Collective motion conceals fitness differences in crowded cellular populations

Synonymous rpsH variants: the common denominator in Escherichia coli adapting to ionizing radiation

Ionizing radiation (IR) in high doses is generally lethal to most organisms. Investigating mechanisms of radiation resistance is crucial for gaining insights into the underlying cellular responses and understanding the damaging effects of IR. In this study, we conducted a comprehensive analysis of sequencing data from an evolutionary experiment aimed at understanding the genetic adaptations to ionizing radiation in Escherichia coli. By including previously neglected synonymous mutations, we identified the rpsH c.294T > G variant, which emerged in all 17 examined isolates across four subpopulations. The identified variant is a synonymous mutation affecting the 30S ribosomal protein S8, and consistently exhibited high detection and low allele frequencies in all subpopulations. This variant, along with two additional rpsH variants, potentially influences translational control of the ribosomal spc operon. The early emergence and stability of these variants suggest their role in adapting to environmental stress, possibly contributing to radiation resistance. Our findings shed light on the dynamics of ribosomal variants during the evolutionary process and their potential role in stress adaptation, providing valuable implications for understanding clinical radiation sensitivity and improving radiotherapy.

Interplay between morphology and competition in two-dimensional colony expansion

In growing populations, the fate of mutations depends on their competitive ability against the ancestor and their ability to colonize new territory. Here we present a theory that integrates both aspects of mutant fitness by coupling the classic description of one-dimensional competition (Fisher equation) to the minimal model of front shape (Kardar-Parisi-Zhang equation). We solve these equations and find three regimes, which are controlled solely by the expansion rates, solely by the competitive abilities, or by both. Collectively, our results provide a simple framework to study spatial competition.

Evaporation-induced hydrodynamics control plasmid transfer during surface-associated microbial growth

Droplet evaporation is a general process in unsaturated environments that results in micro-scale hydrodynamic flows which in turn determine the spatial distributions of microbial cells across surfaces. These spatial distributions can have significant effects on the development and functioning of surface-associated microbial communities, with consequences for important processes such as the spread of plasmids. Here, we experimentally quantified how evaporation-induced hydrodynamic processes modulate the initial deposition patterns of microbial cells (via the coffee ring effect and Marangoni convection) and how these patterns control the spread of an antibiotic resistance-encoding plasmid during surface-associated growth. We found that plasmid spread is a function of the initial density of cells deposited along the droplet periphery, which is a manifestation of the coffee ring effect. Using an individual-based model, we systematically linked how the different initial cell deposition patterns caused by the relative strengths of the coffee ring effect and Marangoni convection determine the extent of plasmid transfer during surface-associated growth. Our study demonstrates that evaporation-induced hydrodynamic processes that are common in nature can alter crucial ecological properties of surface-associated microbial communities and control the proliferation of plasmids, with consequences on the spread of antibiotic resistance and other plasmid-encoded traits.

Antibiotic resistance in bacterial communities

Bacteria are single-celled organisms, but the survival of microbial communities relies on complex dynamics at the molecular, cellular, and ecosystem scales. Antibiotic resistance, in particular, is not just a property of individual bacteria or even single-strain populations, but depends heavily on the community context. Collective community dynamics can lead to counterintuitive eco-evolutionary effects like survival of less resistant bacterial populations, slowing of resistance evolution, or population collapse, yet these surprising behaviors are often captured by simple mathematical models. In this review, we highlight recent progress - in many cases, advances driven by elegant combinations of quantitative experiments and theoretical models - in understanding how interactions between bacteria and with the environment affect antibiotic resistance, from single-species populations to multispecies communities embedded in an ecosystem.

