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Nuñez JG, Paulose J, Möbius W, Beller DA. Range expansions across landscapes with quenched noise. Proc Natl Acad Sci U S A 2024; 121:e2411487121. [PMID: 39136984 PMCID: PMC11348022 DOI: 10.1073/pnas.2411487121] [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: 06/08/2024] [Accepted: 07/01/2024] [Indexed: 08/15/2024] Open
Abstract
When biological populations expand into new territory, the evolutionary outcomes can be strongly influenced by genetic drift, the random fluctuations in allele frequencies. Meanwhile, spatial variability in the environment can also significantly influence the competition between subpopulations vying for space. Little is known about the interplay of these intrinsic and extrinsic sources of noise in population dynamics: When does environmental heterogeneity dominate over genetic drift or vice versa, and what distinguishes their population genetics signatures? Here, in the context of neutral evolution, we examine the interplay between a population's intrinsic, demographic noise and an extrinsic, quenched random noise provided by a heterogeneous environment. Using a multispecies Eden model, we simulate a population expanding over a landscape with random variations in local growth rates and measure how this variability affects genealogical tree structure, and thus genetic diversity. We find that, for strong heterogeneity, the genetic makeup of the expansion front is to a great extent predetermined by the set of fastest paths through the environment. The landscape-dependent statistics of these optimal paths then supersede those of the population's intrinsic noise as the main determinant of evolutionary dynamics. Remarkably, the statistics for coalescence of genealogical lineages, derived from those deterministic paths, strongly resemble the statistics emerging from demographic noise alone in uniform landscapes. This cautions interpretations of coalescence statistics and raises new challenges for inferring past population dynamics.
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Affiliation(s)
- Jimmy Gonzalez Nuñez
- Department of Physics and Astronomy, Johns Hopkins University, Baltimore, MD21218
| | - Jayson Paulose
- Department of Physics, Institute for Fundamental Science, University of Oregon, Eugene, OR97403
| | - Wolfram Möbius
- Living Systems Institute, Faculty of Health and Life Sciences, University of Exeter, ExeterEX4 4QH, United Kingdom
- Physics and Astronomy, Faculty of Environment, Science and Economy, University of Exeter, ExeterEX4 4QL, United Kingdom
| | - Daniel A. Beller
- Department of Physics and Astronomy, Johns Hopkins University, Baltimore, MD21218
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2
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Mukhamadiarov RI, Ciarchi M, Olmeda F, Rulands S. Clonal dynamics of surface-driven growing tissues. Phys Rev E 2024; 109:064407. [PMID: 39021023 DOI: 10.1103/physreve.109.064407] [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: 12/15/2023] [Accepted: 05/17/2024] [Indexed: 07/20/2024]
Abstract
The self-organization of cells into complex tissues relies on a tight coordination of cell behavior. Identifying the cellular processes driving tissue growth is key to understanding the emergence of tissue forms and devising targeted therapies for aberrant growth, such as in cancer. Inferring the mode of tissue growth, whether it is driven by cells on the surface or by cells in the bulk, is possible in cell culture experiments but difficult in most tissues in living organisms (in vivo). Genetic tracing experiments, where a subset of cells is labeled with inheritable markers, have become important experimental tools to study cell fate in vivo. Here we show that the mode of tissue growth is reflected in the size distribution of the progeny of marked cells. To this end, we derive the clone size distributions using analytical calculations in the limit of negligible cell migration and cell death, and we test our predictions with an agent-based stochastic sampling technique. We show that for surface-driven growth the clone size distribution takes a characteristic power-law form with an exponent determined by fluctuations of the tissue surface. Our results propose a possible way of determining the mode of tissue growth from genetic tracing experiments.
