Statistical and Biological Physics

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The fate of every species depends on its ability to colonize new area and to defend it from invaders. Examples of successful range expansions encompass the human migration out of Africa and the recent spreading of pandemic diseases. unfortunately, natural range expansions are exceedingly complex and experimental control is most often lacking. Such control is, however, needed to calibrate mathematical models that can predict whether a species has the ability to survive. While the study of ecological processes remains a difficult challenge on the global scale, new methods of control are currently emerging for life on the microscopic scale. We investigated range expansion abilities for a system of three Escherichia coli strains: a toxin producing strain, a sensitive strain (facing death upon the encounter of toxins), and a resistant strain. Genetic engineering allowed us to study range expansions of the three strains in different ecological scenarios, including a rock-paper-scissors scenario. We acquired experimental data to calibrate a mathematical model of the bacterial expansion that correctly predicted the strains with successful survival strategies. The model allowed us to describe the relationship between factors that influence a strain’s chance of survival in terms of phenomenological "biodiversity laws". Our work provides a thorough analysis of the bacterial model system and demonstrates how integration of experimental study with mathematical modelling benefits the understanding of ecological systems. more

In this letter we study how topological defects affect the degree of polar and crystalline order in active matter at high densities. To this end, we analyze a generic agent-based model, which accounts for both polar alignment and shorted-ranged repulsive interaction. We show that, while defects still play a decisive role, the emerging defect dynamics and phase behavior differ qualitatively from their equilibrium analogues. In active systems, the non-equilibrium steady states include different types of polycrystalline phases, and an intriguing crystalline phase with quasi-long-range translational order but completely devoid of any topological defects. Moreover, we find that absence of defects and polar order are mutually exclusive features. When alignment forces dominate over repulsive forces, polar states are favored. The resulting collective particle flux makes the system highly susceptible to the spontaneous formation of grain boundaries and thereby repeatedly creates small crystalline patches. These spontaneous fracture-like processes are accompanied by propagating sound waves. In contrast, in systems with strong repulsive forces the formation of a crystalline state precludes the formation of collectively moving clusters. Surprisingly, the phonon modes in this active crystalline state lead to quasi-long-range order but the fluctuations generated by the active particle motion do not create topological defects. more