Cue-driven microbial cooperation and communication: evolving quorum sensing with honest signaling.

BACKGROUND: Quorum sensing (QS) is the ability of microorganisms to assess local clonal density by measuring the extracellular concentration of signal molecules that they produce and excrete. QS is also the only known way of bacterial communication that supports the coordination of within-clone cooperative actions requiring a certain threshold density of cooperating cells. Cooperation aided by QS communication is sensitive to cheating in two different ways: laggards may benefit from not investing in cooperation but enjoying the benefit provided by their cooperating neighbors, whereas Liars explicitly promise cooperation but fail to do so, thereby convincing potential cooperating neighbors to help them, for almost free. Given this double vulnerability to cheats, it is not trivial why QS-supported cooperation is so widespread among prokaryotes. RESULTS: We investigated the evolutionary dynamics of QS in populations of cooperators for whom the QS signal is an inevitable side effect of producing the public good itself (cue-based QS). Using spatially explicit agent-based lattice simulations of QS-aided threshold cooperation (whereby cooperation is effective only above a critical cumulative level of contributions) and three different (analytical and numerical) approximations of the lattice model, we explored the dynamics of QS-aided threshold cooperation under a feasible range of parameter values. We demonstrate three major advantages of cue-driven cooperation. First, laggards cannot wipe out cooperation under a wide range of reasonable environmental conditions, in spite of an unconstrained possibility to mutate to cheating; in fact, cooperators may even exclude laggards at high cooperation thresholds. Second, lying almost never pays off, if the signal is an inevitable byproduct (i.e., the cue) of cooperation; even very cheap fake signals are selected against. And thirdly, QS is most useful if local cooperator densities are the least predictable, i.e., if their lattice-wise mean is close to the cooperation threshold with a substantial variance. CONCLUSIONS: Comparing the results of the four different modeling approaches indicates that cue-driven threshold cooperation may be a viable evolutionary strategy for microbes that cannot keep track of past behavior of their potential cooperating partners, in spatially viscous and in well-mixed environments alike. Our model can be seen as a version of the famous greenbeard effect, where greenbeards coexist with defectors in a evolutionarily stable polymorphism. Such polymorphism is maintained by the condition-dependent trade-offs of signal production which are characteristic of cue-based QS.

Cooperation in public goods game does not require assortment and depends on population density.

The threshold public goods game is one of the best-known models of non-linear public goods dilemmas. Cooperators and defectors typically coexist in this game when the population is assumed to follow the so-called structured deme model. In this article, we develop a dynamical model of a general N-player game in which there is no deme structure: Individuals interact with randomly chosen neighbours and selection occurs between randomly chosen pairs of individuals. We show that in the deterministic limit, the dynamics in this model leads to the same replicator dynamics as in the structured deme model, i.e., coexistence of cooperators and defectors is typical in threshold public goods game even when the population is completely well mixed. We extend the model to study the effect of density dependence and density fluctuation on the dynamics. We show analytically and numerically that decreasing population density increases the equilibrium frequency of cooperators till the fixation of this strategy, but below a critical density cooperators abruptly disappear from the population. Our numerical investigations show that weak density fluctuations enhance cooperation, while strong fluctuations suppress it.

A strategic model of a host-microbe-microbe system reveals the importance of a joint host-microbe immune response to combat stress-induced gut dysbiosis.

Microbiomes provide key ecological functions to their host; however, most host-associated microbiomes are too complicated to allow a model of essential host-microbe-microbe interactions. The intestinal microbiota of salmonids may offer a solution since few dominating species often characterize it. Healthy fish coexist with a mutualistic Mycoplasma sp. species, while stress allows the spread of pathogenic strains, such as Aliivibrio sp. Even after a skin infection, the Mycoplasma does not recover; Aliivibrio sp. often remains the dominant species, or Mycoplasma-Aliivibrio coexistence was occasionally observed. We devised a model involving interactions among the host immune system, Mycoplasma sp. plus a toxin-producing pathogen. Our model embraces a complete microbiota community and is in harmony with experimental results that host-Mycoplasma mutualism prevents the spread of pathogens. Contrary, stress suppresses the host immune system allowing dominance of pathogens, and Mycoplasma does not recover after stress disappears.

The Ecology of Spider Sociality: A Spatial Model.

