Session E49: Evolutionary and Ecological Dynamics - I

Neither pulled nor pushed: Genetic drift and front wandering uncover a new class of reaction-diffusion waves

Epidemics, flame propagation, and cardiac rhythms are classic examples of reaction-diffusion waves that describe a switch from one alternative state to another. Only two types of waves are known: pulled, driven by the leading edge, and pushed, driven by the bulk of the wave. Here, we report a distinct class of semi-pushed waves for which both the bulk and the leading edge contribute to the dynamics. These hybrid waves have the kinetics of pushed waves, but exhibit giant fluctuations similar to pulled waves. The transitions between pulled, semi-pushed, and fully-pushed waves occur at universal ratios of the wave velocity to the Fisher velocity linear spreading velocity. We derive these results in the context of a species invading a new habitat by examining front diffusion, rate of genetic drift, and fluctuation-induced corrections to the expansion velocity. All three quantities decrease as a power law of the population density with the same exponent. We calculate this exponent exactly without neglecting the fluctuations in the shape of the wave front. For fully-pushed waves, the exponent is -1 consistent with the central limit theorem. In semi-pushed waves, however, the fluctuations average out much more slowly, and the exponent approaches 0 towards the transition to pulled waves. As a result, a rapid loss of genetic diversity and large fluctuations in front position occur even for populations with cooperative growth and other forms of an Allee effect. The outcome of spatial spreading in such populations could therefore be less predictable than previously thought.   

Life in the trenches: spatial confinement induces evolutionary pattern formation

As cells divide in somatic tissues, multiple clonal groups with distinct mutations may arise in parallel. The physical properties of somatic tissues that influence the evolutionary dynamics of these clones remain largely unexplored. Here, we study the effect of tissue dimensions and geometry. Using stochastic simulations, we show that spatial confinement aligns boundaries between stem cell clones to the confined dimension with clones regularly spaced along the longer axis, forming patterns reminiscent of phase separation. The patterns emerge only as the confinement shrinks below a critical length, which is on the order of a few hundred cell sizes, a scale relevant to many physiological processes. We observed that under spatial confinement, clones spread more slowly and coexist as competing lineages. To determine if our observations can apply to more complex tissues, we extend this model to explicitly incorporate cell differentiation. With differentiated cells acting as buffers between stem cells, the clonal patterns are preserved but their intrinsic length scale increases. Altogether, we predict that the spatial arrangement of cells significantly alters their evolutionary dynamics in tissues.   

Adaptation in pushed waves

Spatial range expansions are ubiquitous in nature, ranging from surface-dwelling biofilms to mammalian species migrating due to climate change and habitat loss. Most of our understanding of evolution during range expansions stems from theoretical studies on pulled traveling waves, in which pioneer individuals living at the edge of the wave have the highest chance of colonizing new territory and reproducing. The corresponding small effective population size leads to inefficient selection, which can cause the accumulation of deleterious mutations at the front with consequent decrease in fitness.

Using theory and simulations, we find that introducing cooperative effects in the population, which changes the dynamics of the wave from pulled to pushed, increases the effect of selection and allows beneficial mutations to establish more readily while purging deleterious mutations. At low mutation rate, in the sequential fixation regime, strong cooperation thus leads to faster adaptation. By contrast, at high mutation rate, clonal interference dominates and the adaptation rate exhibits a non-monotonic trend as a function of cooperation.   

Territorial expansions in public goods games

Demographic noise in ecological species can significantly alter deterministic outcomes, for example concerning the survival of producers (a less fit species) in public goods games. Here, we discuss the importance of stochastic effects, encoded in our work in two different classes of models for the prisoner's dilemma as one type of public goods game, on both producer stability and spatial properties (concerning the expansion of the dominant species). In one model, interaction and reproduction take place locally on a patch, while in the other model, single players on one patch each interact across patches. While pattern formation occurs for both models, it is crucial for determining producer stability only in the latter. We then discuss how these models affect spatial patterns as production costs vary, and focus specifically on the expansion velocity and front properties in these systems. By doing so, we intend to elucidate both the role of spatial habitats and migration between them, as well as identify behaviour that may help to distinguish between these models experimentally.   

Fixation Probabilities in Compressible Turbulence

Competition between two biological species can change dramatically in a turbulent environment, where survival of the fittest, number fluctuations, and fluid advection can all play an important role. Turbulent effects are particularly interesting when the cell generation time is within the inertial range of eddy turnover times, as is often the case for photosynthetic bacteria in oceans and lakes. We couple an off-lattice agent-based simulation of two populations in one dimension with a velocity field generated by a shell model, and find that compressible turbulence can wash out the effect of selective advantage on fixation probabilities. By examining fixation events in simple sinusoidal flows, frozen snapshots of our turbulent velocity field, and well-mixed systems with a time-dependent carrying capacity, we find we can explain a large portion of our results by only considering long wavelength, slowly-varying features of turbulence. We uncover a suppression of fixation probabilities connected to the behavior of Fisher genetic waves.   

On Growth and Form of Range Expansions at Liquid Interfaces

Range expansions coupled with fluid flows are of great importance in understanding the organization and competition of microorganism populations in liquid environments. However, combining growth dynamics of an expanding assembly of cells with hydrodynamics leads to challenging problems, involving the coupling of nonlinear dynamics, stochasticity and transport. We have created an extremely viscous medium that allows us to grow cells on a controlled liquid interface over macroscopic scales. In this talk, I will present laboratory experiments, combined with numerical modelling, focused on the collective dynamics of genetically labelled microorganisms undergoing division and competition in the presence of a flow. I will show that an expanding population of microbes can itself generate a flow, leading to an accelerated propagation and fragmentation of the initial colony. Finally, I will show the mechanism at the origin of this metabolically generated flow and how it affects the growth and morphology of these microbial populations.   

