Abstract
Evolutionary dynamics is fundamentally shaped by stochastic processes: spon-taneous mutations enter populations randomly, and the fate of a mutant lineage is determined by the competition between (random) genetic drift and (determin-istic) selection. In populations undergoing range expansions, fluctuations in the reproductive process and the local motion of individuals are enhanced within a small subpopulation at the edge of the population. Range expansions are typically studied in homogeneous environments, but we argue here that the fluctuations at the range edge are susceptible to small-scale environmental heterogeneities that may have a strong effect on the evolutionary dynamics of the expanding population.
To show this, we tracked the dynamics of the clones of spontaneous mutations with a tunable fitness effect in bacterial colonies grown on randomly disordered surfaces. We find that environmental heterogeneity on scales much larger than an individual, but much smaller than the total population, can dramatically reduce the efficacy of selection. Time lapse microscopy and computer simulations suggest that this effect is a general consequence of 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 individuals with access to expansion paths, increasing the importance of chance and thus limiting the efficacy of selection.
Introduction
Noise, and its competition with deterministic forces, plays an integral role in biology, such as in stochastic gene expression, cellular decision making, and cell differentiation [2]. Stochasticity is also a crucial component of evolutionary dynamics: not only do the mutations entering a population occur at random times in random individuals and at random positions in their genome, but in addition the fate of a mutation and its clonal lineage is largely stochastic and only partly determined by its effect on the individual’s fitness.
The random fluctuations in the frequency of a mutant allele due to the stochasticity associated with reproduction are called genetic drift. Genetic drift is particularly strong at the front of range expansions because only a relatively small number of individuals at the front of the expansion contributes to future growth and thus has any influence on the future genotypic composition of the population. The neutral diversity and adaptation in spatially expanding populations has been studied in computer simulations [11,33], in the field [38,44,50], and in microbial colonies [16,21,24,35], where nutrient gradients and mechanical effects limit the number of proliferating individuals to a small region close to the colony perimeter called the growth layer [21,22]. For mutations occurring inside the growth layer, most mutant offspring are concentrated in a relatively small number of enormously successful lineages that manage to remain at the front and “surf” on the expanding population wave [12]. As a consequence, clones of spontaneous neutral mutations often reach much larger sizes [16], and existing beneficial variants can sweep to high frequency much faster in microbial colonies than in well-mixed populations [21]. Conversely, deleterious mutations are predicted to remain at the population frontier for extended periods because genetic drift is strong at the front [8,19,36,43,47]. The quantitative outcome of the competition of selection and genetic drift in microbial colonies is determined by the local shape and roughness of the front [14,21], which in turn is determined by microscopic details, such as cell-cell adhesion or cell shape affecting the mechanical interactions between cells [18,30,31], although the direct mapping is typically unknown [14].
The evolutionary effects of fluctuations at expanding microbial population fronts have been studied in depth, but these studies have focused only on fluctuations associated with the growth, division, and random motion of cells, whose strength may depend on intrinsic properties of the microbial species, in homogeneous environments. However, any realistic microbial range expansion will experience varying degrees of environmental heterogeneity in the form of, e.g., nutrient or temperature gradients, or imperfections in the surface the population grows on. However, the effects of such environmental heterogeneity, which can be viewed as a source of extrinsic noise, on evolutionary dynamics in microbial populations have received much less attention. Efforts have concentrated mostly on simple temporal and spatial gradients in antibiotic concentration, which have been shown to facilitate the emergence of resistance in shaken cultures [37], microfluidic devices [51] and on agar plates [4], as predicted by theory [20,23,25–27].
The effects of spatial heterogeneity on evolutionary dynamics in expanding microbial populations has been studied in experiments only with neutral alleles in fixed geometries, such as isolated obstacles creating “geometry-enhanced” genetic drift [5,39]. These studies have shown that obstacles obstructing locally the advance of the front can doom lineages that happen to lie on the blocked part of the expanding population, whereas unobstructed lineages close to the edge of the obstacles obtain a boost as they fill the vacant area behind the obstacle. Even for neutral alleles, however, not much is known about the evolutionary dynamics in more complex heterogeneous environments. Moreover, selection during range expansions can dramatically alter the population structure over just a few generations [21], but how the action of selection is affected by environmental heterogeneity has so far remained completely unexplored.
