Tipping points emerge from weak mutualism in metacommunities.

The coexistence of obligate mutualists is often precariously close to tipping points where small environmental changes can drive catastrophic shifts in species composition. For example, microbial ecosystems can collapse by the decline of a strain that provides an essential resource on which other strains cross-feed. Here, we show that tipping points, ecosystem collapse, bistability and hysteresis arise even with very weak (non-obligate) mutualism provided the population is spatially structured. Based on numeric solutions of a metacommunity model and mean-field analyses, we demonstrate that weak mutualism lowers the minimal dispersal rate necessary to avoid stochastic extinction, while species need to overcome a mean threshold density to survive in this low dispersal rate regime. Our results allow us to make numerous predictions for mutualistic metacommunities regarding tipping points, hysteresis effects, and recovery from external perturbations, and let us draw general conclusions for ecosystems even with random, not necessarily mutualistic, interactions and systems with density-dependent dispersal rather than direct mutualistic interactions.

Rediversification following ecotype isolation reveals hidden adaptive potential.

Microbial communities play a critical role in ecological processes, and their diversity is key to their functioning. However, little is known about whether communities can regenerate ecological diversity following ecotype removal or extinction and how the rediversified communities would compare to the original ones. Here, we show that simple two-ecotype communities from the E. coli long-term evolution experiment (LTEE) consistently rediversified into two ecotypes following the isolation of one of the ecotypes, coexisting via negative frequency-dependent selection. Communities separated by more than 30,000 generations of evolutionary time rediversify in similar ways. The rediversified ecotype appears to share a number of growth traits with the ecotype it replaces. However, the rediversified community is also different from the original community in ways relevant to the mechanism of ecotype coexistence-for example, in stationary phase response and survival. We found substantial variation in the transcriptional states between the two original ecotypes, whereas the differences within the rediversified community were comparatively smaller, although the rediversified community showed unique patterns of differential expression. Our results suggest that evolution may leave room for alternative diversification processes even in a maximally reduced community of only two strains. We hypothesize that the presence of alternative evolutionary pathways may be even more pronounced in communities of many species where there are even more potential niches, highlighting an important role for perturbations, such as species removal, in evolving ecological communities.

Rediversification Following Ecotype Isolation Reveals Hidden Adaptive Potential.

Microbial communities play a critical role in ecological processes, and their diversity is key to their functioning. However, little is known about if communities can regenerate ecological diversity following species removal or extinction, and how the rediversified communities would compare to the original ones. Here we show that simple two-ecotype communities from the E. coli Long Term Evolution Experiment (LTEE) consistently rediversified into two ecotypes following the isolation of one of the ecotypes, coexisting via negative frequency-dependent selection. Communities separated by more than 30,000 generations of evolutionary time rediversify in similar ways. The rediversified ecotype appears to share a number of growth traits with the ecotype it replaces. However, the rediversified community is also different compared to the original community in ways relevant to the mechanism of ecotype coexistence, for example in stationary phase response and survival. We found substantial variation in the transcriptional states between the two original ecotypes, whereas the differences within the rediversified community were comparatively smaller, but with unique patterns of differential expression. Our results suggest that evolution may leave room for alternative diversification processes even in a maximally reduced community of only two strains. We hypothesize that the presence of alternative evolutionary pathways may be even more pronounced in communities of many species, highlighting an important role for perturbations, such as species removal, in evolving ecological communities.

Self-consistent dispersal puts tight constraints on the spatiotemporal organization of species-rich metacommunities.

Biodiversity is often attributed to a dynamic equilibrium between the immigration and extinction of species. This equilibrium forms a common basis for studying ecosystem assembly from a static reservoir of migrants-the mainland. Yet, natural ecosystems often consist of many coupled communities (i.e., metacommunities), and migration occurs between these communities. The pool of migrants then depends on what is sustained in the ecosystem, which, in turn, depends on the dynamic migrant pool. This chicken-and-egg problem of survival and dispersal is poorly understood in communities of many competing species, except for the neutral case-the "unified neutral theory of biodiversity." Employing spatiotemporal simulations and mean-field analyses, we show that self-consistent dispersal puts rather tight constraints on the dynamic migration-extinction equilibrium. When the number of species is large, species are pushed to the edge of their global extinction, even when competition is weak. As a consequence, the overall diversity is highly sensitive to perturbations in demographic parameters, including growth and dispersal rates. When dispersal is short range, the resulting spatiotemporal abundance patterns follow broad scale-free distributions that correspond to a directed percolation phase transition. The qualitative agreement of our results for short-range and long-range dispersal suggests that this self-organization process is a general property of species-rich metacommunities. Our study shows that self-sustaining metacommunities are highly sensitive to environmental change and provides insights into how biodiversity can be rescued and maintained.

Snowdrift game induces pattern formation in systems of self-propelled particles.