AbstractThe emergence of animal societies offers unsolved problems for both evolutionary and ecological studies. Social spiders are especially well suited to address this problem given their multiple independent origins and distinct geographic distribution. On the basis of long-term research on the spider genus Anelosimus, we developed a spatial model that re-creates observed macroecological patterns in the distribution of social and subsocial spiders. We show that parallel gradients of increasing insect size and disturbance (rain, predation) with proximity to the lowland tropical rain forest would explain why social species are concentrated in the lowland wet tropics but absent from higher elevations and latitudes. The model further shows that disturbance, which disproportionately affects small colonies, not only creates conditions that require group living but also tempers the dynamics of large social groups. Similarly simple underlying processes, albeit with different players on a somewhat different stage, may explain the diversity of other social systems.

Weak selection helps cheap but harms expensive cooperation in spatial threshold dilemmas.

Public Goods Games (PGGs) are n-person games with dependence of individual fitness benefits on the collective investment by the players. We have studied a simple PGG scenario played out by cooperating (C) and defecting (D) agents, applying the highly nonlinear threshold benefit function in an individual-based lattice model. A semi-analytical approximation of the lattice model has been developed and shown to describe the dynamics fairly well in the vicinity of the steady state. Besides the expected outcomes (i.e., the negative effect on cooperator persistence of higher cooperation costs and/or more intensive mixing of the population) we have found a surprising, counter-intuitive effect of the strength of selection on the steady state of the model. The effect is different at low and high cooperation costs, and it shows up only in the lattice model, suggesting that stochastic effects and higher order spatial correlations due to the emergent spatial clustering of cooperators (not taken into account in the semi-analytical approximation) must be responsible for the unexpected results for which we propose an intuitive explanation, present a tentative demonstration, and shortly discuss their biological relevance.

Degree of anisogamy is unrelated to the intensity of sexual selection.

Males and females often display different behaviours and, in the context of reproduction, these behaviours are labelled sex roles. The Darwin-Bateman paradigm argues that the root of these differences is anisogamy (i.e., differences in size and/or function of gametes between the sexes) that leads to biased sexual selection, and sex differences in parental care and body size. This evolutionary cascade, however, is contentious since some of the underpinning assumptions have been questioned. Here we investigate the relationships between anisogamy, sexual size dimorphism, sex difference in parental care and intensity of sexual selection using phylogenetic comparative analyses of 64 species from a wide range of animal taxa. The results question the first step of the Darwin-Bateman paradigm, as the extent of anisogamy does not appear to predict the intensity of sexual selection. The only significant predictor of sexual selection is the relative inputs of males and females into the care of offspring. We propose that ecological factors, life-history and demography have more substantial impacts on contemporary sex roles than the differences of gametic investments between the sexes.

Density-dependent private benefit leads to bacterial mutualism.

Microorganisms produce and secrete materials that are beneficial for themselves and their neighbors. We modeled the situation when cells can produce different costly secretions which increase the carrying capacity of the population. Strains that lose the function of producing one or more secretions avoid the cost of production and can exhaust the producers. However, secreting substances provides a private benefit for the producers in a density-dependent way. We developed a model to examine the outcome of the selection among different types of producer strains from the nonproducer strain to the partial producers, to the full producer strain. We were interested in circumstances under which selection maintains partners that produce complementary secreted materials thus forming an interdependent mutualistic interaction. We show that interdependent mutualism is selected under a broad range of conditions if private benefit decreases with density. Selection frequently causes the coexistence of more and less generalist cooperative strains, thus cooperation and exploitation co-occur. Interdependent mutualism is evolved under more specific circumstances if private benefit increases with density and these general observations are valid in a well-mixed and a structured deme model. We show that the applied population structure allows the invasion of rare cooperators and supports cooperation in general.

Transition from growth to decay of an epidemic due to lockdown.