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3
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Li LH, Kardar M. Specialization at an expanding front. Phys Rev E 2023; 108:L032402. [PMID: 37849149 DOI: 10.1103/physreve.108.l032402] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/20/2022] [Accepted: 08/11/2023] [Indexed: 10/19/2023]
Abstract
As a population grows, spreading to new environments may favor specialization. In this paper, we introduce and explore a model for specialization at the front of a colony expanding synchronously into new territory. We show through numerical simulations that, by gaining fitness through accumulating mutations, progeny of the initial seed population can differentiate into distinct specialists. With competition and selection limited to the growth front, the emerging specialists first segregate into sectors, which then expand to dominate the entire population. We quantify the scaling of the fixation time with the size of the population and observe different behaviors corresponding to distinct universality classes: unbounded and bounded gains in fitness lead to superdiffusive (z=3/2) and diffusive (z=2) stochastic wanderings of the sector boundaries, respectively.
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Affiliation(s)
- Lauren H Li
- Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Mehran Kardar
- Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
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4
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Golden A, Dukovski I, Segrè D, Korolev KS. Growth instabilities shape morphology and genetic diversity of microbial colonies. Phys Biol 2022; 19:10.1088/1478-3975/ac8514. [PMID: 35901792 PMCID: PMC11209841 DOI: 10.1088/1478-3975/ac8514] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/17/2022] [Accepted: 07/28/2022] [Indexed: 11/11/2022]
Abstract
Cellular populations assume an incredible variety of shapes ranging from circular molds to irregular tumors. While we understand many of the mechanisms responsible for these spatial patterns, little is known about how the shape of a population influences its ecology and evolution. Here, we investigate this relationship in the context of microbial colonies grown on hard agar plates. This a well-studied system that exhibits a transition from smooth circular disks to more irregular and rugged shapes as either the nutrient concentration or cellular motility is decreased. Starting from a mechanistic model of colony growth, we identify two dimensionless quantities that determine how morphology and genetic diversity of the population depend on the model parameters. Our simulations further reveal that population dynamics cannot be accurately described by the commonly-used surface growth models. Instead, one has to explicitly account for the emergent growth instabilities and demographic fluctuations. Overall, our work links together environmental conditions, colony morphology, and evolution. This link is essential for a rational design of concrete, biophysical perturbations to steer evolution in the desired direction.
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Affiliation(s)
- Alexander Golden
- Department of Physics, Graduate Program in Bioinformatics, and Biological Design Center, Boston University, Boston, MA 02215, United States of America
| | - Ilija Dukovski
- Graduate Program in Bioinformatics, and Biological Design Center, Boston University, Boston, MA 02215, United States of America
| | - Daniel Segrè
- Department of Physics, Department of Biology, Department of Biomedical Engineering, Graduate Program in Bioinformatics, and Biological Design Center, Boston University, Boston, MA 02215, United States of America
| | - Kirill S Korolev
- Department of Physics, Graduate Program in Bioinformatics, and Biological Design Center, Boston University, Boston, MA 02215, United States of America
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5
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Marguet B, Reis FDAA, Pierre-Louis O. Interface collisions with diffusive mass transport. Phys Rev E 2022; 106:014802. [PMID: 35974503 DOI: 10.1103/physreve.106.014802] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/19/2022] [Accepted: 06/23/2022] [Indexed: 06/15/2023]
Abstract
We report on a linear Langevin model that describes the evolution of the roughness of two interfaces that move towards each other and are coupled by a diffusion field. This model aims at describing the closing of the gap between two 2D material domains during growth, and the subsequent formation of a rough grain boundary. We assume that deposition occurs in the gap between the two domains and that the growth units diffuse and may attach to the edges of the domains. These units can also detach from edges, diffuse, and reattach elsewhere. For slow growth, the edge roughness increases monotonously and then saturates at some equilibrium value. For fast growth, the roughness exhibits a maximum just before the collision between the two interfaces, which is followed by a minimum. The peak of the roughness can be dominated by statistical fluctuations or by edge instabilities. A phase diagram with three regimes is obtained: Slow growth without peak, peak dominated by statistical fluctuations, and peak dominated by instabilities. These results reproduce the main features observed in kinetic Monte Carlo simulations.