Here, we study the impact of complex environmental disorder on the growth and evolutionary dynamics of microbial colonies. To this end, we introduce plasmid loss in E. coli as a model system for spontaneous mutations with tunable growth rate effects whose clones can be tracked under the microscope. By growing colonies on solid substrates with a weakly patterned surface with random microscopic features much bigger than individual cells, but much smaller than the whole colony, we find that environmental heterogeneity can overpower selection such that even strongly beneficial mutations are unable to establish at rates higher than expected for neutral mutations. Using a minimal computer model of populations expanding in randomly disordered environments, we show that dramatic changes in the efficacy of selection can arise from small changes in the degree of environmental heterogeneity. The limited efficacy of selection is a general consequence of 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 individuals with access to expansion paths, increasing the importance of chance and thus limiting the efficacy of selection. Our results may thus generalize to other spatially growing populations, such as biofilms, tumors, and invasive species, where the growing population front may be transiently hindered by the local environment.
Results
Experiments
We grew colonies from single cells of a strain of E. coli MG1655 on two different substrates: standard, “smooth”, agar plates as well as randomly patterned substrates (see Methods). The strain carries a plasmid that is costly to produce, resulting in a 20% growth rate disadvantage in plasmid-bearing cells compared to their plasmid-less (but otherwise isogenic) conspecifics. This strain loses the plasmid stochastically at a rate of about 5 × 10-3 per cell division (approximately independent of antibiotic concentration, see SI). The plasmid codes for a fluorescence gene and confers resistance to the antibiotic doxycycline (a tetracycline analog) such that by varying the amount of doxycycline in the growth media, the relative growth rates of the plasmid-bearing (“wild type”) and non-bearing (“mutant”) cells can be finely tuned from +20% to –15% (see SI Fig. S1). This allowed us to treat plasmid loss effectively as a spontaneous beneficial, neutral or deleterious mutation whose dynamics can be observed under the microscope. Our approach thus extends previous experimental model systems for evolutionary dynamics during microbial range expansion that employed either an initial mixture of wild-type and mutant cells [21,24,30,34] or were confined to spontaneous neutral [16] or deleterious [36] mutations. The ability to track spontaneous mutations in colonies grown from single cells is essential to ensure identical starting conditions in our experiments, allowing a quantitative comparison of the evolutionary outcomes between the two growth conditions. The primary readout of our experiments is the frequency fMT (a proxy for the rate of adaptation of the population) and surviving number of mutant clones.
Homogeneous environment
Advantageous mutants increased in frequency fMT rapidly as the colony grew: for s = 0.2, mutants made up roughly half of the total population (Fig. 2b) after 72 hours. Grown at higher antibiotic concentration, mutants became first neutral and eventually deleterious (for [DOX] > 0.3µg/ml). In such conditions, the mutant frequency decreased approximately exponentially with the fitness cost (SI Fig. S4) such that mutants made up only a small fraction of the final population.
The evolutionary success probability of individual mutations, measured by the establishment probability u to form a sector, also depended strongly the selective advantage (Fig. 2b), but was very low throughout. Even for the most advantageous mutants, we estimate u ∼ 10-7 per mutation (see SI Fig. S3), making sector formation an extremely rare event. The low success probability is a consequence of two processes: firstly, the mutation must occur in a favorable location, namely in the first layer of cells at the front of the population [21], which reduces the number of mutations eligible for sector formation by a factor of about 1000 (see SI). We estimate that about 2000 mutations per colony arose in favorable positions, each of which had an establishment probability of about 10-3. Secondly, each eligible mutation has to survive genetic drift, which in microbial colonies is manifest in the random fluctuations in the sector boundaries as a consequence of stochastic cell growth and division, and subsequent cell motion due to mechanical pushing of cells on each other [14,24,30].
Thus, most mutations will not manage to create sectors, but instead form ‘bubbles’, individual mutant clones that have lost contact with the front, the size of which we can extract from colony micrographs. The resulting clone size distribution P (X > x) (shown in Fig. 2d, e) is related to the site frequency spectrum in population genetics, where it can be used to predict rare evolutionary outcomes such as fitness valley crossing [49] and evolutionary rescue [16], and is well understood for toy models of microbial colonies [16,42]. For neutral mutations, the clone size distribution is expected to be broad up to a shoulder indicating the typical size of the largest expected bubble. In our experiments, we indeed observed a broad shoulder-like distribution for neutral mutations, consistent with earlier experiments using population sequencing [16] (Fig. 2e). For beneficial mutations, the larger number of bulging sectors created an even broader distribution with maximum clone sizes of almost half the population, while the distribution for strongly deleterious mutations was cut off at small clone sizes. The clone size distribution is consistent with our initial observation that a larger selective advantage s gave rise to a larger overall mutant frequency, but it also shows that even at the largest s ≈ 0.2, most mutant clones remained small, with more than half of the visible clones reaching frequencies of at most 1%.