Proliferating active matter

The fascinating patterns of collective motion created by autonomously driven particles have fuelled active-matter research for over two decades. So far, theoretical active-matter research has often focused on systems with a fixed number of particles. This constraint imposes strict limitations on what behaviours can and cannot emerge. However, a hallmark of life is the breaking of local cell number conservation by replication and death. Birth and death processes must be taken into account, for example, to predict the growth and evolution of a microbial biofilm, the expansion of a tumour, or the development from a fertilized egg into an embryo and beyond. In this Perspective, we argue that unique features emerge in these systems because proliferation represents a distinct form of activity: not only do the proliferating entities consume and dissipate energy, they also inject biomass and degrees of freedom capable of further self-proliferation, leading to myriad dynamic scenarios. Despite this complexity, a growing number of studies document common collective phenomena in various proliferating soft-matter systems. This generality leads us to propose proliferation as another direction of active-matter physics, worthy of a dedicated search for new dynamical universality classes. Conceptual challenges abound, from identifying control parameters and understanding large fluctuations and nonlinear feedback mechanisms to exploring the dynamics and limits of information flow in self-replicating systems. We believe that, by extending the rich conceptual framework developed for conventional active matter to proliferating active matter, researchers can have a profound impact on quantitative biology and reveal fascinating emergent physics along the way.

State-dependent evolutionary models reveal modes of solid tumour growth

Spatial properties of tumour growth have profound implications for cancer progression, therapeutic resistance and metastasis. Yet, how spatial position governs tumour cell division remains difficult to evaluate in clinical tumours. Here, we demonstrate that faster division on the tumour periphery leaves characteristic genetic patterns, which become evident when a phylogenetic tree is reconstructed from spatially sampled cells. Namely, rapidly dividing peripheral lineages branch more extensively and acquire more mutations than slower-dividing centre lineages. We develop a Bayesian state-dependent evolutionary phylodynamic model (SDevo) that quantifies these patterns to infer the differential division rates between peripheral and central cells. We demonstrate that this approach accurately infers spatially varying birth rates of simulated tumours across a range of growth conditions and sampling strategies. We then show that SDevo outperforms state-of-the-art, non-cancer multi-state phylodynamic methods that ignore differential sequence evolution. Finally, we apply SDevo to single-time-point, multi-region sequencing data from clinical hepatocellular carcinomas and find evidence of a three- to six-times-higher division rate on the tumour edge. With the increasing availability of high-resolution, multi-region sequencing, we anticipate that SDevo will be useful in interrogating spatial growth restrictions and could be extended to model non-spatial factors that influence tumour progression.

Evolutionary rescue of resistant mutants is governed by a balance between radial expansion and selection in compact populations

Mutation-mediated treatment resistance is one of the primary challenges for modern antibiotic and anti-cancer therapy. Yet, many resistance mutations have a substantial fitness cost and are subject to purifying selection. How emerging resistant lineages may escape purifying selection via subsequent compensatory mutations is still unclear due to the difficulty of tracking such evolutionary rescue dynamics in space and time. Here, we introduce a system of fluorescence-coupled synthetic mutations to show that the probability of evolutionary rescue, and the resulting long-term persistence of drug resistant mutant lineages, is dramatically increased in dense microbial populations. By tracking the entire evolutionary trajectory of thousands of resistant lineages in expanding yeast colonies we uncover an underlying quasi-stable equilibrium between the opposing forces of radial expansion and natural selection, a phenomenon we term inflation-selection balance. Tailored computational models and agent-based simulations corroborate the fundamental nature of the observed effects and demonstrate the potential impact on drug resistance evolution in cancer. The described phenomena should be considered when predicting multi-step evolutionary dynamics in any mechanically compact cellular population, including pathogenic microbial biofilms and solid tumors. The insights gained will be especially valuable for the quantitative understanding of response to treatment, including emerging evolution-based therapy strategies.

Morphological instability and roughening of growing 3D bacterial colonies

The morphogenesis of two-dimensional bacterial colonies has been well studied. However, little is known about the colony morphologies of bacteria growing in three dimensions, despite the prevalence of three-dimensional environments (e.g., soil, inside hosts) as natural bacterial habitats. Using experiments on bacteria in granular hydrogel matrices, we find that dense multicellular colonies growing in three dimensions undergo a common morphological instability and roughen, adopting a characteristic broccoli-like morphology when they exceed a critical size. Analysis of a continuum “active fluid” model of the expanding colony reveals that this behavior originates from an interplay of competition for nutrients with growth-driven colony expansion, both of which vary spatially. These results shed light on the fundamental biophysical principles underlying growth in three dimensions.