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Affiliation(s)
- Bastien Marguet
- Institut Lumière Matière, UMR5306 Université Lyon 1-CNRS, Université de Lyon, 69622 Villeurbanne, France
| | - F D A Aarão Reis
- Instituto de Física, Universidade Federal Fluminense, Avenida Litorânea s/n, 24210-340 Niterói RJ, Brazil
| | - Olivier Pierre-Louis
- Institut Lumière Matière, UMR5306 Université Lyon 1-CNRS, Université de Lyon, 69622 Villeurbanne, France
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6
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Eghdami A, Paulose J, Fusco D. Branching structure of genealogies in spatially growing populations and its implications for population genetics inference. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2022; 34:294008. [PMID: 35510713 DOI: 10.1088/1361-648x/ac6cd9] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/27/2021] [Accepted: 05/04/2022] [Indexed: 06/14/2023]
Abstract
Spatial models where growth is limited to the population edge have been instrumental to understanding the population dynamics and the clone size distribution in growing cellular populations, such as microbial colonies and avascular tumours. A complete characterization of the coalescence process generated by spatial growth is still lacking, limiting our ability to apply classic population genetics inference to spatially growing populations. Here, we start filling this gap by investigating the statistical properties of the cell lineages generated by the two dimensional Eden model, leveraging their physical analogy with directed polymers. Our analysis provides quantitative estimates for population measurements that can easily be assessed via sequencing, such as the average number of segregating sites and the clone size distribution of a subsample of the population. Our results not only reveal remarkable features of the genealogies generated during growth, but also highlight new properties that can be misinterpreted as signs of selection if non-spatial models are inappropriately applied.
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Affiliation(s)
- Armin Eghdami
- Department of Physics, University of Cambridge, Cambridge, CB3 0HE, United Kingdom
| | - Jayson Paulose
- Department of Physics and Institute for Fundamental Science, University of Oregon, Eugene, OR 97401, United States of America
| | - Diana Fusco
- Department of Physics, University of Cambridge, Cambridge, CB3 0HE, United Kingdom
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7
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Azimzade Y, Saberi AA. Geometrically regulating evolutionary dynamics in biofilms. Phys Rev E 2021; 103:L050401. [PMID: 34134254 DOI: 10.1103/physreve.103.l050401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/02/2020] [Accepted: 04/21/2021] [Indexed: 11/07/2022]
Abstract
The theoretical understanding of evolutionary dynamics in spatially structured populations often relies on nonspatial models. Biofilms are among such populations where a more accurate understanding is of theoretical interest and can reveal new solutions to existing challenges. Here, we studied how the geometry of the environment affects the evolutionary dynamics of expanding populations, using the Eden model. Our results show that fluctuations of subpopulations during range expansion in two- and three-dimensional environments are not Brownian. Furthermore, we found that the substrate's geometry interferes with the evolutionary dynamics of populations that grow upon it. Inspired by these findings, we propose a periodically wedged pattern on surfaces prone to develop biofilms. On such patterned surfaces, natural selection becomes less effective and beneficial mutants would have a harder time establishing. Additionally, this modification accelerates genetic drift and leads to less diverse biofilms. Both interventions are highly desired for biofilms.
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Affiliation(s)
- Youness Azimzade
- Department of Physics, University of Tehran, Tehran 14395-547, Iran
| | - Abbas Ali Saberi
- Department of Physics, University of Tehran, Tehran 14395-547, Iran.,Institut für Theoretische Physik, Universitat zu Köln, Zülpicher Strasse 77, 50937 Köln, Germany
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8
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Chu S, Kardar M, Nelson DR, Beller DA. Evolution in range expansions with competition at rough boundaries. J Theor Biol 2019; 478:153-160. [PMID: 31220465 DOI: 10.1016/j.jtbi.2019.06.018] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/19/2019] [Revised: 06/10/2019] [Accepted: 06/17/2019] [Indexed: 11/30/2022]
Abstract
When a biological population expands into new territory, genetic drift develops an enormous influence on evolution at the propagating front. In such range expansion processes, fluctuations in allele frequencies occur through stochastic spatial wandering of both genetic lineages and the boundaries between genetically segregated sectors. Laboratory experiments on microbial range expansions have shown that this stochastic wandering, transverse to the front, is superdiffusive due to the front's growing roughness, implying much faster loss of genetic diversity than predicted by simple flat front diffusive models. We study the evolutionary consequences of this superdiffusive wandering using two complementary numerical models of range expansions: the stepping stone model, and a new interpretation of the model of directed paths in random media, in the context of a roughening population front. Through these approaches we compute statistics for the times since common ancestry for pairs of individuals with a given spatial separation at the front, and we explore how environmental heterogeneities can locally suppress these superdiffusive fluctuations.
