An Approximate Markov Model for the Wright-Fisher Diffusion and Its Application to Time Series Data

The joint and accurate inference of selection and demography from genetic data is considered a particularly challenging question in population genetics, since both process may lead to very similar patterns of genetic diversity. However, additional information for disentangling these effects may be obtained by observing changes in allele frequencies over multiple time points. Such data are common in experimental evolution studies, as well as in the comparison of ancient and contemporary samples. Leveraging this information, however, has been computationally challenging, particularly when considering multilocus data sets. To overcome these issues, we introduce a novel, discrete approximation for diffusion processes, termed mean transition time approximation, which preserves the long-term behavior of the underlying continuous diffusion process. We then derive this approximation for the particular case of inferring selection and demography from time series data under the classic Wright-Fisher model and demonstrate that our approximation is well suited to describe allele trajectories through time, even when only a few states are used. We then develop a Bayesian inference approach to jointly infer the population size and locus-specific selection coefficients with high accuracy and further extend this model to also infer the rates of sequencing errors and mutations. We finally apply our approach to recent experimental data on the evolution of drug resistance in influenza virus, identifying likely targets of selection and finding evidence for much larger viral population sizes than previously reported.

Influenza Virus Drug Resistance: A Time-Sampled Population Genetics Perspective

Claudia Bank, Gregory Bruce Ewing, Anna Ferrer Admetlla, Matthieu Foll, Jeffrey David Jensen, Hyunjin Shim

Author Summary In recent years, considerable attention has been given to the evolution of drug resistance in the influenza A H1N1 strain. As a major annual cause of morbidity and mortality, combined with the rapid global spread of drug resistance, influenza remains as one of the most important global health concerns. Our work here focuses on a novel multi-faceted population-genetic approach utilizing unique whole-genome multi-time point experimental datasets in both the presence and absence of drug treatment. In addition, we present novel theoretical results and two newly developed and widely applicable statistical methodologies for utilizing time-sampled data - with a focus on distinguishing the relative contribution of genetic drift from that of positive and purifying selection. Results illustrate the available mutational paths to drug resistance, and offer important insights in to the mode and tempo of adaptation in a viral population. The challenge of distinguishing genetic drift from selection remains a central focus of population genetics. Time-sampled data may provide a powerful tool for distinguishing these processes, and we here propose approximate Bayesian, maximum likelihood, and analytical methods for the inference of demography and selection from time course data. Utilizing these novel statistical and computational tools, we evaluate whole-genome datasets of an influenza A H1N1 strain in the presence and absence of oseltamivir (an inhibitor of neuraminidase) collected at thirteen time points. Results reveal a striking consistency amongst the three estimation procedures developed, showing strongly increased selection pressure in the presence of drug treatment. Importantly, these approaches re-identify the known oseltamivir resistance site, successfully validating the approaches used. Enticingly, a number of previously unknown variants have also been identified as being positively selected. Results are interpreted in the light of Fisher's Geometric Model, allowing for a quantification of the increased distance to optimum exerted by the presence of drug, and theoretical predictions regarding the distribution of beneficial fitness effects of contending mutations are empirically tested. Further, given the fit to expectations of the Geometric Model, results suggest the ability to predict certain aspects of viral evolution in response to changing host environments and novel selective pressures.

Public Library of Science2014

Turnover and accumulation of genetic diversity across large time-scale cycles of isolation and connection of populations

Séverine Vuilleumier Varisco

Major climatic and geological events but also population history (secondary contacts) have generated cycles of population isolation and connection of long and short periods. Recent empirical and theoretical studies suggest that fast evolutionary processes might be triggered by such events, as commonly illustrated in ecology by the adaptive radiation of cichlid fishes (isolation and reconnection of lakes and watersheds) and in epidemiology by the fast adaptation of the influenza virus (isolation and reconnection in hosts). We test whether cyclic population isolation and connection provide the raw material (standing genetic variation) for species evolution and diversification. Our analytical results demonstrate that population isolation and connection can provide, to populations, a high excess of genetic diversity compared with what is expected at equilibrium. This excess is either cyclic (high allele turnover) or cumulates with time depending on the duration of the isolation and the connection periods and the mutation rate. We show that diversification rates of animal clades are associated with specific periods of climatic cycles in the Quaternary. We finally discuss the importance of our results for macroevolutionary patterns and for the inference of population history from genomic data

2014

Methods for Single Trial Analysis of Asynchronous EEG Patterns

Nicolas Bourdaud

Processing of electroencephalographic (EEG) signals has mostly focused on analysing correlates that are time-locked to an observable event. However, when the signal is acquired in less controlled environment, like in the context of a brain-computer interface operating in the real-world, this synchronous nature does not hold any longer. The analysis of such signal requires the design of methods that rely less on time-locked nature. These methods are also the requirements for study endogenous processes for which the ground truth of when the process take place in time is not available. In this thesis, we present methods to analyse brain signals, EEG in particular, that are not time-locked to observable events. This thesis documents three major contributions : (i) it proposes a Bayesian formalism to the problem of asynchronous EEG pattern classification, (ii) it shows the importance of generative models to achieve this task and (iii) it shows that such methods can be used to gather information and classify the EEG correlates of decision-making process while classical methods fail at it. First, we propose methods to handle non-time-locked EEG patterns by making the hypothesis that, in each trial, only a part of the signal contains the relevant pattern of interest. This relevant part can appear at any time in the analysis window and differently for each trial. The rest of the trial corresponds to a non-informative part irrelevant to the targeted cognitive task. Starting from a discriminant asynchronous approach handling independently the time-samples in the trial, we extend this method to a generative Bayesian model where each part is formally modelled. This is a main difference compared to the classical approach which usually try to avoid to model the non-informative part. Then, making the assumption that the informative part can be modelled by a time sequence, we adapt the previous method to a Bayesian model of asynchronous template matching which allows the recognition of the time onset of the pattern of interest in each trial. Second, we show the importance of the generative model which, thanks to the Bayesian approach allows us to alleviate the problem of choosing of the hyperparameters of the initial discriminative approach. Compared to the initial discriminant model, us- ing a generative approach leads to use more parameters into the model but whose estimation is helped by the prior we provide. By doing so, we provide a more intuitive way for the experimenter to adapt the method to other problems. Using a generative model and a Bayesian estimation also enables us to improve the generalisation of the model of asynchronous template matching. This model has indeed been tested as benchmark on jittered evoked potential data and has shown to successfully improve the signal-to-noise ratio, recover the evoked response and classify better than classical methods. Finally, we see the importance of asynchronous methods for classification of the EEG correlates of decision-making process. We test this in the context of the study of the exploration/exploitation contrast. Exploration is related to decision making in an uncertain environment. This situation arises a conflict between two opposing needs : gathering information about the environment and exploiting this knowledge in order to optimise the decision. Using an experimental setup that forces the subjects to switch between exploratory or exploitative actions, we show for the first time that it is possible to classify the EEG correlates of the exploratory behaviour. Moreover, we show that synchronous methods fail at classify this contrast thus requiring advanced asynchronous ones. The results also confirm that the brain areas relevant to this switch are mainly the left parietal and medial frontal cortex which is consistent with the neurophysiological findings based on functional magnetic resonance imagery. In addition we have been able to show the importance of alpha rhythm for this contrast. In summary, this thesis provides a formal framework for classification of asynchronous EEG patterns using a generative Bayesian approach. It also provides a methodology to approach the study of EEG correlates of cognitive tasks when little is known about them and when the targeted pattern is reasonably assumed to be non time-locked.