How do growing bacterial colonies get their shapes? While colony morphogenesis is well studied in two dimensions, many bacteria grow as large colonies in three-dimensional (3D) environments, such as gels and tissues in the body or subsurface soils and sediments. Here, we describe the morphodynamics of large colonies of bacteria growing in three dimensions. Using experiments in transparent 3D granular hydrogel matrices, we show that dense colonies of four different species of bacteria generically become morphologically unstable and roughen as they consume nutrients and grow beyond a critical size—eventually adopting a characteristic branched, broccoli-like morphology independent of variations in the cell type and environmental conditions. This behavior reflects a key difference between two-dimensional (2D) and 3D colonies; while a 2D colony may access the nutrients needed for growth from the third dimension, a 3D colony inevitably becomes nutrient limited in its interior, driving a transition to unstable growth at its surface. We elucidate the onset of the instability using linear stability analysis and numerical simulations of a continuum model that treats the colony as an “active fluid” whose dynamics are driven by nutrient-dependent cellular growth. We find that when all dimensions of the colony substantially exceed the nutrient penetration length, nutrient-limited growth drives a 3D morphological instability that recapitulates essential features of the experimental observations. Our work thus provides a framework to predict and control the organization of growing colonies—as well as other forms of growing active matter, such as tumors and engineered living materials—in 3D environments.

Self-consistent dispersal puts tight constraints on the spatiotemporal organization of species-rich metacommunities

Biodiversity is often attributed to a dynamic equilibrium between the immigration and extinction of species. This equilibrium forms a common basis for studying ecosystem assembly from a static reservoir of migrants-the mainland. Yet, natural ecosystems often consist of many coupled communities (i.e., metacommunities), and migration occurs between these communities. The pool of migrants then depends on what is sustained in the ecosystem, which, in turn, depends on the dynamic migrant pool. This chicken-and-egg problem of survival and dispersal is poorly understood in communities of many competing species, except for the neutral case-the "unified neutral theory of biodiversity." Employing spatiotemporal simulations and mean-field analyses, we show that self-consistent dispersal puts rather tight constraints on the dynamic migration-extinction equilibrium. When the number of species is large, species are pushed to the edge of their global extinction, even when competition is weak. As a consequence, the overall diversity is highly sensitive to perturbations in demographic parameters, including growth and dispersal rates. When dispersal is short range, the resulting spatiotemporal abundance patterns follow broad scale-free distributions that correspond to a directed percolation phase transition. The qualitative agreement of our results for short-range and long-range dispersal suggests that this self-organization process is a general property of species-rich metacommunities. Our study shows that self-sustaining metacommunities are highly sensitive to environmental change and provides insights into how biodiversity can be rescued and maintained.

Rare and localized events stabilize microbial community composition and patterns of spatial self-organization in a fluctuating environment

Spatial self-organization is a hallmark of surface-associated microbial communities that is governed by local environmental conditions and further modified by interspecific interactions. Here, we hypothesize that spatial patterns of microbial cell-types can stabilize the composition of cross-feeding microbial communities under fluctuating environmental conditions. We tested this hypothesis by studying the growth and spatial self-organization of microbial co-cultures consisting of two metabolically interacting strains of the bacterium Pseudomonas stutzeri. We inoculated the co-cultures onto agar surfaces and allowed them to expand (i.e. range expansion) while fluctuating environmental conditions that alter the dependency between the two strains. We alternated between anoxic conditions that induce a mutualistic interaction and oxic conditions that induce a competitive interaction. We observed co-occurrence of both strains in rare and highly localized clusters (referred to as “spatial jackpot events”) that persist during environmental fluctuations. To resolve the underlying mechanisms for the emergence of spatial jackpot events, we used a mechanistic agent-based mathematical model that resolves growth and dispersal at the scale relevant to individual cells. While co-culture composition varied with the strength of the mutualistic interaction and across environmental fluctuations, the model provides insights into the formation of spatially resolved substrate landscapes with localized niches that support the co-occurrence of the two strains and secure co-culture function. This study highlights that in addition to spatial patterns that emerge in response to environmental fluctuations, localized spatial jackpot events ensure persistence of strains across dynamic conditions.