Heterogeneous environment
To investigate the effect of environmental heterogeneity on colony growth and adaptation dynamics, we deposited filter paper with a pore size in the range of 9 to 20µm onto melted agar and removed it after cooling and drying, creating an agar surface with random microscopic features. Colonies grown on these rough substrates (hereafter called “rough” colonies) had a rougher front line (Fig. 1d, SI Fig. S5) than those grown on smooth substrates (“smooth” colonies). The filter paper left grooves in the agar surface that the bacteria tended to colonize faster than the surroundings, leading the branch-like outgrowths that grew far ahead of the rest of the population and broadened as they were incorporated into the bulk of the colony (Fig. 1e).
Given the importance of the front morphology for evolutionary dynamics [14,21], we hypothesized that by changing the growth patterns of rough colonies, the structured agar surface should also impact the dynamics of spontaneous mutations. Indeed, the final mutant frequency fMT in rough colonies was markedly different from what we found in smooth colonies (Fig. 2a, blue): while the neutral mutant frequency was roughly the same in both rough and smooth colonies, rough colonies showed no significant increase in mutant frequency with the fitness advantage s of the mutants, in contrast to smooth colonies, where the mutant frequency increased by a factor of 10 at the largest selective advantage s ≈ 0.2 compared to the neutral case. This effect did not stem from an altogether elimination of selection, however, as colonies of mutant and wild type grown separately on rough substrates showed a mutant fitness advantage (as measured by the radial growth rate) over the wild type consistent with the advantage they enjoyed on smooth substrates (Fig. 2a, inset).
The insensitivity of fMT to selective differences can be broken down into a combination of two factors: the number of sectors was lower in rough colonies than in smooth colonies and constant for positive s (Fig. 2b), and the frequency per clone changed only slightly with s for s > 0 in rough colonies, whereas it increased approximately exponentially with s in smooth colonies (Fig. 2c). The discrepancy between mutant dynamics in smooth and rough colonies held also at the level of individual clones (Fig. 2d, e): for all s > 0, the clone size distributions obtained from rough colonies were virtually indistinguishable. By contrast, negative selection tended to decrease the size of mutant clones about equally in both smooth and rough colonies. Thus, beneficial clones in rough colonies behaved effectively neutrally, whereas deleterious mutations were fully affected by their growth rate disadvantage.
In summary, a microscopically randomly patterned growth surface had several effects on evolutionary dynamics in our colonies: it decreased the overall dependence of the final mutant frequency (or, equivalently, the rate of adaptation) on the selective effect of the mutation, it reduced the establishment probability of beneficial mutations, and it altered the distribution of clone sizes. These effects are large, despite the fact that the perturbation we impose is relatively weak. After all, the rough substrate is only distinguished from the smooth substrate by troughs and elevations much smaller than the whole population, or even a single beneficial mutant clone on smooth substrates, and colony growth rate differences are consistent for both substrate types (Fig. 2a, inset).
Minimal model
How can a small change in environmental conditions have such a drastic effect on the evolutionary dynamics? To try to answer this question, we set up a minimal model of range expansions in the presence of environmental disorder to explore under which conditions small amounts of added disorder can generate the observed dramatic reduction in the efficacy of selection. Our model is based on the classical Eden lattice model [10] that is commonly used to model growing microbial colonies [6,16,21]. It has minimal ingredients: only cells with empty neighbors can divide, and a wild type can mutate upon cell division with probability µ to the mutant type carrying a fitness advantage or disadvantage s. Disorder sites (density ρ) confer a reduced growth rate k (0 ≤ k < 1) to any individual growing on it. For k = 0, the disorder sites are impassable obstacles. The simplicity of the model allows us to explore exhaustively the whole parameter space in k and ρ.
