1
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Abbara A, Pagani L, García-Pareja C, Bitbol AF. Mutant fate in spatially structured populations on graphs: Connecting models to experiments. PLoS Comput Biol 2024; 20:e1012424. [PMID: 39241045 PMCID: PMC11410244 DOI: 10.1371/journal.pcbi.1012424] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/10/2024] [Revised: 09/18/2024] [Accepted: 08/15/2024] [Indexed: 09/08/2024] Open
Abstract
In nature, most microbial populations have complex spatial structures that can affect their evolution. Evolutionary graph theory predicts that some spatial structures modelled by placing individuals on the nodes of a graph affect the probability that a mutant will fix. Evolution experiments are beginning to explicitly address the impact of graph structures on mutant fixation. However, the assumptions of evolutionary graph theory differ from the conditions of modern evolution experiments, making the comparison between theory and experiment challenging. Here, we aim to bridge this gap by using our new model of spatially structured populations. This model considers connected subpopulations that lie on the nodes of a graph, and allows asymmetric migrations. It can handle large populations, and explicitly models serial passage events with migrations, thus closely mimicking experimental conditions. We analyze recent experiments in light of this model. We suggest useful parameter regimes for future experiments, and we make quantitative predictions for these experiments. In particular, we propose experiments to directly test our recent prediction that the star graph with asymmetric migrations suppresses natural selection and can accelerate mutant fixation or extinction, compared to a well-mixed population.
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Affiliation(s)
- Alia Abbara
- Institute of Bioengineering, School of Life Sciences, École Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland
- SIB Swiss Institute of Bioinformatics, Lausanne, Switzerland
| | - Lisa Pagani
- Institute of Bioengineering, School of Life Sciences, École Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland
- SIB Swiss Institute of Bioinformatics, Lausanne, Switzerland
| | - Celia García-Pareja
- Institute of Bioengineering, School of Life Sciences, École Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland
- SIB Swiss Institute of Bioinformatics, Lausanne, Switzerland
| | - Anne-Florence Bitbol
- Institute of Bioengineering, School of Life Sciences, École Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland
- SIB Swiss Institute of Bioinformatics, Lausanne, Switzerland
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2
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Sudbrack V, Mullon C. Fixation times of de novo and standing beneficial variants in subdivided populations. Genetics 2024; 227:iyae043. [PMID: 38527860 DOI: 10.1093/genetics/iyae043] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/17/2024] [Revised: 01/17/2024] [Accepted: 03/11/2024] [Indexed: 03/27/2024] Open
Abstract
The rate at which beneficial alleles fix in a population depends on the probability of and time to fixation of such alleles. Both of these quantities can be significantly impacted by population subdivision and limited gene flow. Here, we investigate how limited dispersal influences the rate of fixation of beneficial de novo mutations, as well as fixation time from standing genetic variation. We investigate this for a population structured according to the island model of dispersal allowing us to use the diffusion approximation, which we complement with simulations. We find that fixation may take on average fewer generations under limited dispersal than under panmixia when selection is moderate. This is especially the case if adaptation occurs from de novo recessive mutations, and dispersal is not too limited (such that approximately FST<0.2). The reason is that mildly limited dispersal leads to only a moderate increase in effective population size (which slows down fixation), but is sufficient to cause a relative excess of homozygosity due to inbreeding, thereby exposing rare recessive alleles to selection (which accelerates fixation). We also explore the effect of metapopulation dynamics through local extinction followed by recolonization, finding that such dynamics always accelerate fixation from standing genetic variation, while de novo mutations show faster fixation interspersed with longer waiting times. Finally, we discuss the implications of our results for the detection of sweeps, suggesting that limited dispersal mitigates the expected differences between the genetic signatures of sweeps involving recessive and dominant alleles.