Spatial structure impacts adaptive therapy by shaping intra-tumoral competition

Background

Adaptive therapy aims to tackle cancer drug resistance by leveraging resource competition between drug-sensitive and resistant cells. Here, we present a theoretical study of intra-tumoral competition during adaptive therapy, to investigate under which circumstances it will be superior to aggressive treatment.

Methods

We develop and analyse a simple, 2-D, on-lattice, agent-based tumour model in which cells are classified as fully drug-sensitive or resistant. Subsequently, we compare this model to its corresponding non-spatial ordinary differential equation model, and fit it to longitudinal prostate-specific antigen data from 65 prostate cancer patients undergoing intermittent androgen deprivation therapy following biochemical recurrence.

Results

Leveraging the individual-based nature of our model, we explicitly demonstrate competitive suppression of resistance during adaptive therapy, and examine how different factors, such as the initial resistance fraction or resistance costs, alter competition. This not only corroborates our theoretical understanding of adaptive therapy, but also reveals that competition of resistant cells with each other may play a more important role in adaptive therapy in solid tumours than was previously thought. To conclude, we present two case studies, which demonstrate the implications of our work for: (i) mathematical modelling of adaptive therapy, and (ii) the intra-tumoral dynamics in prostate cancer patients during intermittent androgen deprivation treatment, a precursor of adaptive therapy.

Conclusion

Our work shows that the tumour’s spatial architecture is an important factor in adaptive therapy and provides insights into how adaptive therapy leverages both inter- and intra-specific competition to control resistance.

Cancer therapy traditionally focuses on maximising tumour cell kill with the aim of achieving a cure, but such aggressive treatment can open up space for drug-resistant cells to grow. In contrast, adaptive therapy aims to leverage competition between drug-sensitive and resistant cells by adjusting treatment to maintain the tumour at a tolerable size, whilst preserving drug-sensitive cells. This approach is being tested in trials but is not yet widely used as deeper understanding of cell-cell competition is required. Here, we used a mathematical model to investigate how strongly, and with whom, resistant cells compete during continuous and adaptive therapy, and applied our insights to hormone therapy in prostate cancer where adaptive therapy has recently been successfully trialed. Our results provide new insights into how adaptive therapy works and show that, by shaping cell competition, the tumour’s spatial architecture is important in determining therapy response.

Strobl et al. develop an agent-based spatial model of drug resistance in tumour cells under adaptive therapy. Using this model, they investigate how the tumour’s spatial architecture impacts intratumoural competitive dynamics of drug-sensitive vs. -resistant clones in response to therapy.

Population genetics in microchannels

Many microbial populations proliferate in small channels. In such environments, reproducing cells organize in parallel lanes. Reproducing cells shift these lanes, potentially expelling other cells from the channel. In this paper, we combine theory and experiments to understand how these dynamics affects the diversity of a microbial population. We theoretically predict that genetic diversity is quickly lost along lanes of cells. Our experiments confirm that a population of proliferating Escherichia coli in a microchannel organizes into lanes of genetically identical cells within a few generations. Our findings elucidate the effect of lane formation on populations evolution, with potential applications ranging from microbial ecology in soil to dynamics of epithelial tissues in higher organisms.

