Diversity in times of adversity: probabilistic strategies in microbial survival games

Population diversification strategies are ubiquitous among microbes, encompassing random phase-variation (RPV) of pathogenic bacteria, viral latency as observed in some bacteriophage and HIV, and the non-genetic diversity of bacterial stress responses. Precise conditions under which these diversification strategies confer an advantage have not been well defined. We develop a model of population growth conditioned on dynamical environmental and cellular states. Transitions among cellular states, in turn, may be biased by possibly noisy readings of the environment from cellular sensors. For various types of environmental dynamics and cellular sensor capability, we apply game-theoretic analysis to derive the evolutionarily stable strategy (ESS) for an organism and determine when that strategy is diversification. We find that: (1) RPV, effecting a sort of Parrondo paradox wherein random alternations between losing strategies produce a winning strategy, is selected when transitions between different selective environments cannot be sensed, (2) optimal RPV cell switching rates are a function of environmental lifecycle asymmetries and environmental autocorrelation, (3) probabilistic diversification upon entering a new environment is selected when sensors can detect environmental transitions but have poor precision in identifying new environments, and (4) in the presence of excess additive noise, low-pass filtering is required for evolutionary stability. We show that even when RPV is not the ESS, it may minimize growth rate variance and the risk of extinction due to 'unlucky' environmental dynamics.     

Switching and Growth for Microbial Populations in Catastrophic Responsive Environments

Phase variation, or stochastic switching between alternative states of gene expression, is common among microbes, and may be important in coping with changing environments. We use a theoretical model to assess whether such switching is a good strategy for growth in environments with occasional catastrophic events. We find that switching can be advantageous, but only when the environment is responsive to the microbial population. In our model, microbes switch randomly between two phenotypic states, with different growth rates. The environment undergoes sudden catastrophes, the probability of which depends on the composition of the population. We derive a simple analytical result for the population growth rate. For a responsive environment, two alternative strategies emerge. In the no-switching strategy, the population maximizes its instantaneous growth rate, regardless of catastrophes. In the switching strategy, the microbial switching rate is tuned to minimize the environmental response. Which of these strategies is most favorable depends on the parameters of the model. Previous studies have shown that microbial switching can be favorable when the environment changes in an unresponsive fashion between several states. Here, we demonstrate an alternative role for phase variation in allowing microbes to maximize their growth in catastrophic responsive environments.     

Stochastic gene expression in fluctuating environments

Stochastic mechanisms can cause a group of isogenic bacteria, each subject to identical environmental conditions, to nevertheless exhibit diverse patterns of gene expression. The resulting phenotypic subpopulations will typically have distinct growth rates. This behavior has been observed in several contexts, including sugar metabolism and pili phase variation. Under fixed environmental conditions, the net growth rate of the population is maximized when all cells are of the fastest growing phenotype, so it is unclear what fitness advantage is conferred by population heterogeneity. However, unlike ideal laboratory conditions, natural environments tend to fluctuate, either periodically or randomly. Here we use a stochastic population model to show that, during growth in such fluctuating environments, a dynamically heterogenous bacterial population can sometimes achieve a higher net growth rate than a homogenous one. By using stochastic mechanisms to sample several distinct phenotypes, the bacteria are able to anticipate and take advantage of sudden changes in their environment. However, this heterogeneity is beneficial only if the bacterial response rate is sufficiently low. Our results could be useful in the design of artificial evolution experiments and in the optimization of fermentation processes.     

Bacterial persistence: a model of survival in changing environments

The persistence phenotype is an epigenetic trait exhibited by a subpopulation of bacteria, characterized by slow growth coupled with an ability to survive antibiotic treatment. The phenotype is acquired via a spontaneous, reversible switch between normal and persister cells. These observations suggest that clonal bacterial populations may use persister cells, whose slow division rate under growth conditions leads to lower population fitness, as an "insurance policy" against antibiotic encounters. We present a model of Escherichia coli persistence, and using experimentally derived parameters for both wild type and a mutant strain (hipQ) with markedly different switching rates, we show how fitness loss due to slow persister growth pays off as a risk-reducing strategy. We demonstrate that wild-type persistence is suited for environments in which antibiotic stress is a rare event. The optimal rate of switching between normal and persister cells is found to depend strongly on the frequency of environmental changes and only weakly on the selective pressures of any given environment. In contrast to typical examples of adaptations to features of a single environment, persistence appears to constitute an adaptation that is tuned to the distribution of environmental change.     

