Jonas Cremer

Growth dynamics and the evolution of cooperation in microbial populations

Microbes providing public goods are widespread in nature despite running the risk of being exploited by free-riders. However, the precise ecological factors supporting cooperation are still puzzling. Following recent experiments, we consider the role of population growth and the repetitive fragmentation of populations into new colonies mimicking simple microbial life-cycles. Individual-based modeling reveals that demographic fluctuations, which lead to a large variance in the composition of colonies, promote cooperation. Biased by population dynamics these fluctuations result in two qualitatively distinct regimes of robust cooperation under repetitive fragmentation into groups. First, if the level of cooperation exceeds a threshold, cooperators will take over the whole population. Second, cooperators can also emerge from a single mutant leading to a robust coexistence between cooperators and free-riders. We find frequency and size of population bottlenecks, and growth dynamics to be the major ecological factors determining the regimes and thereby the evolutionary pathway towards cooperation.

Evolutionary Game Theory in Growing Populations

Existing theoretical models of evolution focus on the relative fitness advantages of different mutants in a population while the dynamic behavior of the population size is mostly left unconsidered. We present here a generic stochastic model which combines the growth dynamics of the population and its internal evolution. Our model thereby accounts for the fact that both evolutionary and growth dynamics are based on individual reproduction events and hence are highly coupled and stochastic in nature. We exemplify our approach by studying the dilemma of cooperation in growing populations and show that genuinely stochastic events can ease the dilemma by leading to a transient but robust increase in cooperation.

Effect of flow and peristaltic mixing on bacterial growth in a gut-like channel

Significance The human colon is occupied by trillions of microbial cells. Recent sequencing studies have shown that many diseases lead to substantial changes in the composition of this gut microbiota and suggest a strong influence of composition on host physiology. However, not much is known about the underlying physiological factors shaping the gut microbiota. Here, we focus on the role of flow and mixing by colonic wall contractions. To grow in the proximal colon, microbes have to continuously overcome flow. Our in vitro study suggests that mixing helps to overcome flow, and controlled contractions by the colon strongly influence microbiota density and composition; flow and mixing are essential components toward developing a predictive understanding of the gut microbiota. The ecology of microbes in the gut has been shown to play important roles in the health of the host. To better understand microbial growth and population dynamics in the proximal colon, the primary region of bacterial growth in the gut, we built and applied a fluidic channel that we call the “minigut.” This is a channel with an array of membrane valves along its length, which allows mimicking active contractions of the colonic wall. Repeated contraction is shown to be crucial in maintaining a steady-state bacterial population in the device despite strong flow along the channel that would otherwise cause bacterial washout. Depending on the flow rate and the frequency of contractions, the bacterial density profile exhibits varying spatial dependencies. For a synthetic cross-feeding community, the species abundance ratio is also strongly affected by mixing and flow along the length of the device. Complex mixing dynamics due to contractions is described well by an effective diffusion term. Bacterial dynamics is captured by a simple reaction–diffusion model without adjustable parameters. Our results suggest that flow and mixing play a major role in shaping the microbiota of the colon.

Entropy Production of Cyclic Population Dynamics

Entropy serves as a central observable in equilibrium thermodynamics. However, many biological and ecological systems operate far from thermal equilibrium. Here we show that entropy production can characterize the behavior of such nonequilibrium systems. To this end we calculate the entropy production for a population model that displays nonequilibrium behavior resulting from cyclic competition. At a critical point the dynamics exhibits a transition from large, limit-cycle-like oscillations to small, erratic oscillations. We show that the entropy production peaks very close to the critical point and tends to zero upon deviating from it. We further provide analytical methods for computing the entropy production which agree excellently with numerical simulations.

Evolutionary and population dynamics: A coupled approach

We study the interplay of population growth and evolutionary dynamics using a stochastic model based on birth and death events. In contrast to the common assumption of an independent population size, evolution can be strongly affected by population dynamics in general. Especially for fast reproducing microbes which are subject to selection, both types of dynamics are often closely intertwined. We illustrate this by considering different growth scenarios. Depending on whether microbes die or stop to reproduce (dormancy), qualitatively different behaviors emerge. For cooperating bacteria, a permanent increase of costly cooperation can occur. Even if not permanent, cooperation can still increase transiently due to demographic fluctuations. We validate our analysis via stochastic simulations and analytic calculations. In particular, we derive a condition for an increase in the level of cooperation.

Mobility, fitness collection, and the breakdown of cooperation.