We study the transition of an epidemic from growth phase to decay of the active infections in a population when lockdown health measures are introduced to reduce the probability of disease transmission. Although in the case of uniform lockdown, a simple compartmental model would indicate instantaneous transition to decay of the epidemic, this is not the case when partially isolated active clusters remain with the potential to create a series of small outbreaks. We model this using the Gillespie stochastic simulation algorithm based on a connected set of stochastic susceptible-infected-removed/recovered networks representing the locked-down majority population (in which the reproduction number is less than 1) weakly coupled to a large set of small clusters in which the infection may propagate. We find that the presence of such active clusters can lead to slower than expected decay of the epidemic and significantly delayed onset of the decay phase. We study the relative contributions of these changes, caused by the active clusters within the population, to the additional total infected population. We also demonstrate that limiting the size of the inevitable active clusters can be efficient in reducing their impact on the overall size of the epidemic outbreak. The deceleration of the decay phase becomes apparent when the active clusters form at least 5% of the population.

Effects of social distancing on the spreading of COVID-19 inferred from mobile phone data.

A better understanding of how the COVID-19 pandemic responds to social distancing efforts is required for the control of future outbreaks and to calibrate partial lock-downs. We present quantitative relationships between key parameters characterizing the COVID-19 epidemiology and social distancing efforts of nine selected European countries. Epidemiological parameters were extracted from the number of daily deaths data, while mitigation efforts are estimated from mobile phone tracking data. The decrease of the basic reproductive number ([Formula: see text]) as well as the duration of the initial exponential expansion phase of the epidemic strongly correlates with the magnitude of mobility reduction. Utilizing these relationships we decipher the relative impact of the timing and the extent of social distancing on the total death burden of the pandemic.

Efficient assembly and long-term stability of defensive microbiomes via private resources and community bistability.

Understanding the mechanisms that promote the assembly and maintenance of host-beneficial microbiomes is an open problem. Empirical evidence supports the idea that animal and plant hosts can combine 'private resources' with the ecological phenomenon known as 'community bistability' to favour some microbial strains over others. We briefly review evidence showing that hosts can: (i) protect the growth of beneficial strains in an isolated habitat, (ii) use antibiotics to suppress non-beneficial, competitor strains, and (iii) provide resources that only beneficial strains are able to translate into an increased rate of growth, reproduction, or antibiotic production. We then demonstrate in a spatially explicit, individual-based model that these three mechanisms act similarly by selectively promoting the initial proliferation of preferred strains, that is, by acting as a private resource. The faster early growth of preferred strains, combined with the phenomenon of 'community bistability,' allows those strains to continue to dominate the microbiome even after the private resource is withdrawn or made public. This is because after a beneficial colony reaches a sufficiently large size, it can resist invasion by parasites without further private support from the host. We further explicitly model localized microbial interactions and diffusion dynamics, and we show that an intermediate level of antibiotic diffusion is the most efficient mechanism in promoting preferred strains and that there is a wide range of parameters under which hosts can promote the assembly of a self-sustaining defensive microbiome. This in turn supports the idea that hosts readily evolve to promote host-beneficial defensive microbiomes.

Variable Effect of HIV Superinfection on Clinical Status: Insights From Mathematical Modeling.

HIV superinfection (infection of an HIV positive individual with another strain of the virus) has been shown to result in a deterioration of clinical status in multiple case studies. However, superinfection with no (or positive) clinical outcome might easily go unnoticed, and the typical effect of superinfection is unknown. We analyzed mathematical models of HIV dynamics to assess the effect of superinfection under various assumptions. We extended the basic model of virus dynamics to explore systematically a set of model variants incorporating various details of HIV infection (homeostatic target cell dynamics, bystander killing, interference competition between viral clones, multiple target cell types, virus-induced activation of target cells). In each model, we identified the conditions for superinfection, and investigated whether and how successful invasion by a second viral strain affects the level of uninfected target cells. In the basic model, and in some of its extensions, the criteria for invasion necessarily entail a decrease in the equilibrium abundance of uninfected target cells. However, we identified three novel scenarios where superinfection can substantially increase the uninfected cell count: (i) if the rate of new infections saturates at high infectious titers (due to interference competition or cell-autonomous innate immunity); or when the invading strain is more efficient at infecting activated target cells, but less efficient at (ii) activating quiescent cells or (iii) inducing bystander killing of these cells. In addition, multiple target cell types also allow for modest increases in the total target cell count. We thus conclude that the effect of HIV superinfection on clinical status might be variable, complicated by factors that are independent of the invasion fitness of the second viral strain.

Ecology and Evolution in the RNA World Dynamics and Stability of Prebiotic Replicator Systems.