Exclusion rules, bottlenecks and the evolution of stochastic phenotype switching

Stochastic phenotype switching--often considered a bet hedging or risk-reducing strategy--can enhance the probability of survival in fluctuating environments. A recent experiment provided direct evidence for an adaptive origin by showing the de novo evolution of switching in bacterial populations propagated under a selective regime that captured essential features of the host immune response. The regime involved strong frequency-dependent selection realized via dual imposition of an exclusion rule and population bottleneck. Applied at the point of transfer between environments, the phenotype common in the current environment was assigned a fitness of zero and was thus excluded from participating in the next round (the exclusion rule). In addition, also at the point of transfer, and so as to found the next bout of selection, a single phenotypically distinct type was selected at random from among the survivors (the bottleneck). Motivated by this experiment, we develop a mathematical model to explore the broader significance of key features of the selective regime. Through a combination of analytical and numerical results, we show that exclusion rules and population bottlenecks act in tandem as potent selective agents for stochastic phenotype switching, such that even when initially rare, and when switching engenders a cost in Malthusian fitness, organisms with the capacity to switch can invade non-switching populations and replace non-switching types. Simulations demonstrate the robustness of our findings to alterations in switching rate, fidelity of exclusion, bottleneck size, duration of environmental state and growth rate. We also demonstrate the relevance of our model to a range of biological scenarios such as bacterial persistence and the evolution of sex.     

Phenotype Switching and Mutations in Random Environments

Cell populations can benefit from changing phenotype when the environment changes. One mechanism for generating these changes is stochastic phenotype switching, whereby cells switch stochastically from one phenotype to another according to genetically determined rates, irrespective of the current environment, with the matching of phenotype to environment then determined by selective pressure. This mechanism has been observed in numerous contexts, but identifying the precise connection between switching rates and environmental changes remains an open problem. Here, we introduce a simple model to study the evolution of phenotype switching in a finite population subject to random environmental shocks. We compare the successes of competing genotypes with different switching rates, and analyze how the optimal switching rates depend on the frequency of environmental changes. If environmental changes are as rare as mutations, then the optimal switching rates mimic the rates of environmental changes. If the environment changes more frequently, then the optimal genotype either maximally favors fitness in the more common environment or has the maximal switching rate to each phenotype. Our results also explain why the optimum is relatively insensitive to fitness in each environment.     

Hysteresis Can Grant Fitness in Stochastically Varying Environment

Although the existence of multiple stable phenotypes of living organisms enables random switching between phenotypes as well as non-random history dependent switching called hysteresis, only random switching has been considered in prior experimental and theoretical models of adaptation to variable environments. This work considers the possibility that hysteresis may also evolve together with random phenotype switching to maximize population growth. In addition to allowing the possibility that switching rates between different phenotypes may depend not only on a continuous environmental input variable, but also on the phenotype itself, the present work considers an opportunity cost of the switching events. This opportunity cost arises as a result of a lag phase experimentally observed after phenotype switching and stochastic behavior of the environmental input. It is shown that stochastic environmental variation results in maximal asymptotic growth rate when organisms display hysteresis for sufficiently slowly varying environmental input. At the same time, sinusoidal input does not cause evolution of memory suggesting that the connection between the lag phase, stochastic environmental variation and evolution of hysteresis is a result of a stochastic resonance type phenomenon.     

The evolutionary emergence of stochastic phenotype switching in bacteria

Stochastic phenotype switching - or bet hedging - is a pervasive feature of living systems and common in bacteria that experience fluctuating (unpredictable) environmental conditions. Under such conditions, the capacity to generate variable offspring spreads the risk of being maladapted in the present environment, against offspring likely to have some chance of survival in the future. While a rich subject for theoretical studies, little is known about the selective causes responsible for the evolutionary emergence of stochastic phenotype switching. Here we review recent work - both theoretical and experimental - that sheds light on ecological factors that favour switching types over non-switching types. Of particular relevance is an experiment that provided evidence for an adaptive origin of stochastic phenotype switching by subjecting bacterial populations to a selective regime that mimicked essential features of the host immune response. Central to the emergence of switching types was frequent imposition of 'exclusion rules' and 'population bottlenecks' - two complementary faces of frequency dependent selection. While features of the immune response, exclusion rules and bottlenecks are likely to operate in many natural environments. Together these factors define a set of selective conditions relevant to the evolution of stochastic switching, including antigenic variation and bacterial persistence.     

The evolution of bet-hedging adaptations to rare scenarios

When faced with a variable environment, organisms may switch between different strategies according to some probabilistic rule. In an infinite population, evolution is expected to favor the rule that maximizes geometric mean fitness. If some environments are encountered only rarely, selection may not be strong enough for optimal switching probabilities to evolve. Here we calculate the evolution of switching probabilities in a finite population by analyzing fixation probabilities of alleles specifying switching rules. We calculate the conditions required for the evolution of phenotypic switching as a form of bet-hedging as a function of the population size N, the rate theta at which a rare environment is encountered, and the selective advantage s associated with switching in the rare environment. We consider a simplified model in which environmental switching and phenotypic switching are one-way processes, and mutation is symmetric and rare with respect to the timescale of fixation events. In this case, the approximate requirements for bet-hedging to be favored by a ratio of at least R are that sN>log(R) and thetaN>square root R .     