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Affiliation(s)
- Vitor Sudbrack
- Department of Ecology and Evolution, University of Lausanne, Lausanne 1015, Vaud, Switzerland
| | - Charles Mullon
- Department of Ecology and Evolution, University of Lausanne, Lausanne 1015, Vaud, Switzerland
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3
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Kuo YP, Carja O. Evolutionary graph theory beyond single mutation dynamics: on how network-structured populations cross fitness landscapes. Genetics 2024; 227:iyae055. [PMID: 38639307 PMCID: PMC11151934 DOI: 10.1093/genetics/iyae055] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/07/2024] [Revised: 03/28/2024] [Accepted: 04/01/2024] [Indexed: 04/20/2024] Open
Abstract
Spatially resolved datasets are revolutionizing knowledge in molecular biology, yet are under-utilized for questions in evolutionary biology. To gain insight from these large-scale datasets of spatial organization, we need mathematical representations and modeling techniques that can both capture their complexity, but also allow for mathematical tractability. Evolutionary graph theory utilizes the mathematical representation of networks as a proxy for heterogeneous population structure and has started to reshape our understanding of how spatial structure can direct evolutionary dynamics. However, previous results are derived for the case of a single new mutation appearing in the population and the role of network structure in shaping fitness landscape crossing is still poorly understood. Here we study how network-structured populations cross fitness landscapes and show that even a simple extension to a two-mutational landscape can exhibit complex evolutionary dynamics that cannot be predicted using previous single-mutation results. We show how our results can be intuitively understood through the lens of how the two main evolutionary properties of a network, the amplification and acceleration factors, change the expected fate of the intermediate mutant in the population and further discuss how to link these models to spatially resolved datasets of cellular organization.
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Affiliation(s)
- Yang Ping Kuo
- Computational Biology Department, School of Computer Science, Carnegie Mellon University, Pittsburgh, PA 15232, USA
| | - Oana Carja
- Computational Biology Department, School of Computer Science, Carnegie Mellon University, Pittsburgh, PA 15232, USA
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4
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Freire TFA, Hu Z, Wood KB, Gjini E. Modeling spatial evolution of multi-drug resistance under drug environmental gradients. PLoS Comput Biol 2024; 20:e1012098. [PMID: 38820350 PMCID: PMC11142541 DOI: 10.1371/journal.pcbi.1012098] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/17/2023] [Accepted: 04/23/2024] [Indexed: 06/02/2024] Open
Abstract
Multi-drug combinations to treat bacterial populations are at the forefront of approaches for infection control and prevention of antibiotic resistance. Although the evolution of antibiotic resistance has been theoretically studied with mathematical population dynamics models, extensions to spatial dynamics remain rare in the literature, including in particular spatial evolution of multi-drug resistance. In this study, we propose a reaction-diffusion system that describes the multi-drug evolution of bacteria based on a drug-concentration rescaling approach. We show how the resistance to drugs in space, and the consequent adaptation of growth rate, is governed by a Price equation with diffusion, integrating features of drug interactions and collateral resistances or sensitivities to the drugs. We study spatial versions of the model where the distribution of drugs is homogeneous across space, and where the drugs vary environmentally in a piecewise-constant, linear and nonlinear manner. Although in many evolution models, per capita growth rate is a natural surrogate for fitness, in spatially-extended, potentially heterogeneous habitats, fitness is an emergent property that potentially reflects additional complexities, from boundary conditions to the specific spatial variation of growth rates. Applying concepts from perturbation theory and reaction-diffusion equations, we propose an analytical metric for characterization of average mutant fitness in the spatial system based on the principal eigenvalue of our linear problem, λ1. This enables an accurate translation from drug spatial gradients and mutant antibiotic susceptibility traits to the relative advantage of each mutant across the environment. Our approach allows one to predict the precise outcomes of selection among mutants over space, ultimately from comparing their λ1 values, which encode a critical interplay between growth functions, movement traits, habitat size and boundary conditions. Such mathematical understanding opens new avenues for multi-drug therapeutic optimization.