The spatial arrangement of individuals is thought to overcome the dilemma of cooperation: When cooperators engage in clusters, they might share the benefit of cooperation while being more protected against noncooperating individuals, who benefit from cooperation but save the cost of cooperation. This is paradigmatically shown by the spatial prisoners dilemma model. Here, we study this model in one and two spatial dimensions, but explicitly take into account that in biological setups, fitness collection and selection are separated processes occurring mostly on vastly different time scales. This separation is particularly important to understand the impact of mobility on the evolution of cooperation. We find that even small diffusive mobility strongly restricts cooperation since it enables noncooperative individuals to invade cooperative clusters. Thus, in most biological scenarios, where the mobility of competing individuals is an irrefutable fact, the spatial prisoners dilemma alone cannot explain stable cooperation, but additional mechanisms are necessary for spatial structure to promote the evolution of cooperation. The breakdown of cooperation is analyzed in detail. We confirm the existence of a phase transition, here controlled by mobility and costs, which distinguishes between purely cooperative and noncooperative absorbing states. While in one dimension the model is in the class of the voter model, it belongs to the directed percolation universality class in two dimensions.

Anomalous finite-size effects in the Battle of the Sexes

Abstract.The Battle of the Sexes describes asymmetric conflicts in mating behavior of males and females. Males can be philanderer or faithful, while females are either fast or coy, leading to a cyclic dynamics. The adjusted replicator equation predicts stable coexistence of all four strategies. In this situation, we consider the effects of fluctuations stemming from a finite population size. We show that they unavoidably lead to extinction of two strategies in the population. However, the typical time until extinction occurs strongly prolongs with increasing system size. In the emerging time window, a quasi-stationary probability distribution forms that is anomalously flat in the vicinity of the coexistence state. This behavior originates in a vanishing linear deterministic drift near the fixed point. We provide numerical data as well as an analytical approach to the mean extinction time and the quasi-stationary probability distribution.

Effect of water flow and chemical environment on microbiota growth and composition in the human colon

Significance The human gut is populated by a dense microbial population, strongly impacting health and disease. Metagenomic sequencing has led to crucial insights into microbiota changes in response to various perturbations, but a mechanistic understanding of these changes is largely missing. As the composition of the gut microbiota is a consequence of bacterial growth, we propose an approach that focuses on bacterial growth in the human large intestine and the physiological factors influencing it. Using a combination of experimental analysis and quantitative simulations, we explain the observed variation in microbiota composition among healthy humans and the dominant role of nutrient inflow and stool consistency. Our quantitative modeling framework is a step toward a predictive understanding of microbiota dynamics in the human host. The human gut harbors a dynamic microbial community whose composition bears great importance for the health of the host. Here, we investigate how colonic physiology impacts bacterial growth, which ultimately dictates microbiota composition. Combining measurements of bacterial physiology with analysis of published data on human physiology into a quantitative, comprehensive modeling framework, we show how water flow in the colon, in concert with other physiological factors, determine the abundances of the major bacterial phyla. Mechanistically, our model shows that local pH values in the lumen, which differentially affect the growth of different bacteria, drive changes in microbiota composition. It identifies key factors influencing the delicate regulation of colonic pH, including epithelial water absorption, nutrient inflow, and luminal buffering capacity, and generates testable predictions on their effects. Our findings show that a predictive and mechanistic understanding of microbial ecology in the gut is possible. Such predictive understanding is needed for the rational design of intervention strategies to actively control the microbiota.

The emergence of cooperation from a single mutant during microbial life cycles

Cooperative behaviour is widespread in nature, even though cooperating individuals always run the risk of being exploited by free-riders. Population structure effectively promotes cooperation given that a threshold in the level of cooperation was already reached. However, the question how cooperation can emerge from a single mutant, which cannot rely on a benefit provided by other cooperators, is still puzzling. Here, we investigate this question for a well-defined but generic situation based on typical life cycles of microbial populations where individuals regularly form new colonies followed by growth phases. We analyse two evolutionary mechanisms favouring cooperative behaviour and study their strength depending on the inoculation size and the length of a life cycle. In particular, we find that population bottlenecks followed by exponential growth phases strongly increase the survival and fixation probabilities of a single cooperator in a free-riding population.

Bacterial growth, flow, and mixing shape human gut microbiota density and composition

ABSTRACT The human gut microbiota is highly dynamic, and host physiology and diet exert major influences on its composition. In our recent study, we integrated new quantitative measurements on bacterial growth physiology with a reanalysis of published data on human physiology to build a comprehensive modeling framework. This can generate predictions of how changes in different host factors influence microbiota composition. For instance, hydrodynamic forces in the colon, along with colonic water absorption that manifests as transit time, exert a major impact on microbiota density and composition. This can be mechanistically explained by their effect on colonic pH which directly affects microbiota competition for food. In this addendum, we describe the underlying analysis in more detail. In particular, we discuss the mixing dynamics of luminal content by wall contractions and its implications for bacterial growth and density, as well as the broader implications of our insights for the field of gut microbiota research.