of loci. This model has been widely used in quantitative genetics, but less so in evolutionary biology and the precise conditionsunder which it holds has remained rather vague. In this talk, we shall provide a mathematical justification of the model as the limit as the number M of loci tends to infinity of a model with Mendelian inheritance, which includes different evolutionary processes (genetic drift, recombination, selection, mutation, population structure, ...). Generalisations of the simple version of the infinitesimal model presented here, as well as some applications, will be presented in the following talks by Nick Barton and Alison Etheridge.[-]