The radial expansion speed of the colonies depends on both the obstacle density ρ and the growth reduction factor k (Fig. 3b). For relatively weak growth rate reduction at obstacles sites (i.e., k ≈ 1), the expansion speed decreases slightly with the obstacle density. For increasing growth reduction, i.e., for k → 0, the expansion speed decreases first slowly and then rapidly as the density reaches a critical value ρc ≈ 0.4 (dotted line). For impassable obstacles (k = 0) at densities ρ > ρc, the obstacles form a closed ring around the incipient colony and prevented further growth (Fig. 3b, black line); thus, there is a phase transition at a critical density ρc ≈ 0.4. This transition is called the pinning transition of the interface (discussed in detail in the SI) and corresponds to the scenario where the colony can no longer percolate through the network of obstacles, suggesting that ρc is equivalent to the site percolation threshold 1 – 0.592… = 0.407… [3,7]. Close to the phase transition, small changes in obstacle density can have dramatic effects: not only does the colony expansion speed decrease rapidly, but as we shall see below, it also impacts evolutionary dynamics, such as the establishment probability of beneficial mutations and the final frequency of mutants.
In the presence of high obstacle densities, the interface is characterized by a character-istic length scale that diverges as the critical density ρc is approached. Over this length scale, the interface is pinned, i.e., it cannot advance locally. This pinning effect, which we also observed in our experiments (see Fig. 2e), is indicated as arrows in Fig. 3d. As a result of the local pinning of the colony interface, the colony morphology depends on the density of obstacles, most drastically for impassable obstacles on which we concentrate in Fig. 3c. Without obstacles, the colonies are compact and relatively smooth. At inter-mediate obstacles densities, colonies are punctured by small holes and the overall density of the colony decreases. At the critical density ρc the colony is characterized by the fragmented morphology of percolation clusters with a large number of holes and a very rough exterior (see SI Fig. S7 for a quantitative analysis of the colony interfaces). In the following, we investigate how this change in colony morphology affects the evolutionary dynamics.
We begin by replicating the experimental situation to assess the efficacy of selection in the presence of environmental heterogeneity. We simulated mutations conferring a selective advantage s (i.e., increasing the growth rate by a factor 1 + s), shown in Fig. 4. Relatively weak obstacles (growth rate k at obstacle site k = 0.1, Fig. 4a) only have a mild effect on the mutant frequency fMT. As in our experiments, fMT increases roughly exponentially with s, albeit slightly weaker at intermediate ρ ≈ 0.5 than at the extremes ρ ≈0 or ρ ≈1. This reduction in the sensitivity of fMT to s becomes much more dramatic as the growth rate on disorder sites is decreased (see Fig. 4b for the extreme case k = 0). In addition, as the critical density ρc is approached, the frequency of neutral mutants increases, resulting in mutant frequencies that are elevated relative to the homogeneous scenario for neutral and deleterious mutations, but reduced for beneficial mutations.
To quantify the effects of varying k and ρ and summarize the simulation results over many parameter combinations, we introduce the selection efficacy ks by parametrizing the mutant frequency with an exponential function . This choice is merely heuristic, but is justified by rescaling mutant frequency curves for a range of values of ρ and k by the fitted values for the neutral diversity f0 and the selection efficacy ks, which collapses all data onto a single master curve given by a simple exponential (Fig. 4f). The selection efficacy ks has a minimum near ρc, which is increasingly sharp for decreasing k. It vanishes entirely as ρ approaches ρc for obstacles (k = 0), indicating that selection is completely unable to affect the final mutation frequency in this limit. The virtual independence of the evolutionary dynamics of the per-capita fitness s holds even at the scale of individual clones, whose size distributions for different values of s are practically indistinguishable for obstacle densities near ρc (SI Fig. S6). Thus, while we find a proper phase transition only for k = 0, the percolation transition is also manifest in the evolutionary dynamics in populations grown in generic heterogeneous environments. As a consequence, tiny changes in environmental parameters near a non-trivial critical obstacle density ρc can have a dramatic effect on colony morphologies and evolutionary dynamics. The direct connection between colony morphology and evolutionary dynamics is underscored by the dsicovery that the two descriptive parameters, the selection efficacy ks and the neutral diversity f0, introduced as independent parameters measured directly from the simulations, are not independent in practice (Fig. 4e). Plotting ks vs. f0 for various choices of k and ρ reveals that the two parameters represent two sides of the same coin: environmental disorder alters the growth pattern of the colony, which in turn affects both the neutral diversity and the selection efficacy.
From a classical population genetics perspective, the fact that the addition of extrinsic noise effectively weakens selection is not surprising, as other sources of noise, such as small population sizes, are known to push evolutionary dynamics towards the neutral limit [17]. However, the environmental heterogeneity in our simulations changes the evolutionary dynamics on a fundamental level that is not consistent with a mere increase in total noise. To show this, consider the neutral diversity f0 in Fig. 4e, which corresponds to the rate at which neutral mutations accumulate in the population. On average, this rate is µ(N/π)1/2 since a fraction µ of cells at the population front acquire new neutral mutations in every generation, and the front scales as the square root of the population size N [16]. Importantly, this result in independent of the level of noise in the system since it concerns only the average over many populations. Since the population size is the same across all our simulation, we would expect the same neutral diversity for all parameter values ρ and k, but our simulations show clear systematic deviations from the expected value (dotted line in Fig. 4e); in particular, for small k, the neutral diversity f0 has a pronounced maximum near ρc (Fig. 4d).