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Affiliation(s)
- Tomas Ferreira Amaro Freire
- Center for Computational and Stochastic Mathematics, Instituto Superior Técnico, University of Lisbon, Lisbon, Portugal
| | - Zhijian Hu
- Departments of Biophysics and Physics, University of Michigan, United States of America
| | - Kevin B. Wood
- Departments of Biophysics and Physics, University of Michigan, United States of America
| | - Erida Gjini
- Center for Computational and Stochastic Mathematics, Instituto Superior Técnico, University of Lisbon, Lisbon, Portugal
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5
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Svoboda J, Joshi S, Tkadlec J, Chatterjee K. Amplifiers of selection for the Moran process with both Birth-death and death-Birth updating. PLoS Comput Biol 2024; 20:e1012008. [PMID: 38551989 PMCID: PMC11006194 DOI: 10.1371/journal.pcbi.1012008] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/17/2024] [Revised: 04/10/2024] [Accepted: 03/18/2024] [Indexed: 04/11/2024] Open
Abstract
Populations evolve by accumulating advantageous mutations. Every population has some spatial structure that can be modeled by an underlying network. The network then influences the probability that new advantageous mutations fixate. Amplifiers of selection are networks that increase the fixation probability of advantageous mutants, as compared to the unstructured fully-connected network. Whether or not a network is an amplifier depends on the choice of the random process that governs the evolutionary dynamics. Two popular choices are Moran process with Birth-death updating and Moran process with death-Birth updating. Interestingly, while some networks are amplifiers under Birth-death updating and other networks are amplifiers under death-Birth updating, so far no spatial structures have been found that function as an amplifier under both types of updating simultaneously. In this work, we identify networks that act as amplifiers of selection under both versions of the Moran process. The amplifiers are robust, modular, and increase fixation probability for any mutant fitness advantage in a range r ∈ (1, 1.2). To complement this positive result, we also prove that for certain quantities closely related to fixation probability, it is impossible to improve them simultaneously for both versions of the Moran process. Together, our results highlight how the two versions of the Moran process differ and what they have in common.
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Affiliation(s)
| | | | - Josef Tkadlec
- Computer Science Institute, Charles University, Prague, Czech Republic
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6
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Kuo YP, Carja O. Evolutionary graph theory beyond pairwise interactions: Higher-order network motifs shape times to fixation in structured populations. PLoS Comput Biol 2024; 20:e1011905. [PMID: 38489353 DOI: 10.1371/journal.pcbi.1011905] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/10/2023] [Revised: 03/27/2024] [Accepted: 02/12/2024] [Indexed: 03/17/2024] Open
Abstract
To design population topologies that can accelerate rates of solution discovery in directed evolution problems or for evolutionary optimization applications, we must first systematically understand how population structure shapes evolutionary outcome. Using the mathematical formalism of evolutionary graph theory, recent studies have shown how to topologically build networks of population interaction that increase probabilities of fixation of beneficial mutations, at the expense, however, of longer fixation times, which can slow down rates of evolution, under elevated mutation rate. Here we find that moving beyond dyadic interactions in population graphs is fundamental to explain the trade-offs between probabilities and times to fixation of new mutants in the population. We show that higher-order motifs, and in particular three-node structures, allow the tuning of times to fixation, without changes in probabilities of fixation. This gives a near-continuous control over achieving solutions that allow for a wide range of times to fixation. We apply our algorithms and analytic results to two evolutionary optimization problems and show that the rate of solution discovery can be tuned near continuously by adjusting the higher-order topology of the population. We show that the effects of population structure on the rate of evolution critically depend on the optimization landscape and find that decelerators, with longer times to fixation of new mutants, are able to reach the optimal solutions faster than accelerators in complex solution spaces. Our results highlight that no one population topology fits all optimization applications, and we provide analytic and computational tools that allow for the design of networks suitable for each specific task.
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Affiliation(s)
- Yang Ping Kuo
- Computational Biology Department, School of Computer Science, Carnegie Mellon University, Pittsburgh, Pennsylvania, United States of America
- Joint Carnegie Mellon University-University of Pittsburgh Ph.D. Program in Computational Biology, Carnegie Mellon University, Pittsburgh, Pennsylvania, United States of America
| | - Oana Carja
- Computational Biology Department, School of Computer Science, Carnegie Mellon University, Pittsburgh, Pennsylvania, United States of America
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7
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Moawad A, Abbara A, Bitbol AF. Evolution of cooperation in deme-structured populations on graphs. Phys Rev E 2024; 109:024307. [PMID: 38491653 DOI: 10.1103/physreve.109.024307] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/18/2023] [Accepted: 12/19/2023] [Indexed: 03/18/2024]
Abstract
Understanding how cooperation can evolve in populations despite its cost to individual cooperators is an important challenge. Models of spatially structured populations with one individual per node of a graph have shown that cooperation, modeled via the prisoner's dilemma, can be favored by natural selection. These results depend on microscopic update rules, which determine how birth, death, and migration on the graph are coupled. Recently, we developed coarse-grained models of spatially structured populations on graphs, where each node comprises a well-mixed deme, and where migration is independent from division and death, thus bypassing the need for update rules. Here, we study the evolution of cooperation in these models in the rare-migration regime, within the prisoner's dilemma. We find that cooperation is not favored by natural selection in these coarse-grained models on graphs where overall deme fitness does not directly impact migration from a deme. This is due to a separation of scales, whereby cooperation occurs at a local level within demes, while spatial structure matters between demes.