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Affiliation(s)
- Sherry Chu
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
| | - Mehran Kardar
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
| | - David R Nelson
- Department of Physics, Department of Molecular and Cellular Biology and School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138, USA
| | - Daniel A Beller
- Department of Physics, University of California, Merced, CA 95343, USA.
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9
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Horowitz JM, Kardar M. Bacterial range expansions on a growing front: Roughness, fixation, and directed percolation. Phys Rev E 2019; 99:042134. [PMID: 31108639 DOI: 10.1103/physreve.99.042134] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/01/2018] [Indexed: 06/09/2023]
Abstract
Directed percolation (DP) is a classic model for nonequilibrium phase transitions into a single absorbing state (fixation). It has been extensively studied by analytical and numerical techniques in diverse contexts. Recently, DP has appeared as a generic model for the evolutionary and ecological dynamics of competing bacterial populations. Range expansion-the stochastic reproduction of bacteria competing for space to be occupied by their progeny-leads to a fluctuating and rough growth front, which is known from experiment and simulation to affect the underlying critical behavior of the DP transition. In this work, we employ symmetry arguments to construct a pair of nonlinear stochastic partial differential equations describing the coevolution of surface roughness with the composition field of DP. Macroscopic manifestations (phenomenology) of these equations on growth patterns and genealogical tracks of range expansion are discussed; followed by a renormalization group analysis of possible scaling behaviors at the DP transition.
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Affiliation(s)
- Jordan M Horowitz
- Physics of Living Systems Group, Department of Physics, Massachusetts Institute of Technology, 400 Technology Square, Cambridge, Massachusetts 02139, USA
- Department of Biophysics, University of Michigan, Ann Arbor, Michigan 48109, USA
- Center for the Study of Complex Systems, University of Michigan, Ann Arbor, Michigan 48104, USA
| | - Mehran Kardar
- Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
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10
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Abstract
We provide a theoretical framework to analyze the properties of frontal collisions of two growing interfaces considering different short-range interactions between them. Due to their roughness, the collision events spread in time and form rough domain boundaries, which defines collision interfaces in time and space. We show that statistical properties of such interfaces depend on the kinetics of the growing interfaces before collision, but are independent of the details of their interaction and of their fluctuations during the collision. Those properties exhibit dynamic scaling with exponents related to the growth kinetics, but their distributions may be nonuniversal. Our results are supported by simulations of lattice models with irreversible dynamics and local interactions. Relations to first passage processes are discussed and a possible application to grain-boundary formation in two-dimensional materials is suggested.
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Affiliation(s)
- F D A Aarão Reis
- Instituto de Física, Universidade Federal Fluminense, Avenida Litorânea s/n, 24210-340 Niterói RJ, Brazil
| | - O Pierre-Louis
- Institut Lumière Matière, UMR5306 Université Lyon 1-CNRS, Université de Lyon 69622 Villeurbanne, France
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11
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Abstract
A Euclidean first passage percolation model describing the competing growth between k different types of infection is considered. We focus on the long-time behavior of this multitype growth process and we derive multitype shape results related to its morphology.
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12
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Abstract
A Euclidean first passage percolation model describing the competing growth between k different types of infection is considered. We focus on the long-time behavior of this multitype growth process and we derive multitype shape results related to its morphology.