As of today, the most credible scientific paradigm pertaining to the origin of life on Earth is undoubtedly the RNA World scenario. It is built on the assumption that catalytically active replicators (most probably RNA-like macromolecules) may have been responsible for booting up life almost four billion years ago. The many different incarnations of nucleotide sequence (string) replicator models proposed recently are all attempts to explain on this basis how the genetic information transfer and the functional diversity of prebiotic replicator systems may have emerged, persisted and evolved into the first living cell. We have postulated three necessary conditions for an RNA World model system to be a dynamically feasible representation of prebiotic chemical evolution: (1) it must maintain and transfer a sufficient diversity of information reliably and indefinitely, (2) it must be ecologically stable and (3) it must be evolutionarily stable. In this review, we discuss the best-known prebiotic scenarios and the corresponding models of string-replicator dynamics and assess them against these criteria. We suggest that the most popular of prebiotic replicator systems, the hypercycle, is probably the worst performer in almost all of these respects, whereas a few other model concepts (parabolic replicator, open chaotic flows, stochastic corrector, metabolically coupled replicator system) are promising candidates for development into coherent models that may become experimentally accessible in the future.

Analysis of stability to cheaters in models of antibiotic degrading microbial communities.

Antibiotic resistance carried out by antibiotic degradation has been suggested recently as a new mechanism to maintain coexistence of microbial species competing on a single limiting resource, even in well-mixed homogeneous environments. Species diversity and community stability, however, critically depend on resistance against social cheaters, mutants that do not invest in production, but still enjoy the benefits provided by others. Here we investigate how different mutant cheaters affect the stability of antibiotic producing and degrading microbial communities. We consider two cheater types, production and degradation cheaters. We generalize the mixed inhibition-zone and chemostat models introduced previously [Kelsic, E. D., Zhao, J., Vetsigian, K., Kishony, R., 2015. Counteraction of an tibiotic production and degradation stabilizes microbial communities. Nature521, 516-519.] to study the population dynamics of microbial communities in well-mixed environment, and analyze the invasion of different cheaters in these models. We show that production cheaters, mutants that cease producing antibiotics, always destroy coexistence whenever there is a cost of producing these antibiotics. Degradation cheaters, mutants that loose their function of producing extracellular antibiotic degrading molecules, induce community collapse only if the cost of producing the degradation factors is above a critical level. Our analytical studies, supported by numerical simulations, highlight the sensitivity of antibiotic producing and degrading communities to loss-of-function mutants.

Evolution of optimal Hill coefficients in nonlinear public goods games.

In evolutionary game theory, the effect of public goods like diffusible molecules has been modelled using linear, concave, sigmoid and step functions. The observation that biological systems are often sigmoid input-output functions, as described by the Hill equation, suggests that a sigmoid function is more realistic. The Michaelis-Menten model of enzyme kinetics, however, predicts a concave function, and while mechanistic explanations of sigmoid kinetics exist, we lack an adaptive explanation: what is the evolutionary advantage of a sigmoid benefit function? We analyse public goods games in which the shape of the benefit function can evolve, in order to determine the optimal and evolutionarily stable Hill coefficients. We find that, while the dynamics depends on whether output is controlled at the level of the individual or the population, intermediate or high Hill coefficients often evolve, leading to sigmoid input-output functions that for some parameters are so steep to resemble a step function (an on-off switch). Our results suggest that, even when the shape of the benefit function is unknown, biological public goods should be modelled using a sigmoid or step function rather than a linear or concave function.

Deception Undermines the Stability of Cooperation in Games of Indirect Reciprocity.

Indirect reciprocity is often claimed as one of the key mechanisms of human cooperation. It works only if there is a reputational score keeping and each individual can inform with high probability which other individuals were good or bad in the previous round. Gossip is often proposed as a mechanism that can maintain such coherence of reputations in the face of errors of transmission. Random errors, however, are not the only source of uncertainty in such situations. The possibility of deceptive communication, where the signallers aim to misinform the receiver cannot be excluded. While there is plenty of evidence for deceptive communication in humans the possibility of deception is not yet incorporated into models of indirect reciprocity. Here we show that when deceptive strategies are allowed in the population it will cause the collapse of the coherence of reputations and thus in turn it results the collapse of cooperation. This collapse is independent of the norms and the cost and benefit values. It is due to the fact that there is no selection for honest communication in the framework of indirect reciprocity. It follows that indirect reciprocity can be only proposed plausibly as a mechanism of human cooperation if additional mechanisms are specified in the model that maintains honesty.

