Session E35: Population and Evolutionary Dynamics I

A non-classical phase diagram for virus-bacterial co-evolution mediated by CRISPR.

CRISPR is a newly discovered prokaryotic immune system. Bacteria and archaea with this system incorporate genetic material from invading viruses into their genomes, providing protection against future infection by similar viruses. Due to the cost of CRISPR, bacteria can lose the acquired immunity. We will show an intriguing phase diagram of the virus extinction probability, which when the rate of losing the acquired immunity is small, is more complex than that of the classic predator-prey model. As the CRISPR incorporates genetic material, viruses are under pressure to evolve to escape the recognition by CRISPR, and this co-evolution leads to a non-trivial phase structure that cannot be explained by the classical predator-prey model.   

Bacterial Invasion Dynamics in Zebrafish Gut Microbial Communities

Microbial communities residing in the vertebrate intestine play an important role in host development and health. These communities must be in part shaped by interactions between microbial species as they compete for resources in a physically constrained system. To better understand these interactions, we use light sheet microscopy and zebrafish as a model organism to image established gut microbial communities as they are invaded by robustly-colonizing challengers. We demonstrate that features of the challenger, including motility and spatial distribution, impact success in invasion and in outcompeting the original community. We also show that physical characteristics of the host, such as the motility of the gut, play important roles in mediating inter-species competition. Finally, we examine the influence of the contact-dependent type VI secretion system (T6SS), which is used by specific bacteria to cause cell lysis by injecting toxic effector proteins into competitors. Our findings provide insights into the determinants of microbial success in the complex ecosystems found in the gut.   

Multiple Cancer Cell Population Dynamics in a Complex Ecology

We have developed a technology for study of complex ecology cancer population dynamics. The technology includes complex drug gradients, full bright field/dark field/fluorescence imaging of areas of several square millimeters and thin gas-permable membranes which allow single cell extraction and analysis. We will present results of studies of prostate cancer cell dynamics.   

Migration in asymmetric, random environments

Migration is a key mechanism for expansion of communities. As a population migrates, it experiences a changing environment. In heterogeneous environments, rapid adaption is key to the evolutionary success of the population. In the case of human migration, environmental heterogeneity is naturally asymmetric in the North-South and East-West directions. We here consider migration in random, asymmetric, modularly correlated environments. Knowledge about the environment determines the fitness of each individual. We find that the speed of migration is proportional to the inverse of environmental change, and in particular we find that North-South migration rates are lower than East-West migration rates. Fast communication within the population of pieces of knowledge between individuals, similar to horizontal gene transfer in genetic systems, can help to spread beneficial knowledge among individuals. We show that increased modularity of the relation between knowledge and fitness enhances the rate of evolution. We investigate the relation between optimal information exchange rate and modularity of the dependence of fitness on knowledge. These results for the dependence of migration rate on heterogeneity, asymmetry, and modularity are consistent with existing archaeological facts.   

Velocity locking and pulsed invasions of fragmented habitats with seasonal growth

From crystal growth to epidemics, spatial spreading is a common mechanism of change in nature. Typically, spreading results from two processes: growth and dispersal in ecology or chemical reactions and diffusion in physics. These two processes combine to produce a reaction-diffusion wave, an invasion front advancing at a constant velocity. We show that the properties of these waves are remarkably different depending whether space and time are continuous, as they are for a chemical reaction, or discrete, as they are for a pest invading a patchy habitat in seasonal climates. For discrete space and time, we report a new type of expansions with velocities that can lock into specific values and become insensitive to changes in dispersal and growth, i.e. the dependence of the velocity on model parameters exhibits plateaus or pauses. As a result, the evolution and response to perturbations in locked expansions can be markedly different compared to the expectations based on continuous models. The phenomenon of velocity locking requires cooperative growth and does not occur when per capita growth rate decline monotonically with population density. We obtain both numerical and analytical results describing highly non-analytic properties of locked expansions.   

Spatial organization of cooperation.

The structure of the environment spatially confines bacteria inside groups where they live and evolve with their siblings. This population structure may not only select for individual abilities but also for group properties that would eventually enhance the fitness of the colony. In poor media, we might think that maximizing the contact with the environment would maximize the fitness of individual cells. However, we will show that the microcolony of P. aeruginosa adapts its morphogenesis to maximize cell-cell contacts rather than cell-environment interactions when iron becomes scarce in the environment. In this case, reducing the surface of exchange with the environment allows to limit the loss of secreted molecules required to efficiently fetch extracelllular iron at very low concentration.   

\textbf{Non-equilibrium relaxation in a two-dimensional stochastic lattice Lotka-Volterra model}

We employ Monte Carlo simulations to study a stochastic Lotka-Volterra model on a two-dimensional square lattice with periodic boundary conditions. There are stable states when the predators and prey coexist. If the local prey carrying capacity is finite, there emerges an extinction threshold for the predator population at a critical value of the predation rate. We investigate the non-equilibrium relaxation of the predator density in the vicinity of this critical point. The expected power law dependence between the relaxation time and predation rate is observed (critical slowing down). The numerically determined associated critical exponents are in accord with the directed percolation universality class. Following a sudden predation rate change to its critical value, one observes critical aging for the predator density autocorrelation function with a universal scaling exponent. This aging scaling signature of the absorbing state phase transition emerges at significantly earlier times than stationary critical power laws, and could thus serve as an advanced indicator of the population's proximity to its extinction threshold.   