Evolutionary games between species are known to lead to intriguing spatiotemporal patterns in systems of diffusing agents. However, the role of interspecies interactions is hardly studied when agents are (self-)propelled, as is the case in many biological systems. Here, we combine aspects from active matter and evolutionary game theory and study a system of two species whose individuals are (self-)propelled and interact through a snowdrift game. We derive hydrodynamic equations for the density and velocity fields of both species from which we identify parameter regimes in which one or both species form macroscopic orientational order as well as regimes of propagating wave patterns. Interestingly, we find simultaneous wave patterns in both species that result from the interplay between alignment and snowdrift interactions-a feedback mechanism that we call game-induced pattern formation. We test these results in agent-based simulations and confirm the different regimes of order and spatiotemporal patterns as well as game-induced pattern formation.

Pattern-induced local symmetry breaking in active-matter systems.

The emergence of macroscopic order and patterns is a central paradigm in systems of (self-)propelled agents and a key component in the structuring of many biological systems. The relationships between the ordering process and the underlying microscopic interactions have been extensively explored both experimentally and theoretically. While emerging patterns often show one specific symmetry (e.g., nematic lane patterns or polarized traveling flocks), depending on the symmetry of the alignment interactions patterns with different symmetries can apparently coexist. Indeed, recent experiments with an actomysin motility assay suggest that polar and nematic patterns of actin filaments can interact and dynamically transform into each other. However, theoretical understanding of the mechanism responsible remains elusive. Here, we present a kinetic approach complemented by a hydrodynamic theory for agents with mixed alignment symmetries, which captures the experimentally observed phenomenology and provides a theoretical explanation for the coexistence and interaction of patterns with different symmetries. We show that local, pattern-induced symmetry breaking can account for dynamically coexisting patterns with different symmetries. Specifically, in a regime with moderate densities and a weak polar bias in the alignment interaction, nematic bands show a local symmetry-breaking instability within their high-density core region, which induces the formation of polar waves along the bands. These instabilities eventually result in a self-organized system of nematic bands and polar waves that dynamically transform into each other. Our study reveals a mutual feedback mechanism between pattern formation and local symmetry breaking in active matter that has interesting consequences for structure formation in biological systems.

MinE conformational switching confers robustness on self-organized Min protein patterns.

Protein patterning is vital for many fundamental cellular processes. This raises two intriguing questions: Can such intrinsically complex processes be reduced to certain core principles and, if so, what roles do the molecular details play in individual systems? A prototypical example for protein patterning is the bacterial Min system, in which self-organized pole-to-pole oscillations of MinCDE proteins guide the cell division machinery to midcell. These oscillations are based on cycling of the ATPase MinD and its activating protein MinE between the membrane and the cytoplasm. Recent biochemical evidence suggests that MinE undergoes a reversible, MinD-dependent conformational switch from a latent to a reactive state. However, the functional relevance of this switch for the Min network and pattern formation remains unclear. By combining mathematical modeling and in vitro reconstitution of mutant proteins, we dissect the two aspects of MinE's switch, persistent membrane binding and a change in MinE's affinity for MinD. Our study shows that the MinD-dependent change in MinE's binding affinity for MinD is essential for patterns to emerge over a broad and physiological range of protein concentrations. Mechanistically, our results suggest that conformational switching of an ATPase-activating protein can lead to the spatial separation of its distinct functional states and thereby confer robustness on an intracellular protein network with vital roles in bacterial cell division.

Ecological suicide in microbes.

The growth and survival of organisms often depend on interactions between them. In many cases, these interactions are positive and caused by a cooperative modification of the environment. Examples are the cooperative breakdown of complex nutrients in microbes or the construction of elaborate architectures in social insects, in which the individual profits from the collective actions of her peers. However, organisms can similarly display negative interactions by changing the environment in ways that are detrimental for them, for example by resource depletion or the production of toxic byproducts. Here we find an extreme type of negative interactions, in which Paenibacillus sp. bacteria modify the environmental pH to such a degree that it leads to a rapid extinction of the whole population, a phenomenon that we call ecological suicide. Modification of the pH is more pronounced at higher population densities, and thus ecological suicide is more likely to occur with increasing bacterial density. Correspondingly, promoting bacterial growth can drive populations extinct whereas inhibiting bacterial growth by the addition of harmful substances-such as antibiotics-can rescue them. Moreover, ecological suicide can cause oscillatory dynamics, even in single-species populations. We found ecological suicide in a wide variety of microbes, suggesting that it could have an important role in microbial ecology and evolution.

Active Curved Polymers Form Vortex Patterns on Membranes.

Recent in vitro experiments with FtsZ polymers show self-organization into different dynamic patterns, including structures reminiscent of the bacterial Z ring. We model FtsZ polymers as active particles moving along chiral, circular paths by Brownian dynamics simulations and a Boltzmann approach. Our two conceptually different methods point to a generic phase behavior. At intermediate particle densities, we find self-organization into vortex structures including closed rings. Moreover, we show that the dynamics at the onset of pattern formation is described by a generalized complex Ginzburg-Landau equation.