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Register a new userDiscrete Eulerian model for population genetics and dynamics under flow
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Marine species reproduce and compete while being advected by turbulent flows. It is largely unknown, both theoretically and experimentally, how population dynamics and genetics are changed by the presence of fluid flows. Discrete agent-based simulations in continuous space allow for accurate treatment of advection and number fluctuations, but can be computationally expensive for even modest organism densities. In this report, we propose an algorithm to overcome some of these challenges. We first provide a thorough validation of the algorithm in one and two dimensions without flow. Next, we focus on the case of weakly compressible flows in two dimensions. This models organisms such as phytoplankton living at a specific depth in the three-dimensional, incompressible ocean experiencing upwelling and/or downwelling events. We show that organisms born at sources in a two-dimensional time-independent flow experience an increase in fixation probability.
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The key findings of classical population genetics are derived using a framework based on information theory using the entropies of the allele frequency distribution as a basis. The common results for drift, mutation, selection, and gene flow will be rewritten both in terms of information theoretic measurements and used to draw the classic conclusions for balance conditions and common features of one locus dynamics. Linkage disequilibrium will also be discussed including the relationship between mutual information and r^2 and a simple model of hitchhiking.
Spatial constraints such as rigid barriers affect the dynamics of cell populations, potentially altering the course of natural evolution. In this paper, we study the population genetics of Escherichia coli proliferating in microchannels with open ends. Our experiments reveal that competition among two fluorescently labeled E. coli strains growing in a microchannel generates a stripe pattern aligned with the axial direction of the channel. To account for this observation, we study a lattice population model in which reproducing cells push entire lanes of cells towards the open ends of the channel. By combining mathematical theory, numerical simulations, and experiments, we find that the fixation dynamics is extremely fast along the axial direction, with a logarithmic dependence on the number of cells per lane. In contrast, competition among lanes is a much slower process. We also demonstrate that random mutations that appear in the middle and at the boundaries of the channel are highly likely to reach fixation. By theoretically studying competition between strains of different fitness, we find that the population structure in such a spatially confined system strongly suppresses selection.
Many questions that we have about the history and dynamics of organisms have a geographical component: How many are there, and where do they live? How do they move and interbreed across the landscape? How were they moving a thousand years ago, and where were the ancestors of a particular individual alive today? Answers to these questions can have profound consequences for our understanding of history, ecology, and the evolutionary process. In this review, we discuss how geographic aspects of the distribution, movement, and reproduction of organisms are reflected in their pedigree across space and time. Because the structure of the pedigree is what determines patterns of relatedness in modern genetic variation, our aim is to thus provide intuition for how these processes leave an imprint in genetic data. We also highlight some current methods and gaps in the statistical toolbox of spatial population genetics.
Probability modelling for DNA sequence evolution is well established and provides a rich framework for understanding genetic variation between samples of individuals from one or more populations. We show that both classical and more recent models for coalescence (with or without recombination) can be described in terms of the so-called phase-type theory, where complicated and tedious calculations are circumvented by the use of matrices. The application of phase-type theory consists of describing the stochastic model as a Markov model by appropriately setting up a state space and calculating the corresponding intensity and reward matrices. Formulae of interest are then expressed in terms of these aforementioned matrices. We illustrate this by a few examples calculating the mean, variance and even higher order moments of the site frequency spectrum in the multiple merger coalescent models, and by analysing the mean and variance for the number of segregating sites for multiple samples in the two-locus ancestral recombination graph. We believe that phase-type theory has great potential as a tool for analysing probability models in population genetics. The compact matrix notation is useful for clarification of current models, in particular their formal manipulation (calculation), but also for further development or extensions.
This work is about statistical genetics, an interdisciplinary topic between Statistical Physics and Population Biology. Our focus is on the phase of Quasi-Linkage Equilibrium (QLE) which has many similarities to equilibrium statistical mechanics, and how the stability of that phase is lost. The QLE phenomenon was discovered by Motoo Kimura and was extended and generalized to the global genome scale by Neher & Shraiman (2011). What we will refer to as the Kimura-Neher-Shraiman (KNS) theory describes a population evolving due to the mutations, recombination, genetic drift, natural selection (pairwise epistatic fitness). The main conclusion of KNS is that QLE phase exists at sufficiently high recombination rate ($r$) with respect to the variability in selection strength (fitness). Combining these results with the techniques of the Direct Coupling Analysis (DCA) we show that in QLE epistatic fitness can be inferred from the knowledge of the (dynamical) distribution of genotypes in a population. Extending upon our earlier work Zeng & Aurell (2020) here we present an extension to high mutation and recombination rate. We further consider evolution of a population at higher selection strength with respect to recombination and mutation parameters ($r$ and $mu$). We identify a new bi-stable phase which we call the Non-Random Coexistence (NRC) phase where genomic mutations persist in the population without either fixating or disappearing. We also identify an intermediate region in the parameter space where a finite population jumps stochastically between QLE-like state and NRC-like behaviour. The existence of NRC-phase demonstrates that even if statistical genetics at high recombination closely mirrors equilibrium statistical physics, a more apt analogy is non-equilibrium statistical physics with broken detailed balance, where self-sustained dynamical phenomena are ubiquitous.
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