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Affiliation(s)
- Alix Moawad
- Institute of Bioengineering, School of Life Sciences, École Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland and SIB Swiss Institute of Bioinformatics, CH-1015 Lausanne, Switzerland
| | - Alia Abbara
- Institute of Bioengineering, School of Life Sciences, École Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland and SIB Swiss Institute of Bioinformatics, CH-1015 Lausanne, Switzerland
| | - Anne-Florence Bitbol
- Institute of Bioengineering, School of Life Sciences, École Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland and SIB Swiss Institute of Bioinformatics, CH-1015 Lausanne, Switzerland
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8
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Freire T, Hu Z, Wood KB, Gjini E. Modeling spatial evolution of multi-drug resistance under drug environmental gradients. BIORXIV : THE PREPRINT SERVER FOR BIOLOGY 2023:2023.11.16.567447. [PMID: 38014279 PMCID: PMC10680811 DOI: 10.1101/2023.11.16.567447] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/29/2023]
Abstract
Multi-drug combinations to treat bacterial populations are at the forefront of approaches for infection control and prevention of antibiotic resistance. Although the evolution of antibiotic resistance has been theoretically studied with mathematical population dynamics models, extensions to spatial dynamics remain rare in the literature, including in particular spatial evolution of multi-drug resistance. In this study, we propose a reaction-diffusion system that describes the multi-drug evolution of bacteria, based on a rescaling approach (Gjini and Wood, 2021). We show how the resistance to drugs in space, and the consequent adaptation of growth rate is governed by a Price equation with diffusion. The covariance terms in this equation integrate features of drug interactions and collateral resistances or sensitivities to the drugs. We study spatial versions of the model where the distribution of drugs is homogeneous across space, and where the drugs vary environmentally in a piecewise-constant, linear and nonlinear manner. Applying concepts from perturbation theory and reaction-diffusion equations, we propose an analytical characterization of average mutant fitness in the spatial system based on the principal eigenvalue of our linear problem. This enables an accurate translation from drug spatial gradients and mutant antibiotic susceptibility traits, to the relative advantage of each mutant across the environment. Such a mathematical understanding allows to predict the precise outcomes of selection over space, ultimately from the fundamental balance between growth and movement traits, and their diversity in a population.
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Affiliation(s)
- Tomas Freire
- Center for Computational and Stochastic Mathematics, Instituto Superior Técnico, University of Lisbon, Lisbon, Portugal
| | - Zhijian Hu
- Departments of Biophysics and Physics, University of Michigan, USA
| | - Kevin B. Wood
- Departments of Biophysics and Physics, University of Michigan, USA
| | - Erida Gjini
- Center for Computational and Stochastic Mathematics, Instituto Superior Técnico, University of Lisbon, Lisbon, Portugal
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9
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Abbara A, Bitbol AF. Frequent asymmetric migrations suppress natural selection in spatially structured populations. PNAS NEXUS 2023; 2:pgad392. [PMID: 38024415 PMCID: PMC10667037 DOI: 10.1093/pnasnexus/pgad392] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 07/16/2023] [Accepted: 11/06/2023] [Indexed: 12/01/2023]
Abstract
Natural microbial populations often have complex spatial structures. This can impact their evolution, in particular the ability of mutants to take over. While mutant fixation probabilities are known to be unaffected by sufficiently symmetric structures, evolutionary graph theory has shown that some graphs can amplify or suppress natural selection, in a way that depends on microscopic update rules. We propose a model of spatially structured populations on graphs directly inspired by batch culture experiments, alternating within-deme growth on nodes and migration-dilution steps, and yielding successive bottlenecks. This setting bridges models from evolutionary graph theory with Wright-Fisher models. Using a branching process approach, we show that spatial structure with frequent migrations can only yield suppression of natural selection. More precisely, in this regime, circulation graphs, where the total incoming migration flow equals the total outgoing one in each deme, do not impact fixation probability, while all other graphs strictly suppress selection. Suppression becomes stronger as the asymmetry between incoming and outgoing migrations grows. Amplification of natural selection can nevertheless exist in a restricted regime of rare migrations and very small fitness advantages, where we recover the predictions of evolutionary graph theory for the star graph.