The effects of sudden changes in environmental conditions on the non-equilibrium relaxation of ecological systems

We study the responses of predator-prey systems to temporary changes in environmental conditions. Such changes can cause a variation in species' predatory preferences which in our model appears as a perturbation in a many-species system. The type of perturbation that we consider in this study is a sudden change in the interaction scheme. We focus on systems evolving on a two-dimensional lattice and discuss the way the systems transition from one steady state to another. Using Monte Carlo simulations we monitor these transitions via the space-time correlation function and the derived correlation length.   

Effect of flow and active mixing on bacterial growth in a colon-like geometry

The large intestine harbors bacteria from hundreds of species, with bacterial densities reaching up to $10^{12}$ cells per gram. Many different factors influence bacterial growth dynamics and thus bacterial density and microbiota composition. One dominant force is flow which can in principle lead to a washout of bacteria from the proximal colon. Active mixing by contractions of the colonic wall together with bacterial growth might counteract such flow-forces and allow high bacterial densities to occur. As a step towards understanding bacterial growth in the presence of mixing and flow, we constructed an in-vitro setup where controlled wall-deformations of a channel emulate contractions. We investigate growth along the channel under a steady nutrient inflow. In the limits of no or very frequent contractions, the device behaves like a plug-flow reactor and a chemostat respectively. Depending on mixing and flow, we observe varying spatial gradients in bacterial density along the channel. Active mixing by deformations of the channel wall is shown to be crucial in maintaining a steady-state bacterial population in the presence of flow. The growth-dynamics is quantitatively captured by a simple mathematical model, with the effect of mixing described by an effective diffusion term.   

Predicting community composition from pairwise interactions

The ability to predict the structure of complex, multispecies communities is crucial for understanding the impact of species extinction and invasion on natural communities, as well as for engineering novel, synthetic communities. Communities are often modeled using phenomenological models, such as the classical generalized Lotka–Volterra (gLV) model. While a lot of our intuition comes from such models, their predictive power has rarely been tested experimentally. To directly assess the predictive power of this approach, we constructed synthetic communities comprised of up to 8 soil bacteria. We measured the outcome of competition between all species pairs, and used these measurements to predict the composition of communities composed of more than 2 species. The pairwise competitions resulted in a diverse set of outcomes, including coexistence, exclusion, and bistability, and displayed evidence for both interference and facilitation. Most pair outcomes could be captured by the gLV framework, and the composition of multispecies communities could be predicted for communities composed solely of such pairs. Our results demonstrate the predictive ability and utility of simple phenomenology, which enables accurate predictions in the absence of mechanistic details.   

A field-theoretic approach to the May-Leonard cyclic population dynamics model

Spatially extended stochastic population dynamics models with cyclic predation interactions display intriguing time evolution and spontaneous structure formation. We study a version of the May-Leonard cyclic competition model in d dimensions with diffusive particle propagation. We use the second-quantized Doi-Peliti formalism and ensuing coherent-state path integral representation to construct its continuum representation and explore its collective dynamics. Expanding the resulting action about the mean-field species concentrations enables us to compute the diagonalized harmonic propagators and hence 'masses', i.e., relaxation rates and eigenfrequencies of the fundamental modes. Furthermore, operating near the Hopf bifurcation point, we identify the validity range for the necessary time scale separation that allows us to project out the purely relaxing eigenmode. The remaining oscillating fields obey the complex Ginzburg-Landau equation, which is consistent with spiral pattern formation.   

Range expansions transition from pulled to pushed waves with increasing cooperativity in an experimental microbial population

Range expansions are becoming more frequent due to environmental changes and rare long distance dispersal, often facilitated by anthropogenic activities. Simple models in theoretical ecology explain many emergent properties of range expansions, such as a constant expansion velocity, in terms of organism-level properties such as growth and dispersal rates. Testing these quantitative predictions in natural populations is difficult because of large environmental variability. Here, we used a controlled microbial model system to study range expansions of populations with and without intra-specific cooperativity. For non-cooperative growth, the expansion dynamics were dominated by population growth at the low-density front, which pulled the expansion forward. We found these expansions to be in close quantitative agreement with the classical theory of pulled waves by Fisher and Skellam, suitably adapted to our experimental system. However, as cooperativity increased, the expansions transitioned to being pushed, i.e. controlled by growth in the bulk as well as in the front. Although both pulled and pushed waves expand at a constant velocity and appear otherwise similar, their distinct dynamics leads to very different evolutionary consequences. Given the prevalence of cooperative growth in nature, understanding the effects of cooperativity is essential to managing invading species and understanding their evolution.   

Selection of Cooperation in Spatially Structured Populations

The social dilemma games give rise to an emergence of cooperation in which altruistic individuals survive the natural selection at higher rate than random chance. We try to extend our understanding of this spatial reciprocity by including the impact of degree-degree correlation on the propensity toward prosocial behaviour in an otherwise well-mixed population. In a stochastic death-birth process with weak selection, we find that the disassortative degree mixing, or negative correlation between the degrees of neighbouring nodes significantly promotes the fixation of cooperators whereas the assortative mixing acts to suppress it. This is consistent with the fact that the spatial heterogeneity weakens the average tendency of a population to cooperate, which we describe in a unified scheme of the effective isothermality in coarse-grained networks. We also discuss the individual-level incentives that indirectly foster restructuring the social networks toward the more cooperative topologies.