Steady-state running rate sets the speed and accuracy of accumulation of swimming bacteria

We study the chemotaxis of a population of genetically identical swimming bacteria undergoing run and tumble dynamics driven by stochastic switching between clockwise and counterclockwise rotation of the flagellar rotary system, where the steady-state rate of the switching changes in different environments. Understanding chemotaxis quantitatively requires that one links the measured steady-state switching rates of the rotary system, as well as the directional changes of individual swimming bacteria in a gradient of chemoattractant/repellant, to the efficiency of a population of bacteria in moving up/down the gradient. Here we achieve this by using a probabilistic model, parametrized with our experimental data, and show that the response of a population to the gradient is complex. We find the changes to the steady-state switching rate in the absence of gradients affect the average speed of the swimming bacterial population response as well as the width of the distribution. Both must be taken into account when optimizing the overall response of the population in complex environments.     

Memory shapes microbial populations

Correct decision making is fundamental for all living organisms to thrive under environmental changes. The patterns of environmental variation and the quality of available information define the most favourable strategy among multiple options, from randomly adopting a phenotypic state to sensing and reacting to environmental cues. Cellular memory—the ability to track and condition the time to switch to a different phenotypic state—can help withstand environmental fluctuations. How does memory manifest itself in unicellular organisms? We describe the population-wide consequences of phenotypic memory in microbes through a combination of deterministic modelling and stochastic simulations. Moving beyond binary switching models, our work highlights the need to consider a broader range of switching behaviours when describing microbial adaptive strategies. We show that memory in individual cells generates patterns at the population level coherent with overshoots and non-exponential lag times distributions experimentally observed in phenotypically heterogeneous populations. We emphasise the implications of our work in understanding antibiotic tolerance and, in general, bacterial survival under fluctuating environments.     

EVOLUTION AND EXTINCTION IN A CHANGING ENVIRONMENT: A QUANTITATIVE-GENETIC ANALYSIS

Because of the ubiquity of genetic variation for quantitative traits, virtually all populations have some capacity to respond evolutionarily to selective challenges. However, natural selection imposes demographic costs on a population, and if these costs are sufficiently large, the likelihood of extinction will be high. We consider how the mean time to extinction depends on selective pressures (rate and stochasticity of environmental change, and strength of selection), population parameters (carrying capacity, and reproductive capacity), and genetics (rate of polygenic mutation). We assume that in a randomly mating, finite population subject to density-dependent population growth, individual fitness is determined by a single quantitative-genetic character under Gaussian stabilizing selection with the optimum phenotype exhibiting directional change, or random fluctuations, or both. The quantitative trait is determined by a finite number of freely recombining, mutationally equivalent, additive loci. The dynamics of evolution and extinction are investigated, assuming that the population is initially under mutation-selection-drift balance. Under this model, in a directionally changing environment, the mean phenotype lags behind the optimum, but on the average evolves parallel to it. The magnitude of the lag determines the vulnerability to extinction. In finite populations, stochastic variation in the genetic variance can be quite pronounced, and bottlenecks in the genetic variance temporarily can impair the population's adaptive capacity enough to cause extinction when it would otherwise be unlikely in an effectively infinite population. We find that maximum sustainable rates of evolution or, equivalently, critical rates of environmental change, may be considerably less than 10% of a phenotypic standard deviation per generation.     

Contact switching as a control strategy for epidemic outbreaks

We study the effects of switching social contacts as a strategy to control epidemic outbreaks. Connections between susceptible and infective individuals can be broken by either individual, and then reconnected to a randomly chosen member of the population. It is assumed that the reconnecting individual has no previous information on the epidemiological condition of the new contact. We show that reconnection can completely suppress the disease, both by continuous and discontinuous transitions between the endemic and the infection-free states. For diseases with an asymptomatic phase, we analyze the conditions for the suppression of the disease, and show that—even when these conditions are not met—the increase of the endemic infection level is usually rather small. We conclude that, within some simple epidemiological models, contact switching is a quite robust and effective control strategy. This suggests that it may also be an efficient method in more complex situations.     