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13
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Reiter M, Rulands S, Frey E. Range expansion of heterogeneous populations. PHYSICAL REVIEW LETTERS 2014; 112:148103. [PMID: 24766021 DOI: 10.1103/physrevlett.112.148103] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/31/2013] [Indexed: 06/03/2023]
Abstract
Risk spreading in bacterial populations is generally regarded as a strategy to maximize survival. Here, we study its role during range expansion of a genetically diverse population where growth and motility are two alternative traits. We find that during the initial expansion phase fast-growing cells do have a selective advantage. By contrast, asymptotically, generalists balancing motility and reproduction are evolutionarily most successful. These findings are rationalized by a set of coupled Fisher equations complemented by stochastic simulations.
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Affiliation(s)
- Matthias Reiter
- Department of Physics, Arnold-Sommerfeld-Center for Theoretical Physics and Center for NanoScience, Ludwig-Maximilians-Universität München, Theresienstrasse 37, D-80333 München, Germany
| | - Steffen Rulands
- Department of Physics, Arnold-Sommerfeld-Center for Theoretical Physics and Center for NanoScience, Ludwig-Maximilians-Universität München, Theresienstrasse 37, D-80333 München, Germany
| | - Erwin Frey
- Department of Physics, Arnold-Sommerfeld-Center for Theoretical Physics and Center for NanoScience, Ludwig-Maximilians-Universität München, Theresienstrasse 37, D-80333 München, Germany
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14
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Lavrentovich MO, Nelson DR. Asymmetric mutualism in two- and three-dimensional range expansions. PHYSICAL REVIEW LETTERS 2014; 112:138102. [PMID: 24745459 DOI: 10.1103/physrevlett.112.138102] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/24/2013] [Indexed: 06/03/2023]
Abstract
Genetic drift at the frontiers of two-dimensional range expansions of microorganisms can frustrate local cooperation between different genetic variants, demixing the population into distinct sectors. In a biological context, mutualistic or antagonistic interactions will typically be asymmetric between variants. By taking into account both the asymmetry and the interaction strength, we show that the much weaker demixing in three dimensions allows for a mutualistic phase over a much wider range of asymmetric cooperative benefits, with mutualism prevailing for any positive, symmetric benefit. We also demonstrate that expansions with undulating fronts roughen dramatically at the boundaries of the mutualistic phase, with severe consequences for the population genetics along the transition lines.
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Affiliation(s)
| | - David R Nelson
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
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15
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Ali A, Ball RC, Grosskinsky S, Somfai E. Scale-invariant growth processes in expanding space. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 87:020102. [PMID: 23496438 DOI: 10.1103/physreve.87.020102] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/13/2012] [Indexed: 06/01/2023]
Abstract
Many growth processes lead to intriguing stochastic patterns and complex fractal structures which exhibit local scale invariance properties. Such structures can often be described effectively by space-time trajectories of interacting particles, and their large scale behavior depends on the overall growth geometry. We establish an exact relation between statistical properties of structures in uniformly expanding and fixed geometries, which preserves the local scale invariance and is independent of other properties such as the dimensionality. This relation generalizes standard conformal transformations as the natural symmetry of self-affine growth processes. We illustrate our main result numerically for various structures of coalescing Lévy flights and fractional Brownian motions, including also branching and finite particle sizes. One of the main benefits of this approach is a full, explicit description of the asymptotic statistics in expanding domains, which are often nontrivial and random due to amplification of initial fluctuations.