Spatial constraints, such as rigid barriers, affect the dynamics of cell populations, potentially altering the course of natural evolution. In this paper, we investigate the population genetics of Escherichia coli proliferating in microchannels with open ends. Our analysis is based on a population model, in which reproducing cells shift entire lanes of cells toward the open ends of the channel. The model predicts that diversity is lost very rapidly within lanes but at a much slower pace among lanes. As a consequence, two mixed, neutral E. coli strains competing in a microchannel must organize into an ordered regular stripe pattern in the course of a few generations. These predictions are in quantitative agreement with our experiments. We also demonstrate that random mutations appearing in the middle of the channel are much more likely to reach fixation than those occurring elsewhere. Our results illustrate fundamental mechanisms of microbial evolution in spatially confined space.

Antagonism between killer yeast strains as an experimental model for biological nucleation dynamics

Antagonistic interactions are widespread in the microbial world and affect microbial evolutionary dynamics. Natural microbial communities often display spatial structure, which affects biological interactions, but much of what we know about microbial antagonism comes from laboratory studies of well-mixed communities. To overcome this limitation, we manipulated two killer strains of the budding yeast Saccharomyces cerevisiae, expressing different toxins, to independently control the rate at which they released their toxins. We developed mathematical models that predict the experimental dynamics of competition between toxin-producing strains in both well-mixed and spatially structured populations. In both situations, we experimentally verified theory's prediction that a stronger antagonist can invade a weaker one only if the initial invading population exceeds a critical frequency or size. Finally, we found that toxin-resistant cells and weaker killers arose in spatially structured competitions between toxin-producing strains, suggesting that adaptive evolution can affect the outcome of microbial antagonism in spatial settings.

Spatial segregation and cooperation in radially expanding microbial colonies under antibiotic stress

Antibiotic resistance in microbial communities reflects a combination of processes operating at different scales. In this work, we investigate the spatiotemporal dynamics of bacterial colonies comprised of drug-resistant and drug-sensitive cells undergoing range expansion under antibiotic stress. Using the opportunistic pathogen Enterococcus faecalis with plasmid-encoded β-lactamase, we track colony expansion dynamics and visualize spatial patterns in fluorescently labeled populations exposed to antibiotics. We find that the radial expansion rate of mixed communities is approximately constant over a wide range of drug concentrations and initial population compositions. Imaging of the final populations shows that resistance to ampicillin is cooperative, with sensitive cells surviving in the presence of resistant cells at otherwise lethal concentrations. The populations exhibit a diverse range of spatial segregation patterns that depend on drug concentration and initial conditions. Mathematical models indicate that the observed dynamics are consistent with global cooperation, despite the fact that β-lactamase remains cell-associated. Experiments confirm that resistant colonies provide a protective effect to sensitive cells on length scales multiple times the size of a single colony, and populations seeded with (on average) no more than a single resistant cell can produce mixed communities in the presence of the drug. While biophysical models of drug degradation suggest that individual resistant cells offer only short-range protection to neighboring cells, we show that long-range protection may arise from synergistic effects of multiple resistant cells, providing surprisingly large protection zones even at small population fractions.

Theoretical modelling of competitive microbial range expansion with heterogeneous mechanical interactions

Microbial range expansion experiments provide insight into the complex link between dynamic structure, pattern formation and evolutionary dynamics of growing populations. In this work, we develop a theoretical model in order to investigate the interplay of growth statistics and mechanical interactions which are implemented as division driven pushing and swapping of cells. For the case of the competitive growth of a strongly and a weakly interacting strain we investigate the influence of different mean division times, as well as different mechanical interactions on the development of the colony. Our results show that the susceptibility to cell division induced pushing has a much stronger influence on the structure of the colony than cell sorting towards the colony's perimeter. Motivated by microbial range expansion experiments of Neisseria gonorrhoeae bacteria, we also consider the influence of mutating cells on the structure of the colony. We show that the outgrowth of the three different strains is strongly influenced by the relative strengths of their mechanical interaction. The experimentally observed patterns are reproduced for mechanical interactions of the mutants, which range between those of the strongly and weakly interacting strain.