Evolution of learning in fluctuating environments: when selection favors both social and exploratory individual learning

Cumulative cultural change requires organisms that are capable of both exploratory individual learning and faithful social learning. In our model, an organism's phenotype is initially determined innately (by its genotypic value) or by social learning (copying a phenotype from the parental generation), and then may or may not be modified by individual learning (exploration around the initial phenotype). The environment alternates periodically between two states, each defined as a certain range of phenotypes that can survive. These states may overlap, in which case the same phenotype can survive in both states, or they may not. We find that a joint social and exploratory individual learning strategy-the strategy that supports cumulative culture-is likely to spread when the environmental states do not overlap. In particular, when the environmental states are contiguous and mutation is allowed among the genotypic values, this strategy will spread in either moderately or highly stable environments, depending on the exact nature of the individual learning applied. On the other hand, natural selection often favors a social learning strategy without exploration when the environmental states overlap. We find only partial support for the "consensus" view, which holds that individual learning, social learning, and innate determination of behavior will evolve at short, intermediate, and long environmental periodicities, respectively.     

The Population and Evolutionary Dynamics of Homologous Gene Recombination in Bacteria

In bacteria, recombination is a rare event, not a part of the reproductive process. Nevertheless, recombination—broadly defined to include the acquisition of genes from external sources, i.e., horizontal gene transfer (HGT)—plays a central role as a source of variation for adaptive evolution in many species of bacteria. Much of niche expansion, resistance to antibiotics and other environmental stresses, virulence, and other characteristics that make bacteria interesting and problematic, is achieved through the expression of genes and genetic elements obtained from other populations of bacteria of the same and different species, as well as from eukaryotes and archaea. While recombination of homologous genes among members of the same species has played a central role in the development of the genetics and molecular biology of bacteria, the contribution of homologous gene recombination (HGR) to bacterial evolution is not at all clear. Also, not so clear are the selective pressures responsible for the evolution and maintenance of transformation, the only bacteria-encoded form of HGR. Using a semi-stochastic simulation of mutation, recombination, and selection within bacterial populations and competition between populations, we explore (1) the contribution of HGR to the rate of adaptive evolution in these populations and (2) the conditions under which HGR will provide a bacterial population a selective advantage over non-recombining or more slowly recombining populations. The results of our simulation indicate that, under broad conditions: (1) HGR occurring at rates in the range anticipated for bacteria like Streptococcus pneumoniae, Escherichia coli, Haemophilus influenzae, and Bacillus subtilis will accelerate the rate at which a population adapts to environmental conditions; (2) once established in a population, selection for this capacity to increase rates of adaptive evolution can maintain bacteria-encoded mechanisms of recombination and prevent invasion of non-recombining populations, even when recombination engenders a modest fitness cost; and (3) because of the density- and frequency-dependent nature of HGR in bacteria, this capacity to increase rates of adaptive evolution is not sufficient as a selective force to provide a recombining population a selective advantage when it is rare. Under realistic conditions, homologous gene recombination will increase the rate of adaptive evolution in bacterial populations and, once established, selection for higher rates of evolution will promote the maintenance of bacteria-encoded mechanisms for HGR. On the other hand, increasing rates of adaptive evolution by HGR is unlikely to be the sole or even a dominant selective pressure responsible for the original evolution of transformation.     

Optimal resting-growth strategies of microbial populations in fluctuating environments

Bacteria spend most of their lifetime in non-growing states which allow them to survive extended periods of stress and starvation. When environments improve, they must quickly resume growth to maximize their share of limited nutrients. Cells with higher stress resistance often survive longer stress durations at the cost of needing more time to resume growth, a strong disadvantage in competitive environments. Here we analyze the basis of optimal strategies that microorganisms can use to cope with this tradeoff. We explicitly show that the prototypical inverse relation between stress resistance and growth rate can explain much of the different types of behavior observed in stressed microbial populations. Using analytical mathematical methods, we determine the environmental parameters that decide whether cells should remain vegetative upon stress exposure, downregulate their metabolism to an intermediate optimum level, or become dormant. We find that cell-cell variability, or intercellular noise, is consistently beneficial in the presence of extreme environmental fluctuations, and that it provides an efficient population-level mechanism for adaption in a deteriorating environment. Our results reveal key novel aspects of responsive phenotype switching and its role as an adaptive strategy in changing environments.     

Genome hyperevolution and the success of a parasite

The strategy of antigenic variation is to present a constantly changing population phenotype that enhances parasite transmission, through evasion of immunity arising within, or existing between, host animals. Trypanosome antigenic variation occurs through spontaneous switching among members of a silent archive of many hundreds of variant surface glycoprotein (VSG) antigen genes. As with such contingency systems in other pathogens, switching appears to be triggered through inherently unstable DNA sequences. The archive occupies subtelomeres, a genome partition that promotes hypermutagenesis and, through telomere position effects, singular expression of VSG. Trypanosome antigenic variation is augmented greatly by the formation of mosaic genes from segments of pseudo-VSG, an example of implicit genetic information. Hypermutation occurs apparently evenly across the whole archive, without direct selection on individual VSG, demonstrating second-order selection of the underlying mechanisms. Coordination of antigenic variation, and thereby transmission, occurs through networking of trypanosome traits expressed at different scales from molecules to host populations.