Evolution of heritable behavioural differences in a model of social division of labour.

The spectacular diversity of personality and behaviour of animals and humans has evoked many hypotheses intended to explain its developmental and evolutionary background. Although the list of the possible contributing mechanisms seems long, we propose that an underemphasised explanation is the division of labour creating negative frequency dependent selection. We use analytical and numerical models of social division of labour to show how selection can create consistent and heritable behavioural differences in a population, where randomly sampled individuals solve a collective task together. We assume that the collective task needs collaboration of individuals performing one of the two possible subtasks. The total benefit of the group is highest when the ratio of different subtasks is closest to 1. The probability of choosing one of the two costly subtasks and the costs assigned to them are under selection. By using adaptive dynamics we show that if a trade-off between the costs of the subtasks is strong enough, then evolution leads to coexistence of specialized individuals performing one of the subtasks with high probability and low cost. Our analytical results were verified and extended by numerical simulations.

Diffusive public goods and coexistence of cooperators and cheaters on a 1D lattice.

Many populations of cells cooperate through the production of extracellular materials. These materials (enzymes, siderophores) spread by diffusion and can be applied by both the cooperator and cheater (non-producer) cells. In this paper the problem of coexistence of cooperator and cheater cells is studied on a 1D lattice where cooperator cells produce a diffusive material which is beneficial to the individuals according to the local concentration of this public good. The reproduction success of a cell increases linearly with the benefit in the first model version and increases non-linearly (saturates) in the second version. Two types of update rules are considered; either the cooperative cell stops producing material before death (death-production-birth, DpB) or it produces the common material before it is selected to die (production-death-birth, pDB). The empty space is occupied by its neighbors according to their replication rates. By using analytical and numerical methods I have shown that coexistence of the cooperator and cheater cells is possible although atypical in the linear version of this 1D model if either DpB or pDB update rule is assumed. While coexistence is impossible in the non-linear model with pDB update rule, it is one of the typical behaviors in case of the non-linear model with DpB update rule.

Invasion of cooperators in lattice populations: linear and non-linear public good games.

A generalized version of the N-person volunteer's dilemma (NVD) Game has been suggested recently for illustrating the problem of N-person social dilemmas. Using standard replicator dynamics it can be shown that coexistence of cooperators and defectors is typical in this model. However, the question of how a rare mutant cooperator could invade a population of defectors is still open. Here we examined the dynamics of individual based stochastic models of the NVD. We analyze the dynamics in well-mixed and viscous populations. We show in both cases that coexistence between cooperators and defectors is possible; moreover, spatial aggregation of types in viscous populations can easily lead to pure cooperation. Furthermore we analyze the invasion of cooperators in populations consisting predominantly of defectors. In accordance with analytical results, in deterministic systems, we found the invasion of cooperators successful in the well-mixed case only if their initial concentration was higher than a critical threshold, defined by the replicator dynamics of the NVD. In the viscous case, however, not the initial concentration but the initial number determines the success of invasion. We show that even a single mutant cooperator can invade with a high probability, because the local density of aggregated cooperators exceeds the threshold defined by the game. Comparing the results to models using different benefit functions (linear or sigmoid), we show that the role of the benefit function is much more important in the well-mixed than in the viscous case.

Trading public goods stabilizes interspecific mutualism.

The existence of cooperation between species raises a fundamental problem for evolutionary theory. Why provide costly services to another species if the feedback of this provision also happens to benefit intra-specific competitors that provide no service? Rewarding cooperators and punishing defectors can help maintain mutualism; this is not possible, however, when one can only respond to the collective action of one's partners, which is likely to be the case in many common symbioses. We show how the theory of public goods can explain the stability of mutualism when discrimination between cooperators and defectors is not possible: if two groups of individuals trade goods that are non-linear, increasing functions of the number of contributions, their mutualistic interaction is maintained by the exchange of these public goods, even when it is not possible to punish defectors, which can persist at relatively high frequencies. This provides a theoretical justification and testable predictions for the evolution of mutualism in the absence of discrimination mechanisms.