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Affiliation(s)
- Alia Abbara
- Institute of Bioengineering, School of Life Sciences, École Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
- SIB Swiss Institute of Bioinformatics, CH-1015 Lausanne, Switzerland
| | - Anne-Florence Bitbol
- Institute of Bioengineering, School of Life Sciences, École Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
- SIB Swiss Institute of Bioinformatics, CH-1015 Lausanne, Switzerland
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10
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Sharma N, Yagoobi S, Traulsen A. Self-loops in evolutionary graph theory: Friends or foes? PLoS Comput Biol 2023; 19:e1011387. [PMID: 37656739 PMCID: PMC10501642 DOI: 10.1371/journal.pcbi.1011387] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/27/2023] [Revised: 09/14/2023] [Accepted: 07/25/2023] [Indexed: 09/03/2023] Open
Abstract
Evolutionary dynamics in spatially structured populations has been studied for a long time. More recently, the focus has been to construct structures that amplify selection by fixing beneficial mutations with higher probability than the well-mixed population and lower probability of fixation for deleterious mutations. It has been shown that for a structure to substantially amplify selection, self-loops are necessary when mutants appear predominately in nodes that change often. As a result, for low mutation rates, self-looped amplifiers attain higher steady-state average fitness in the mutation-selection balance than well-mixed populations. But what happens when the mutation rate increases such that fixation probabilities alone no longer describe the dynamics? We show that self-loops effects are detrimental outside the low mutation rate regime. In the intermediate and high mutation rate regime, amplifiers of selection attain lower steady-state average fitness than the complete graph and suppressors of selection. We also provide an estimate of the mutation rate beyond which the mutation-selection dynamics on a graph deviates from the weak mutation rate approximation. It involves computing average fixation time scaling with respect to the population sizes for several graphs.
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Affiliation(s)
- Nikhil Sharma
- Department of Theoretical Biology, Max Planck Institute for Evolutionary Biology, Plön, Germany
| | - Sedigheh Yagoobi
- Department of Theoretical Biology, Max Planck Institute for Evolutionary Biology, Plön, Germany
| | - Arne Traulsen
- Department of Theoretical Biology, Max Planck Institute for Evolutionary Biology, Plön, Germany
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11
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Liu R, Masuda N. Fixation dynamics on hypergraphs. PLoS Comput Biol 2023; 19:e1011494. [PMID: 37751462 PMCID: PMC10558078 DOI: 10.1371/journal.pcbi.1011494] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/16/2023] [Revised: 10/06/2023] [Accepted: 09/05/2023] [Indexed: 09/28/2023] Open
Abstract
Hypergraphs have been a useful tool for analyzing population dynamics such as opinion formation and the public goods game occurring in overlapping groups of individuals. In the present study, we propose and analyze evolutionary dynamics on hypergraphs, in which each node takes one of the two types of different but constant fitness values. For the corresponding dynamics on conventional networks, under the birth-death process and uniform initial conditions, most networks are known to be amplifiers of natural selection; amplifiers by definition enhance the difference in the strength of the two competing types in terms of the probability that the mutant type fixates in the population. In contrast, we provide strong computational evidence that a majority of hypergraphs are suppressors of selection under the same conditions by combining theoretical and numerical analyses. We also show that this suppressing effect is not explained by one-mode projection, which is a standard method for expressing hypergraph data as a conventional network. Our results suggest that the modeling framework for structured populations in addition to the specific network structure is an important determinant of evolutionary dynamics, paving a way to studying fixation dynamics on higher-order networks including hypergraphs.
