3,885 research outputs found
Genetic drift at expanding frontiers promotes gene segregation
Competition between random genetic drift and natural selection plays a
central role in evolution: Whereas non-beneficial 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.Comment: Please visit http://www.pnas.org/content/104/50/19926.abstract for
published articl
Life at the front of an expanding population
Recent microbial experiments 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 to explain these
neutral patterns and predict the effect of natural selection. Our model
attributes the observed gradual decrease in the number of sectors at the
leading edge to an unbiased random walk of sector boundaries. Natural selection
introduces a deterministic bias in the wandering of domain boundaries that
renders beneficial mutations more likely to escape genetic drift and become
established in a sector. We find that the opening angle of those sectors and
the rate at which they become established depend 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 unusual high frequencies. As a
consequence, expanding frontiers are susceptible to deleterious mutations as
revealed by the 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.Comment: Updat
Survival Probabilities at Spherical Frontiers
Motivated by tumor growth and spatial population genetics, we study the
interplay between evolutionary and spatial dynamics at the surfaces of
three-dimensional, spherical range expansions. We consider range expansion
radii that grow with an arbitrary power-law in time:
, where is a growth exponent, is the
initial radius, and is a characteristic time for the growth, to be
affected by the inflating geometry. We vary the parameters and
to capture a variety of possible growth regimes. Guided by recent results for
two-dimensional inflating range expansions, we identify key dimensionless
parameters that describe the survival probability of a mutant cell with a small
selective advantage arising at the population frontier. Using analytical
techniques, we calculate this probability for arbitrary . We compare
our results to simulations of linearly inflating expansions (
spherical Fisher-Kolmogorov-Petrovsky-Piscunov waves) and treadmilling
populations (, with cells in the interior removed by apoptosis or a
similar process). We find that mutations at linearly inflating fronts have
survival probabilities enhanced by factors of 100 or more relative to mutations
at treadmilling population frontiers. We also discuss the special properties of
"marginally inflating" expansions.Comment: 35 pages, 11 figures, revised versio
How Obstacles Perturb Population Fronts and Alter Their Genetic Structure
This is the final version of the article. Available from Public Library of Science via the DOI in this record.As populations spread into new territory, environmental heterogeneities can shape the population front and genetic composition. We focus here on the effects of an important building block of heterogeneous environments, isolated obstacles. With a combination of experiments, theory, and simulation, we show how isolated obstacles both create long-lived distortions of the front shape and amplify the effect of genetic drift. A system of bacteriophage T7 spreading on a spatially heterogeneous Escherichia coli lawn serves as an experimental model system to study population expansions. Using an inkjet printer, we create well-defined replicates of the lawn and quantitatively study the population expansion of phage T7. The transient perturbations of the population front found in the experiments are well described by a model in which the front moves with constant speed. Independent of the precise details of the expansion, we show that obstacles create a kink in the front that persists over large distances and is insensitive to the details of the obstacle’s shape. The small deviations between experimental findings and the predictions of the constant speed model can be understood with a more general reaction-diffusion model, which reduces to the constant speed model when the obstacle size is large compared to the front width. Using this framework, we demonstrate that frontier genotypes just grazing the side of an isolated obstacle increase in abundance, a phenomenon we call ‘geometry-enhanced genetic drift’, complementary to the founder effect associated with spatial bottlenecks. Bacterial range expansions around nutrient-poor barriers and stochastic simulations confirm this prediction. The effect of the obstacle on the genealogy of individuals at the front is characterized by simulations and rationalized using the constant speed model. Lastly, we consider the effect of two obstacles on front shape and genetic composition of the population illuminating the effects expected from complex environments with many obstacles.Support for this work was provided by the National Institute of General Medical Sciences Grant P50GM068763 of the National Centers for Systems Biology (www.nih.gov, awarded to AWM), by the National Science Foundation through grant DMR1306367 and through the Harvard Materials Research and Engineering Center through Grant DMR-1420570 (www.nsf.gov/div/index.jsp?div=DMR, awarded to DRN). WM was supported by the Leopoldina Postdoc Scholarship LPDS 2009-51 (www.leopoldina.org) and by grants from the National Philanthropic Trust Grant RFP-12-15 (www.templeton.org, awarded to AWM), and from the Human Frontiers Science Program Grant RGP0041/2014 (www.hfsp.org, awarded to AWM). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript
Range expansion with mutation and selection: dynamical phase transition in a two-species Eden model
The colonization of unoccupied territory by invading species, known as range expansion, is a spatially heterogeneous non-equilibrium growth process. We introduce a two-species Eden growth model to analyze the interplay between uni-directional (irreversible) mutations and selection at the expanding front. While the evolutionary dynamics leads to coalescence of both wild-type and mutant clusters, the non-homogeneous advance of the colony results in a rough front. We show that roughening and domain dynamics are strongly coupled, resulting in qualitatively altered bulk and front properties. For beneficial mutations the front is quickly taken over by mutants and growth proceeds Eden-like. In contrast, if mutants grow slower than wild-types, there is an antagonism between selection pressure against mutants and growth by the merging of mutant domains with an ensuing absorbing state phase transition to an all-mutant front. We find that surface roughening has a marked effect on the critical properties of the absorbing state phase transition. While reference models, which keep the expanding front flat, exhibit directed percolation critical behavior, the exponents of the two-species Eden model strongly deviate from it. In turn, the mutation-selection process induces an increased surface roughness with exponents distinct from that of the classical Eden model
Emergence of Spatial Structure in Cell Groups and the Evolution of Cooperation
On its own, a single cell cannot exert more than a microscopic influence on its immediate surroundings. However, via strength in numbers and the expression of cooperative phenotypes, such cells can enormously impact their environments. Simple cooperative phenotypes appear to abound in the microbial world, but explaining their evolution is challenging because they are often subject to exploitation by rapidly growing, non-cooperative cell lines. Population spatial structure may be critical for this problem because it influences the extent of interaction between cooperative and non-cooperative individuals. It is difficult for cooperative cells to succeed in competition if they become mixed with non-cooperative cells, which can exploit the public good without themselves paying a cost. However, if cooperative cells are segregated in space and preferentially interact with each other, they may prevail. Here we use a multi-agent computational model to study the origin of spatial structure within growing cell groups. Our simulations reveal that the spatial distribution of genetic lineages within these groups is linked to a small number of physical and biological parameters, including cell growth rate, nutrient availability, and nutrient diffusivity. Realistic changes in these parameters qualitatively alter the emergent structure of cell groups, and thereby determine whether cells with cooperative phenotypes can locally and globally outcompete exploitative cells. We argue that cooperative and exploitative cell lineages will spontaneously segregate in space under a wide range of conditions and, therefore, that cellular cooperation may evolve more readily than naively expected
Fluctuation Induced Instabilities in Front Propagation up a Co-Moving Reaction Gradient in Two Dimensions
We study 2D fronts propagating up a co-moving reaction rate gradient in
finite number reaction-diffusion systems. We show that in a 2D rectangular
channel, planar solutions to the deterministic mean-field equation are stable
with respect to deviations from planarity. We argue that planar fronts in the
corresponding stochastic system, on the other hand, are unstable if the channel
width exceeds a critical value. Furthermore, the velocity of the stochastic
fronts is shown to depend on the channel width in a simple and interesting way,
in contrast to fronts in the deterministic MFE. Thus, fluctuations alter the
behavior of these fronts in an essential way. These affects are shown to be
partially captured by introducing a density cutoff in the reaction rate. Some
of the predictions of the cutoff mean-field approach are shown to be in
quantitative accord with the stochastic results
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