Microbial range expansions in time-varying environments

Classical population genetics studies assume that populations are well-mixed and environments are constant in time, a situation that is rarely encountered in nature. Here, we investigate how temporal fluctuations of the environment affect the interaction of different genotypes at the front of microbial range expansions. We perform experiments with different strains of the budding yeast, S. cerevisiae, whose relative fitness switches following changes in the environmental state. Our experiments show that physical interactions such as growth-induced pressure gradients can significantly enhance the survival of less fit genotypes at the front of range expansions, thus aiding their recovery following environmental changes that increase their selective advantage. We investigate the physical causes of such an enhanced survival using continuum models inspired by overdamped fluid dynamics and use them to investigate spatial population genetics in fluctuating environments.   

Mutations in Expanding Populations

In spatially constrained growing populations, such as tumors or biofilms, cells at the edge of expanding front have significant advantages because of the high accessibility to nutrients and spaces. Therefore, mutations that happen at the front have a large probability to surf at the edge of the population. A previous population sequencing study has shown that this effect leaves characteristic features in the mutation frequency spectrum. However, sequencing experiments cannot capture the behavior of low-frequency variants. Here, we constructed a microfluidic device to track mutations which happened at the front of a population growth. Combining with agent-based simulations and theoretical studies, we found that low-frequency mutant clones have broadly distributed shapes and sizes, which result from the combination of growth and excluded volume interactions. These results could be relevant to the emergence of drug resistance in crowded cellular populations.   

Coexistence and Pattern Formation in Bacterial Mixtures with Contact-dependent Killing and Long-range Inhibition

Multi-strain microbial communities often exhibit complex spatial organization that emerges due to the interplay of various cooperative and competitive interaction mechanisms. One strong competitive mechanism is contact-dependent neighbor killing, such as that enabled by the type VI secretion system (T6SS). It has been previously shown that contact-dependent killing can result in bistability of bacterial mixtures, so that only one strain survives and displaces the other. However, it remains unclear whether stable coexistence is possible in such mixtures. Using a population dynamics model for a mixture of two bacterial strains, we found that coexistence can be made possible by combining contact-dependent killing with long-range growth inhibition, leading to the formation of various cellular patterns. These patterns emerge in a much broader parameter range than that required for the Turing instability, suggesting this may be a more robust mechanism for pattern formation.   

Effects of Pattern Formation in Bacillus subtilis Biofilms on Evolutionary Dynamics

Biofilms are a ubiquitous form of microbial growth where individual cells interact mechanically and chemically to allow collective behavior at the population level. This collective behavior often leads to the formation of patterns, of which one prominent example is wrinkling of the entire colony into the third dimension. Our experiments with Bacillus subtilis biofilms on agar surfaces suggest that there is a correlation between wrinkle formation and natural selection. Our goal is to investigate whether the presence or the absence of certain patterns such as wrinkles lead to different evolutionary dynamics. We will present results on how pattern formation affects natural selection and as well as how selection feeds back onto the organization of the pattern. These results could lend insight into drug resistance evolution in microbial biofilms.   

Spatial Structure in Microbial Competition Models

Understanding the structure and behavior of diverse microbial communities is currently a major challenge in the life sciences. The interactions shaping these communities are physical processes, but are often modeled in a mean-field limit that neglects spatial structure. How does spatial structure affect the community-level properties of microbial ecosystems? We have developed a spatial model of two fundamental interactions between microbes: competition for resources and “chemical warfare” via secreted antibiotics. Our group recently showed that a metabolic trade-off constraint in a non-spatial model allows for degenerate steady states with diverse coexisting species. We find that 1D space preserves diversity, but selects a unique steady-state abundance and introduces a new dynamical time scale for relaxation to this steady state. The new time scale characterizes a regime where population dynamics slow down as resource diffusion speeds up. Interestingly, population fluctuations lead to rank-abundance curves that are indistinguishable from neutral and non-spatial models, suggesting a surprising universality at the ecosystem level.   

Spatiotemporal dynamics of phage-biofilm interactions

Bacteriophage (`phage') - viruses that infect and lyse bacteria - can be deployed therapeutically to treat infections caused by bacterial pathogens. However most reported studies of the therapeutic potential of phage neglect the spatial heterogeneity in bacterial communities, e.g., in microcolonies and biofilms. Here, we present experiments, theory, and simulations that investigate the spatiotemporal dynamics arising from interactions between P. aeruginosa and phage. Time-dependent high resolution confocal imaging is used to examine how phage propagate through spatial domains of bacteria. Together with a three dimensional multi-scale modeling approach, our results shed light on how phage shape the emergence (and potential collapse) of microcolonies and biofilms.   

Inferring interactions in microbe-phage communities

Microbes are found in high abundances in the environment and in human-associated microbiomes, often exceeding one million cells per milliliter. Viruses of microbes, or phages, are found in even higher abundances. Phages are estimated to turn over 10 to 40 percent of microbes daily, contributing to microbial mortality and redirecting nutrient flow between trophic levels. Understanding the ecological dynamics of microbial communities requires knowledge of phage “host-range” i.e. which microbes a phage can infect. However elucidating phage host-range in situ remains a difficult and open question. Here, we discuss current approaches to the host-range inference problem and benchmark their performance using in silico microbe-phage communities. Contrary to widespread use, correlation and correlation-based approaches on abundance time-series do not recapitulate phage host-range (Coenen and Weitz, 2017). Model-based approaches, which compute regressions on discretized mechanistic models, can accurately recover host-range and are robust to variation in network structure and life history traits (Jover et al, 2016). Finally, we extend the model-based approach to simultaneously infer heterogeneous microbe-microbe competition in the presence of phages.