Spatial organization in microbial range expansion emerges from trophic dependencies and successful lineages

Evidence suggests that bacterial community spatial organization affects their ecological function, yet details of the mechanisms that promote spatial patterns remain difficult to resolve experimentally. In contrast to bacterial communities in liquid cultures, surface-attached range expansion fosters genetic segregation of the growing population with preferential access to nutrients and reduced mechanical restrictions for cells at the expanding periphery. Here we elucidate how localized conditions in cross-feeding bacterial communities shape community spatial organization. We combine experiments with an individual based mathematical model to resolve how trophic dependencies affect localized growth rates and nucleate successful cell lineages. The model tracks individual cell lineages and attributes these with trophic dependencies that promote counterintuitive reproductive advantages and result in lasting influences on the community structure, and potentially, on its functioning. We examine persistence of lucky lineages in structured habitats where expansion is interrupted by physical obstacles to gain insights into patterns in porous domains.

Mutant Evolution in Spatially Structured and Fragmented Expanding Populations

Mutant evolution in spatially structured systems is important for a range of biological systems, but aspects of it still require further elucidation. Adding to previous work, we provide a simple derivation of growth laws that characterize the number of mutants of different relative fitness in expanding populations in spatial models of different dimensionalities. These laws are universal and independent of "microscopic" modeling details. We further study the accumulation of mutants and find that, with advantageous and neutral mutants, more of them are present in spatially structured, compared to well-mixed colonies of the same size. The behavior of disadvantageous mutants is subtle: if they are disadvantageous through a reduction in division rates, the result is the same, and it is the opposite if the disadvantage is due to a death rate increase. Finally, we show that in all cases, the same results are observed in fragmented, nonspatial patch models. This suggests that the patterns observed are the consequence of population fragmentation, and not spatial restrictions per se We provide an intuitive explanation for the complex dependence of disadvantageous mutant evolution on spatial restriction, which relies on desynchronized dynamics in different locations/patches, and plays out differently depending on whether the disadvantage is due to a lower division rate or a higher death rate. Implications for specific biological systems, such as the evolution of drug-resistant cell mutants in cancer or bacterial biofilms, are discussed.

Radial Expansion Facilitates the Maintenance of Double Antibiotic Resistances

Most microbes live in spatially confined subpopulations. Under spatial structure conditions, the efficacy of natural selection is often reduced (relative to homogeneous conditions) due to the increased importance of genetic drift and local competition. Additionally, under spatial structure conditions, the fittest genotype may not always be the one with better access to the heterogeneous distribution of nutrients. The effect of radial expansion may be particularly relevant for the elimination of antibiotic resistance mutations, as their dynamics within bacterial populations are strongly dependent on their growth rate. Here, we use Escherichia coli to systematically compare the allele frequency of streptomycin, rifampin, and fluoroquinolone single and double resistance mutants after 24 h of coexistence with a susceptible strain under radial expansion (local competition) and homogeneous (global competition) conditions. We show that there is a significant effect of structure on the maintenance of double resistances which is not observed for single resistances. Radial expansion also facilitates the persistence of double resistances when competing against their single counterparts. Importantly, we found that spatial structure reduces the rate of compensation of the double mutant RpsL^K43T RpoB^H526Y and that a strongly compensatory mutation in homogeneous conditions becomes deleterious under spatial structure conditions. Overall, our results unravel the importance of spatial structure for facilitating the maintenance and accumulation of multiple resistances over time and for determining the identity of compensatory mutations.

Drivers of Spatial Structure in Social Microbial Communities

Microbes are social organisms, interacting primarily through secreted biomolecules. Many traits have evolved based solely on their effects upon other community members, yet even individually beneficial traits often create social side effects that are mediated by spatial population structure. Predicting the evolution of many microbial traits thus requires a comprehensive understanding of their social consequences. In this review, we examine the critical role of population spatial structure in microbial social evolution. We briefly review key mechanisms structuring microbial communities, focusing primarily on the universal roles of cellular death and reproduction. Finally, we explain how spatial assortment can be efficiently calculated in two-dimensional, surface-attached populations.