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Affiliation(s)
- Ruodan Liu
- Department of Mathematics, State University of New York at Buffalo, Buffalo, New York, United States of America
| | - Naoki Masuda
- Department of Mathematics, State University of New York at Buffalo, Buffalo, New York, United States of America
- Computational and Data-Enabled Sciences and Engineering Program, State University of New York at Buffalo, Buffalo, New York, United States of America
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12
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Servajean R, Bitbol AF. Impact of population size on early adaptation in rugged fitness landscapes. Philos Trans R Soc Lond B Biol Sci 2023; 378:20220045. [PMID: 37004726 PMCID: PMC10067268 DOI: 10.1098/rstb.2022.0045] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/11/2022] [Accepted: 01/12/2023] [Indexed: 04/04/2023] Open
Abstract
Owing to stochastic fluctuations arising from finite population size, known as genetic drift, the ability of a population to explore a rugged fitness landscape depends on its size. In the weak mutation regime, while the mean steady-state fitness increases with population size, we find that the height of the first fitness peak encountered when starting from a random genotype displays various behaviours versus population size, even among small and simple rugged landscapes. We show that the accessibility of the different fitness peaks is key to determining whether this height overall increases or decreases with population size. Furthermore, there is often a finite population size that maximizes the height of the first fitness peak encountered when starting from a random genotype. This holds across various classes of model rugged landscapes with sparse peaks, and in some experimental and experimentally inspired ones. Thus, early adaptation in rugged fitness landscapes can be more efficient and predictable for relatively small population sizes than in the large-size limit. This article is part of the theme issue 'Interdisciplinary approaches to predicting evolutionary biology'.
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Affiliation(s)
- Richard Servajean
- Institute of Bioengineering, School of Life Sciences, École Polytechnique Fédérale de Lausanne (EPFL), 1015 Lausanne, Switzerland
- SIB Swiss Institute of Bioinformatics, 1015 Lausanne, Switzerland
| | - Anne-Florence Bitbol
- Institute of Bioengineering, School of Life Sciences, École Polytechnique Fédérale de Lausanne (EPFL), 1015 Lausanne, Switzerland
- SIB Swiss Institute of Bioinformatics, 1015 Lausanne, Switzerland
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13
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Yagoobi S, Sharma N, Traulsen A. Categorizing update mechanisms for graph-structured metapopulations. J R Soc Interface 2023; 20:20220769. [PMID: 36919418 PMCID: PMC10015335 DOI: 10.1098/rsif.2022.0769] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/16/2023] Open
Abstract
The structure of a population strongly influences its evolutionary dynamics. In various settings ranging from biology to social systems, individuals tend to interact more often with those present in their proximity and rarely with those far away. A common approach to model the structure of a population is evolutionary graph theory. In this framework, each graph node is occupied by a reproducing individual. The links connect these individuals to their neighbours. The offspring can be placed on neighbouring nodes, replacing the neighbours-or the progeny of its neighbours can replace a node during the course of ongoing evolutionary dynamics. Extending this theory by replacing single individuals with subpopulations at nodes yields a graph-structured metapopulation. The dynamics between the different local subpopulations is set by an update mechanism. There are many such update mechanisms. Here, we classify update mechanisms for structured metapopulations, which allows to find commonalities between past work and illustrate directions for further research and current gaps of investigation.
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Affiliation(s)
- Sedigheh Yagoobi
- Department of Evolutionary Theory, Max Planck Institute for Evolutionary Biology, August-Thienemann Strasse 2, Plön 24306, Germany
| | - Nikhil Sharma
- Department of Evolutionary Theory, Max Planck Institute for Evolutionary Biology, August-Thienemann Strasse 2, Plön 24306, Germany
| | - Arne Traulsen
- Department of Evolutionary Theory, Max Planck Institute for Evolutionary Biology, August-Thienemann Strasse 2, Plön 24306, Germany
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14
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Sharma N, Traulsen A. Suppressors of fixation can increase average fitness beyond amplifiers of selection. Proc Natl Acad Sci U S A 2022; 119:e2205424119. [PMID: 36067304 PMCID: PMC9478682 DOI: 10.1073/pnas.2205424119] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/28/2022] [Accepted: 08/03/2022] [Indexed: 11/18/2022] Open
Abstract
Evolutionary dynamics on graphs has remarkable features: For example, it has been shown that amplifiers of selection exist that-compared to an unstructured population-increase the fixation probability of advantageous mutations, while they decrease the fixation probability of disadvantageous mutations. So far, the theoretical literature has focused on the case of a single mutant entering a graph-structured population, asking how the graph affects the probability that a mutant takes over a population and the time until this typically happens. For continuously evolving systems, the more relevant case is that mutants constantly arise in an evolving population. Typically, such mutations occur with a small probability during reproduction events. We thus focus on the low mutation rate limit. The probability distribution for the fitness in this process converges to a steady state at long times. Intuitively, amplifiers of selection are expected to increase the population's mean fitness in the steady state. Similarly, suppressors of selection are expected to decrease the population's mean fitness in the steady state. However, we show that another set of graphs, called suppressors of fixation, can attain the highest population mean fitness. The key reason behind this is their ability to efficiently reject deleterious mutants. This illustrates the importance of the deleterious mutant regime for the long-term evolutionary dynamics, something that seems to have been overlooked in the literature so far.