To further characterize the qualitative changes on the neutral dynamics induced by environmental heterogeneity, we computed the spatially resolved phylogenetic tree of the population, obtained by tracing the lineages of all individuals at the population front back to the origin. For simplicity, we concentrate on the case of no (ρ = 0) and critical (ρ = ρc) obstacles (i.e., k = 0). As shown in Fig. 5a, b, the tree has a vastly different appearance depending on the environmental heterogeneity. Without obstacles (panel a) the lineages are relatively straight and roughly aligned with the radial direction. By contrast, at the critical obstacle density, where the colony has a rough exterior, lineages are erratic and often have segments oriented perpendicular to the radial direction. The lineages shown in Fig. 5a,b are intimately related to the shape and orientation of individual neutral clones (Fig. 5g-j). Mutant clones have an approximately ellipsoidal shape oriented preferentially along the radial direction in the absence of heterogeneity, whereas they have essentially random orientations in rough colonies (Fig. 5i), in agreement with the observation that lineages lose their radial orientation as the number of obstacles increased. Similarly, the scaling of the clone width with its length l|| changed from ζ = 2/3 for ρ = 0 (consistent with KPZ interface statistics [16]), to ζ 0.95 for ρ = ρc (Fig. 5j), indicating roughly isotropic neutral clones.
To quantify how environmental heterogeneity impacts neutral lineage dynamics, we focused on the strength of lineage fluctuations and the coalescence “time” measured in lattice sites (see Fig. 5c). First, the lateral lineage fluctuations l⊥∼ tξ as a function of distance t from the origin are not only rougher in absolute value, but also in terms of their scaling in rough colonies. Whereas in the standard Eden model we recover the known scaling ξ = 0.66 ± 0.006 [29], we find a larger scaling exponent ξ = 0.86 ± 0.006 in rough colonies (ρ = 0.4). This is consistent with the corresponding change of the statistical properties of the colony interface, which transitions from the Kardar-Parisi-Zhang (KPZ) universality class to the quenched Edwards-Wilkinson (QEW) universality class (see SI). Second, the increased roughness of lineages is also reflected in the number of successful lineages emanating from the initial population founder. We quantify this by computing the pairwise coalescence time T2 (Fig. 5e,f), i.e., how long ago two individuals a distance Δx apart at the front had their most recent common ancestor. We find that, for a given sample distance, the relative coalescence time and persistence probability (i.e., the probability of not having a common ancestor until time T2, panel f) is always smaller in the presence of obstacles. This indicates that fewer lineages reach the population edge in the presence of environmental heterogeneity. This makes intuitive sense from the phylogenetic trees shown in Fig. 5a, b, where in rough colonies all individuals at the front coalesce quickly into a small number of large lineages. In summary, the observed differences in selection efficacy, neutral diversity, lineage scaling properties, and (neutral) coalescence structure between populations expanding in homogeneous or heterogeneous environments rule out the interpretation of environmental disorder as simply another additive noise. Instead, we find that environmental disorder can fundamental alter the population genetics of range expansions.
Discussion
Evolution can be viewed as the result of a competition between the deterministic force of selection and various sources of randomness: firstly, intrinsic noise, which encompasses genetic drift, the nature and timing of mutations, etc., only depends on the inherent properties of the population, such as the species (including its microscopic characteristics like adhesion strength, cell shape, or growth rate) and the population size. The second source of randomness is extrinsic noise, by which we mean spatio-temporal gradients and fluctuations in environmental conditions, such as temperature, nutrient availability, or antibiotic concentration. To fully understand evolutionary dynamics, the relative strength of all three factors have to be taken into account. In evolution experiments, extrinsic noise is typically either deliberately prevented, or added in a very controlled fashion, such as periodic changes in conditions.