Cooperation in Microbial Populations: Theory and Experimental Model Systems

Cooperative behavior, the costly provision of benefits to others, is common across all domains of life. This review article discusses cooperative behavior in the microbial world, mediated by the exchange of extracellular products called public goods. We focus on model species for which the production of a public good and the related growth disadvantage for the producing cells are well described. To unveil the biological and ecological factors promoting the emergence and stability of cooperative traits we take an interdisciplinary perspective and review insights gained from both mathematical models and well-controlled experimental model systems. Ecologically, we include crucial aspects of the microbial life cycle into our analysis and particularly consider population structures where ensembles of local communities (subpopulations) continuously emerge, grow, and disappear again. Biologically, we explicitly consider the synthesis and regulation of public good production. The discussion of the theoretical approaches includes general evolutionary concepts, population dynamics, and evolutionary game theory. As a specific but generic biological example, we consider populations of Pseudomonas putida and its regulation and use of pyoverdines, iron scavenging molecules, as public goods. The review closes with an overview on cooperation in spatially extended systems and also provides a critical assessment of the insights gained from the experimental and theoretical studies discussed. Current challenges and important new research opportunities are discussed, including the biochemical regulation of public goods, more realistic ecological scenarios resembling native environments, cell-to-cell signaling, and multispecies communities.

Nucleation of antagonistic organisms and cellular competitions on curved, inflating substrates

We consider the dynamics of spatially distributed, diffusing populations of organisms with antagonistic interactions. These interactions are found on many length scales, ranging from kilometer-scale animal range dynamics with selection against hybrids to micron-scale interactions between poison-secreting microbial populations. We find that the dynamical line tension at the interface between antagonistic organisms suppresses survival probabilities of small clonal clusters: the line tension introduces a critical cluster size that an organism with a selective advantage must achieve before deterministically spreading through the population. We calculate the survival probability as a function of selective advantage δ and antagonistic interaction strength σ. Unlike a simple Darwinian selective advantage, the survival probability depends strongly on the spatial diffusion constant D_{s} of the strains when σ>0, with suppressed survival when both species are more motile. Finally, we study the survival probability of a single mutant cell at the frontier of a growing spherical cluster of cells, such as the surface of an avascular spherical tumor. Both the inflation and curvature of the frontier significantly enhance the survival probability by changing the critical size of the nucleating cell cluster.

Environmental heterogeneity can tip the population genetics of range expansions

The population genetics of most range expansions is thought to be shaped by the competition between Darwinian selection and random genetic drift at the range margins. Here, we show that the evolutionary dynamics during range expansions is highly sensitive to additional fluctuations induced by environmental heterogeneities. Tracking mutant clones with a tunable fitness effect in bacterial colonies grown on randomly patterned surfaces we found that environmental heterogeneity can dramatically reduce the efficacy of selection. Time-lapse microscopy and computer simulations suggest that this effect arises generically from a local 'pinning' of the expansion front, whereby stretches of the front are slowed down on a length scale that depends on the structure of the environmental heterogeneity. This pinning focuses the range expansion into a small number of 'lucky' individuals with access to expansion paths, altering the neutral evolutionary dynamics and increasing the importance of chance relative to selection.

Effective models and the search for quantitative principles in microbial evolution

Microbes evolve rapidly. Yet they do so in idiosyncratic ways, which depend on the specific mutations that are beneficial or deleterious in a given situation. At the same time, some population-level patterns of adaptation are strikingly similar across different microbial systems, suggesting that there may also be simple, quantitative principles that unite these diverse scenarios. We review the search for simple principles in microbial evolution, ranging from the biophysical level to emergent evolutionary dynamics. A key theme has been the use of effective models, which coarse-grain over molecular and cellular details to obtain a simpler description in terms of a few effective parameters. Collectively, these theoretical approaches provide a set of quantitative principles that facilitate understanding, prediction, and potentially control of evolutionary phenomena, though formidable challenges remain due to the ecological complexity of natural populations.