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 prisoner's 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 prisoner's 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. DOI: 10.1103/PhysRevE.87.04271

Effective dynamics of microorganisms that interact with their own trail

Like ants, some microorganisms are known to leave trails on surfaces to communicate. We explore how trail-mediated self-interaction could affect the behavior of individual microorganisms when diffusive spreading of the trail is negligible on the timescale of the microorganism using a simple phenomenological model for an actively moving particle and a finite-width trail. The effective dynamics of each microorganism takes on the form of a stochastic integral equation with the trail interaction appearing in the form of short-term memory. For moderate coupling strength below an emergent critical value, the dynamics exhibits effective diffusion in both orientation and position after a phase of superdiffusive reorientation. We report experimental verification of a seemingly counterintuitive perpendicular alignment mechanism that emerges from the model.Comment: new figure with experimental results; expanded appendi

Collective behaviour of chemotactic microorganisms in a viscous environment

The aim of this DPhil thesis is the investigation of collective effects that can occur in a colony of interacting bacteria. The non-equilibrium dynamics of living organisms can lead to fascinating patterns and behaviours which cannot be found in equilibrium systems. It is our goal to obtain a better understanding of bacterial colonies and to develop a general theoretical description for living systems undergoing chemotaxis. Some types of bacteria are able to release chemical attractants to their environ- ment, which enables them to sense each other and to form biofilms in a coordinated way. E. Coli, for example, secrete aspartate if succinate is present, which diffuses in their environment and enables interactions. In the first part of the thesis we will derive a general model for bacteria or cells that interact with each other via chemo- taxis and also undergo divisions. Using Renormalization Group calculations we will show that division and chemotactic terms are of the same relevance, and that the competition between them can lead to a rich phase diagram and a transition from controlled behaviour to uncontrolled growth. In the second chapter, we will examine microorganism interaction in the limit where the secreted particles are effectively non-diffusive. On a surface, Pseudomonas aeruginosa bacteria leave a trail of polysaccharides behind them, which is followed by other P. aeruginosa bacteria [1,2]. These interactions between individuals can lead to a local accumulation and spatial correlations of bacteria [3, 4], which are important at the early stages of the biofilm formation. Starting with a generic single microorganism, we will derive the underlying equations of motion. As an important qualitative feature, we will obtain trail alignment with the gradient in addition to a trail-dependent velocity in conventional chemotaxis. Using a simplified version of the model, we will analytically investigate the effects of autochemotaxis with a self-deposited trail and show that it can lead to enhanced rotational diffusion and even trapping. However, if a microorganism is following an existing trail, it can also lead to oscillatory behaviour and to perpendicular trail escapes. We will then compare the full model to experimental results and find that it can both explain single-bacteria behaviour and collective microcolony formation of P. aeruginosa. The collective polysaccharide distributions can also be understood within the framework of a simple calculation inspired by network theory, which gives surprisingly good results.</p