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Affiliation(s)
- Adnan Ali
- Centre for Complexity Science, University of Warwick, Coventry CV4 7AL, United Kingdom
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16
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Lavrentovich MO, Korolev KS, Nelson DR. Radial Domany-Kinzel models with mutation and selection. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 87:012103. [PMID: 23410279 DOI: 10.1103/physreve.87.012103] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/17/2012] [Indexed: 06/01/2023]
Abstract
We study the effect of spatial structure, genetic drift, mutation, and selective pressure on the evolutionary dynamics in a simplified model of asexual organisms colonizing a new territory. Under an appropriate coarse-graining, the evolutionary dynamics is related to the directed percolation processes that arise in voter models, the Domany-Kinzel (DK) model, contact process, and so on. We explore the differences between linear (flat front) expansions and the much less familiar radial (curved front) range expansions. For the radial expansion, we develop a generalized, off-lattice DK model that minimizes otherwise persistent lattice artifacts. With both simulations and analytical techniques, we study the survival probability of advantageous mutants, the spatial correlations between domains of neutral strains, and the dynamics of populations with deleterious mutations. "Inflation" at the frontier leads to striking differences between radial and linear expansions. For a colony with initial radius R(0) expanding at velocity v, significant genetic demixing, caused by local genetic drift, occurs only up to a finite time t(*)=R(0)/v, after which portions of the colony become causally disconnected due to the inflating perimeter of the expanding front. As a result, the effect of a selective advantage is amplified relative to genetic drift, increasing the survival probability of advantageous mutants. Inflation also modifies the underlying directed percolation transition, introducing novel scaling functions and modifications similar to a finite-size effect. Finally, we consider radial range expansions with deflating perimeters, as might arise from colonization initiated along the shores of an island.
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17
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Ali A, Somfai E, Grosskinsky S. Reproduction-time statistics and segregation patterns in growing populations. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 85:021923. [PMID: 22463260 DOI: 10.1103/physreve.85.021923] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/09/2011] [Revised: 01/20/2012] [Indexed: 05/31/2023]
Abstract
Pattern formation in microbial colonies of competing strains under purely space-limited population growth has recently attracted considerable research interest. We show that the reproduction time statistics of individuals has a significant impact on the sectoring patterns. Generalizing the standard Eden growth model, we introduce a simple one-parameter family of reproduction time distributions indexed by the variation coefficient δ∈[0,1], which includes deterministic (δ=0) and memory-less exponential distribution (δ=1) as extreme cases. We present convincing numerical evidence and heuristic arguments that the generalized model is still in the Kardar-Parisi-Zhang (KPZ) universality class, and the changes in patterns are due to changing prefactors in the scaling relations, which we are able to predict quantitatively. With the example of Saccharomyces cerevisiae, we show that our approach using the variation coefficient also works for more realistic reproduction time distributions.
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Affiliation(s)
- Adnan Ali
- Centre for Complexity Science, University of Warwick, Coventry CV4 7AL, United Kingdom
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18
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Saito Y, Omura S. Domain competition during ballistic deposition: effect of surface diffusion and surface patterning. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 84:021601. [PMID: 21928993 DOI: 10.1103/physreve.84.021601] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/30/2011] [Indexed: 05/31/2023]
Abstract
We investigate domain competition occurring during aggregate growth under ballistic deposition on a one-dimensional substrate by kinetic Monte Carlo simulations. In order to capture adsorbate molecules being deposited vertically, domains grow tall by extending their branches laterally and suppress the growth of neighboring short domains. When molecules are deposited on a flat substrate and frozen at the deposition site, the population density of domains, ρ, decreases by a power law as ρ ∼ h(-2/3) at height h. In contrast, if the effect of surface diffusion is taken into account, the domain density decreases rapidly as ρ ∼ 1/h. On a substrate patterned with an array of nanopillars, domains growing from pillar tops tend to envelop those growing from gaps between pillars. To completely suppress the growth of domains in gaps, pillar periodicity λ should be smaller than a critical value λ(c). We estimate this value approximately using the slope angle and the aspect ratio of a single isolated domain.
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Affiliation(s)
- Yukio Saito
- Department of Physics, Keio University, Yokohama 223-8522, Japan.