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Affiliation(s)
- Nikhil Sharma
- Department of Evolutionary Theory, Max Planck Institute for Evolutionary Biology, 24306 Plön, Germany
| | - Arne Traulsen
- Department of Evolutionary Theory, Max Planck Institute for Evolutionary Biology, 24306 Plön, Germany
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15
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Spaulding CB, Teimouri H, Kolomeisky AB. The role of spatial structures of tissues in cancer initiation dynamics. Phys Biol 2022; 19. [PMID: 35901794 DOI: 10.1088/1478-3975/ac8515] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/19/2022] [Accepted: 07/28/2022] [Indexed: 11/12/2022]
Abstract
It is widely believed that biological tissues evolved to lower the risks of cancer development. One of the specific ways to minimize the chances of tumor formation comes from proper spatial organization of tissues. However, the microscopic mechanisms of underlying processes remain not fully understood. We present a theoretical investigation on the role of spatial structures in cancer initiation dynamics. In our approach, the dynamics of single mutation fixations are analyzed using analytical calculations and computer simulations by mapping them to Moran processes on graphs with different connectivity that mimic various spatial structures. It is found that while the fixation probability is not affected by modifying the spatial structures of the tissues, the fixation times can change dramatically. The slowest dynamics is observed in "quasi-one-dimensional" structures, while the fastest dynamics is observed in "quasi-three-dimensional" structures. Theoretical calculations also suggest that there is a critical value of the degree of graph connectivity, which mimics the spatial dimension of the tissue structure, above which the spatial structure of the tissue has no effect on the mutation fixation dynamics. An effective discrete-state stochastic model of cancer initiation is utilized to explain our theoretical results and predictions. Our theoretical analysis clarifies some important aspects on the role of the tissue spatial structures in the cancer initiation processes.
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Affiliation(s)
- Cade B Spaulding
- Department of Chemistry, Rice University, 6100 Main Street, Houston, Texas, 77005-1892, UNITED STATES
| | - Hamid Teimouri
- Department of Chemistry, Rice University, 6100 Main Street, Houston, Texas, 77005-1892, UNITED STATES
| | - Anatoly B Kolomeisky
- Department of Chemistry and Rice Quantum Institute, Rice University, 6100 Main Street, USA, Houston, Texas, 77005-1892, UNITED STATES
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Labavić D, Loverdo C, Bitbol AF. Hydrodynamic flow and concentration gradients in the gut enhance neutral bacterial diversity. Proc Natl Acad Sci U S A 2022; 119:e2108671119. [PMID: 34969835 PMCID: PMC8740595 DOI: 10.1073/pnas.2108671119] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 11/08/2021] [Indexed: 01/23/2023] Open
Abstract
The gut microbiota features important genetic diversity, and the specific spatial features of the gut may shape evolution within this environment. We investigate the fixation probability of neutral bacterial mutants within a minimal model of the gut that includes hydrodynamic flow and resulting gradients of food and bacterial concentrations. We find that this fixation probability is substantially increased, compared with an equivalent well-mixed system, in the regime where the profiles of food and bacterial concentration are strongly spatially dependent. Fixation probability then becomes independent of total population size. We show that our results can be rationalized by introducing an active population, which consists of those bacteria that are actively consuming food and dividing. The active population size yields an effective population size for neutral mutant fixation probability in the gut.
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Affiliation(s)
- Darka Labavić
- CNRS, Institut de Biologie Paris-Seine, Laboratoire Jean Perrin (UMR 8237), Sorbonne Université, F-75005 Paris, France
| | - Claude Loverdo
- CNRS, Institut de Biologie Paris-Seine, Laboratoire Jean Perrin (UMR 8237), Sorbonne Université, F-75005 Paris, France;
| | - Anne-Florence Bitbol
- Institute of Bioengineering, School of Life Sciences, École Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland;
- SIB Swiss Institute of Bioinformatics, CH-1015 Lausanne, Switzerland
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