Here, we have shown that extrinsic noise in the form of random environmental disorder can dramatically impact the fates of spontaneous mutations in microbial colonies. By leveraging plasmid loss in E. coli as a model system for spontaneous mutations with tunable growth rate effect, we have overcome previous experimental limitations, which required the mixture of two strains to study the effects of beneficial mutation. We have confirmed previous theoretical predictions about the evolutionary dynamics of spontaneous mutations in microbial colonies grown on homogeneous substrates: mutants with larger selective advantages are more likely to establish clonal sectors that expand rapidly and quickly become highly abundant in the population; overall, however, even very advantageous mutations are undividually extremely unlikely to be successful, leaving the evolutionary fate of the population in the hands of a few lucky clonal lineages.
By growing colonies on heterogeneous substrates, we found that microscale ridges and troughs in the growth substrate were enough to reduce the ability of beneficial mutations to establish and expand. Our minimal model simulations showed that this reduction in selection efficacy on heterogeneous substrate can be explained by a local pinning of the colony front. Since mutations occur only within the growing population at the front, the properties of the front dictate the evolutionary dynamics, including the strength of selection and the size of individual clones. Local pinning impacts the dynamics at the front by reducing the expansion speed of some parts of the population, leading to an effective reduction in the number of expansion paths that can actively contribute successful mutations. Thus, only a few lucky lineages will be able to find the paths along unpinned front positions; most lineages will get stuck in dead-ends. Given local establishment, lineage success is then roughly independent of the fitness of the mutants; whether a sector can form or not depends entirely on where the mutation arises and not at all on its growth rate. Similarly, the size of mutant clones is constrained by the network of obstacles, and whether and when a given mutant clone goes extinct depends only marginally on the fitness of its founder. In this sense locally pinned expansions bear little resemblance to unconstrained radial expansions (see Fig. 6). Rather, expansions along each available path more closely correspond to linear expansions, e.g., along a coastline, where mutations spread deterministically after local establishment [15]. Overall, the observed differences in selection efficacy, neutral diversity, lineage scaling properties, and (neutral) coalescence structure between populations expanding in homogeneous or heterogeneous environments rule out the interpretation of environmental disorder as simply another additive noise. Instead, we find that environmental disorder can alter the population genetics of range expansions at a fundamental level.
Environmental disorder arguably impacts not only the rate of adaptation due to beneficial mutations. Since deleterious mutations are typically more numerous than beneficial ones, environmental disorder may also increase the chances of an overall decrease in population fitness through the accumulation of deleterious mutations, which is already more likely in range expansions than in well-mixed populations [19,36,43]. Thus, heterogeneities in the environment may not only slow down the process of adaptation but also lead to entirely different long-term evolutionary outcomes. Since many mutations conferring resistance to antibiotics are often associated with a fitness cost, environmental disorder may also favor the evolution of resistance in microbial populations in this way. However, our results on the fates of deleterious mutations remain ambiguous: while our simulations predict that deleterious mutations should be more successful in disordered environments, our experiments found no significant differences in the size of deleterious clones between smooth and rough colonies. A potential reason for this discrepancy is may be that the disorder imposed in our experiments is not correlation-free. A beneficial mutation has to overcome genetic drift, and to do so, it must grow to a lateral size large enough for selection to take over [21]. However, if the characteristic length scale of the environmental disorder is smaller than this “establishment size”, then the evolutionary dynamics is effectively neutral. On the other hand, a deleterious mutation born on a ridge or in a trough never grows to large enough size to “see” the disorder in the first place and thus its dynamics are largely unaffected by the environmental disorder.
While we have focused here on microbial populations, we expect our principal result of reduced selection efficacy in disordered environments to generalize to other dense cellular populations, such as tumors and biofilms, but also to macroscopic range expansions, as well. After all, when a population undergoes a range expansion, it will arguably not experience a completely homogeneous environments: at the very least, some areas will be more hospitable than others, but other parts of the environment may also be entirely inaccessible to the population because of, e.g., rivers and lakes, a strong local competitor or predator, or lack of resources. Environmental heterogeneity is thus arguably the rule rather than the exception. Our results suggest that since range expansions in strongly heterogeneous environments can generate approximately neutral patterns of genetic diversity from mutations carrying significant fitness effects, attempts to interpret such patterns in invasive species, or generally species having undergone recent range expansions, must take into account the role the environment plays in shaping these patterns.
Acknowlegdments
The authors thank Jona Kayser, Diana Fusco, Jayson Paulose, and all members of the Hallatschek lab for helpful discussions. Research reported in this publication was supported by the National Institute of General Medical Sciences of the National Institutes of Health under award R01GM115851, a National Science Foundation CAREER Award (#1555330) and a Simons Investigator award from the Simons Foundation (#327934).