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19
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Lizana L, Mitarai N, Sneppen K, Nakanishi H. Modeling the spatial dynamics of culture spreading in the presence of cultural strongholds. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 83:066116. [PMID: 21797450 DOI: 10.1103/physreve.83.066116] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/20/2011] [Revised: 04/07/2011] [Indexed: 05/31/2023]
Abstract
Cultural competition has throughout our history shaped and reshaped the geography of boundaries between humans. Language and culture are intimately connected and linguists often use distinctive keywords to quantify the dynamics of information spreading in societies harboring strong culture centers. One prominent example, which is addressed here, is Kyoto's historical impact on Japanese culture. We construct a minimal model, based on shared properties of linguistic maps, to address the interplay between information flow and geography. We show that spreading of information over Japan in the premodern time can be described by an Eden growth process with noise levels corresponding to coherent spatial patches of sizes given by a single day's walk (~15 km), and that new words appear in Kyoto at times comparable to the time between human generations (~30 yr).
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Affiliation(s)
- Ludvig Lizana
- Niels Bohr Institute, Blegdamsvej 17, DK-2100 Copenhagen, Denmark
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20
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Korolev KS, Avlund M, Hallatschek O, Nelson DR. Genetic demixing and evolution in linear stepping stone models. REVIEWS OF MODERN PHYSICS 2010; 82:1691-1718. [PMID: 21072144 PMCID: PMC2975585 DOI: 10.1103/revmodphys.82.1691] [Citation(s) in RCA: 130] [Impact Index Per Article: 9.3] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/17/2023]
Abstract
Results for mutation, selection, genetic drift, and migration in a one-dimensional continuous population are reviewed and extended. The population is described by a continuous limit of the stepping stone model, which leads to the stochastic Fisher-Kolmogorov-Petrovsky-Piscounov equation with additional terms describing mutations. Although the stepping stone model was first proposed for population genetics, it is closely related to "voter models" of interest in nonequilibrium statistical mechanics. The stepping stone model can also be regarded as an approximation to the dynamics of a thin layer of actively growing pioneers at the frontier of a colony of micro-organisms undergoing a range expansion on a Petri dish. The population tends to segregate into monoallelic domains. This segregation slows down genetic drift and selection because these two evolutionary forces can only act at the boundaries between the domains; the effects of mutation, however, are not significantly affected by the segregation. Although fixation in the neutral well-mixed (or "zero-dimensional") model occurs exponentially in time, it occurs only algebraically fast in the one-dimensional model. An unusual sublinear increase is also found in the variance of the spatially averaged allele frequency with time. If selection is weak, selective sweeps occur exponentially fast in both well-mixed and one-dimensional populations, but the time constants are different. The relatively unexplored problem of evolutionary dynamics at the edge of an expanding circular colony is studied as well. Also reviewed are how the observed patterns of genetic diversity can be used for statistical inference and the differences are highlighted between the well-mixed and one-dimensional models. Although the focus is on two alleles or variants, q-allele Potts-like models of gene segregation are considered as well. Most of the analytical results are checked with simulations and could be tested against recent spatial experiments on range expansions of inoculations of Escherichia coli and Saccharomyces cerevisiae.
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Affiliation(s)
- K S Korolev
- Department of Physics and FAS Center for Systems Biology, Harvard University, Cambridge, Massachusetts 02138, USA
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Abstract
Environmental changes have caused episodes of habitat expansions in the evolutionary history of many species. These range changes affect the dynamics of biological evolution in multiple ways. Recent microbial experiments as well as simulations suggest that enhanced genetic drift at the frontier of a two-dimensional range expansion can cause genetic sectoring patterns with fractal domain boundaries. Here, we propose and analyze a simple model of asexual biological evolution at expanding frontiers that explains these neutral patterns and predicts the effect of natural selection. We find that beneficial mutations give rise to sectors with an opening angle that depends sensitively on the selective advantage of the mutants. Deleterious mutations, on the other hand, are not able to establish a sector permanently. They can, however, temporarily "surf" on the population front, and thereby reach unusually high frequencies. As a consequence, expanding frontiers are loaded with a high fraction of mutants at mutation-selection balance. Numerically, we also determine the condition at which the wild type is lost in favor of deleterious mutants (genetic meltdown) at a growing front. Our prediction for this error threshold differs qualitatively from existing well-mixed theories, and sets tight constraints on sustainable mutation rates for populations that undergo frequent range expansions.
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Affiliation(s)
- Oskar Hallatschek
- Max Planck Research Group for Biological Physics and Evolutionary Dynamics, Max Planck Institute for Dynamics and Self-Organization, 37073 Göttingen, Germany.
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Hallatschek O, Hersen P, Ramanathan S, Nelson DR. Genetic drift at expanding frontiers promotes gene segregation. Proc Natl Acad Sci U S A 2007; 104:19926-30. [PMID: 18056799 PMCID: PMC2148399 DOI: 10.1073/pnas.0710150104] [Citation(s) in RCA: 429] [Impact Index Per Article: 25.2] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/07/2007] [Indexed: 11/18/2022] Open
Abstract
Competition between random genetic drift and natural selection play a central role in evolution: Whereas nonbeneficial mutations often prevail in small populations by chance, mutations that sweep through large populations typically confer a selective advantage. Here, however, we observe chance effects during range expansions that dramatically alter the gene pool even in large microbial populations. Initially well mixed populations of two fluorescently labeled strains of Escherichia coli develop well defined, sector-like regions with fractal boundaries in expanding colonies. The formation of these regions is driven by random fluctuations that originate in a thin band of pioneers at the expanding frontier. A comparison of bacterial and yeast colonies (Saccharomyces cerevisiae) suggests that this large-scale genetic sectoring is a generic phenomenon that may provide a detectable footprint of past range expansions.
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Affiliation(s)
- Oskar Hallatschek
- *Department of Physics and
- FAS Center for Systems Biology, Harvard University, Cambridge, MA 02138
| | - Pascal Hersen
- FAS Center for Systems Biology, Harvard University, Cambridge, MA 02138
- Centre National de la Recherche Scientifique, Laboratoire Matière et Systèmes Complexes, Université Paris VII, 75013 Paris, France; and
| | - Sharad Ramanathan
- FAS Center for Systems Biology, Harvard University, Cambridge, MA 02138
- Bell Laboratories, Alcatel-Lucent, Murray Hill, NJ 07974
| | - David R. Nelson
- *Department of Physics and
- FAS Center for Systems Biology, Harvard University, Cambridge, MA 02138
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Ferrari PA, Martin JB, Pimentel LPR. Roughening and inclination of competition interfaces. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 73:031602. [PMID: 16605532 DOI: 10.1103/physreve.73.031602] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/22/2005] [Revised: 01/10/2006] [Indexed: 05/08/2023]
Abstract
We study the competition interface between two clusters growing over a random vacant sector of the plane in a simple setup which allows us to perform formal computations and obtain analytical solutions. We demonstrate that a phase transition occurs for the asymptotic inclination of this interface when the final macroscopic shape goes from curved to noncurved. In the first case it is random while in the second one it is deterministic. We also show that the flat case (stationary growth) is a critical point for the fluctuations: for curved and flat final profiles the fluctuations are in the Kardar-Parisi-Zhang (KPZ) scale (2/3); for noncurve final profile the fluctuations are in the same scale of the fluctuations of the initial conditions, which in our model are Gaussian (1/2).
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Affiliation(s)
- Pablo A Ferrari
- Instituto de Matemática e Estatística, Universidade de São Paulo, Caixa Postal 66281, 05311-970 São Paulo, Brazil.
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Chuang WT, Hong PD, Chuah HH. Effects of crystallization behavior on morphological change in poly(trimethylene terephthalate) spherulites. POLYMER 2004. [DOI: 10.1016/j.polymer.2004.01.048] [Citation(s) in RCA: 67] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/01/2022]
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Lebovka NI, Vygornitskii NV. How does the geometry affect the criticality in two-component spreading phenomena? ACTA ACUST UNITED AC 1999. [DOI: 10.1088/0305-4470/31/46/010] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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Vandewalle N, Ausloos M. Two-component spreading phenomena: Why the geometry makes the criticality. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1996; 54:3006-3008. [PMID: 9965422 DOI: 10.1103/physreve.54.3006] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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