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.     

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.     

Selective consequences of catastrophes for growth rates in a stream-dwelling salmonid

Optimal life histories in a fluctuating environment are likely to differ from those that are optimal in a constant environment, but we have little understanding of the consequences of bounded fluctuations versus episodic massive mortality events. Catastrophic disturbances, such as floods, droughts, landslides and fires, substantially alter the population dynamics of affected populations, but little has been done to investigate how catastrophes may act as a selective agent for life-history traits. We use an individual-based model of population dynamics of the stream-dwelling salmonid marble trout (Salmo marmoratus) to investigate how trade-offs between the growth and mortality of individuals and density-dependent body growth can lead to the maintenance of a wide or narrow range of individual variation in body growth rates in environments that are constant (i.e., only demographic stochasticity), variable (i.e., environmental stochasticity), or variable with catastrophic events that cause massive mortalities (e.g., flash floods). We find that occasional episodes of massive mortality can substantially reduce persistent variability in individual growth rates. Lowering the population density reduces density dependence and allows for higher fitness of more opportunistic strategies (rapid growth and early maturation) during the recovery period.     

A microbial modified prisoner's dilemma game: how frequency-dependent selection can lead to random phase variation

Random phase variation (RPV) is a control strategy in which the expression of a cell state or phenotype randomly alternates between discrete 'on' and 'off' states. Though this mode of control is common for bacterial virulence factors like pili and toxins, precise conditions under which RPV confers an advantage have not been well defined. In Part I of this study, we predicted that fluctuating environments select for RPV if transitions between different selective environments cannot be reliably sensed (J. Theor. Biol. (2005)). However, selective forces both inside and outside of human hosts are also likely to be frequency dependent in the sense that the fitnesses of some bacterial states are greatest when rare. Here we show that RPV at slow rates can provide a survival advantage in such a frequency-dependent environment by generating population heterogeneity, essentially mimicking a polymorphism. More surprisingly, RPV at a faster 'optimal' rate can shift the population composition toward an optimal growth rate that exceeds that possible for polymorphic populations, but this optimal strategy is not evolutionarily stable. The population would be most fit if all cells randomly phase varied at the optimal rate, but individual cells have a growth-rate incentive to defect (mutate) to other switching rates or non-phase variable phenotype expression, leading to an overall loss of fitness of the individual and the population. This scenario describes a modified Prisoner's Dilemma game (Evolution and the Theory of Games, Cambridge University Press, Cambridge, New York, 1982, viii, 224pp.; Nature 398 (6726) (1999) 367), with random phase variation at optimal switching rates serving as the cooperation strategy.     

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.     

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.     

Sheltered from the storm? Population viability analysis of a rare endemic under periodic catastrophe regimes

Rare species are important targets for biodiversity conservation efforts because rarity often equates to small populations and increased endangerment. Rare species are prone to stochastic extinction events and may be particularly susceptible to catastrophes. Therefore, understanding how rare species respond to disturbances is critical for evaluating extinction risk and guiding conservation managers. Population viability analyses (PVAs) are essential for assessing rare species' status yet they seldom consider catastrophic events. Accordingly, we present a PVA of a rare tropical epiphyte, Lepanthes caritensis (Orchidaceae), under simulated disturbance regimes to evaluate its demographics and extinction risk. We aimed to test how demographic models incorporating catastrophes affect population viability estimates. Our goal was to better guide management of these orchids and other rare plants. Results revealed L. caritensis numbers have declined recently, but projected growth rates indicated that most subpopulations should increase in size if undisturbed. Still, projection models show that moderate catastrophes reduce growth rates, increase stochasticity in subpopulation sizes, and elevate extinction risk. Severe catastrophes had a more pronounced effect in simulations; growth rates fell below replacement level, there was greater variation in projected population sizes, and extinction risk was significantly higher. PVAs incorporating periodic catastrophes indicate that rare species may have greater extinction probabilities than standard models suggest. Thus, precautionary conservation measures should be taken in disturbance prone settings and we encourage careful monitoring after environmental catastrophes. Future rare plant PVAs should incorporate catastrophes and aim to determine if rescue and reintroduction efforts are necessary after disturbances to insure long-term population viability.     

Survival and colonisation potential of photoautotrophic microorganisms within a glacierised catchment on Svalbard, High Arctic

The survival and colonisation potential of photoautotrophic microbes (cyanobacteria and microalgae) were investigated in three terrestrial environments within a glacierised catchment on Svalbard: old vegetation-covered soil, recently deglaciated barren soil and subglacial sediments. One-year reciprocal transplant incubations of photoautotrophic microbial communities from the three soil/sediment environments were conducted in order to reveal the autochthonous or allochthonous origin of the present photoautotrophs. The abundance and taxonomic composition of photoautotrophic microbes and their changes over time and between soil/sediment types and physico-chemical characteristics of the soils/sediments were determined. The recovery time of a photoautotrophic community by import of cells was between several months in subglacial and vegetated soils and up to 27 years in proglacial soils. No active growth was recorded in subglacial sediments, whilst positive growth, and so the potential for autochthonous recovery, was found in proglacial and vegetated soils. The most suitable environment for the survival of transplanted microbes was provided in proglacial soil. We show here that the new proglacial substrata can be successfully colonised by photoautotrophic microbes, and that input of allochthonous cells may, in some cases, exceed in situ microbial growth. Whilst the subglacial environment is rather a conduit for photoautotrophic microbes than a place of growth and production, the supply of viable photoautotrophs in it is relatively high and may serve as a significant resource of nutrients for subglacial microbial communities.     

Perception and Regulatory Principles of Microbial Growth Control

Fast growth represents an effective strategy for microbial organisms to survive in competitive environments. To accomplish this task, cells must adapt their metabolism to changing nutrient conditions in a way that maximizes their growth rate. However, the regulation of the growth related metabolic pathways can be fundamentally different among microbes. We therefore asked whether growth control by perception of the cell’s intracellular metabolic state can give rise to higher growth than by direct perception of extracellular nutrient availability. To answer this question, we created a simplified dynamical computer model of a cellular metabolic network whose regulation was inferred by an optimization approach. We used this model for a competing species experiment, where a species with extracellular nutrient perception competes against one with intracellular nutrient perception by evaluating their respective average growth rate. We found that the intracellular perception is advantageous under situations where the up and down regulation of pathways cannot follow the fast changing nutrient availability in the environment. In this case, optimal regulation ignores any other nutrients except the most preferential ones, in agreement with the phenomenon of catabolite repression in prokaryotes. The corresponding metabolic pathways remain activated, despite environmental fluctuations. Therefore, the cell can take up preferential nutrients as soon as they are available without any prior regulation. As a result species that rely on intracellular perception gain a relevant fitness advantage in fluctuating nutrient environments, which enables survival by outgrowing competitors.     

Harvesting in seasonal environments

Most harvest theory is based on an assumption of a constant or stochastic environment, yet most populations experience some form of environmental seasonality. Assuming that a population follows logistic growth we investigate harvesting in seasonal environments, focusing on maximum annual yield (M.A.Y.) and population persistence under five commonly used harvest strategies. We show that the optimal strategy depends dramatically on the intrinsic growth rate of population and the magnitude of seasonality. The ordered effectiveness of these alternative harvest strategies is given for different combinations of intrinsic growth rate and seasonality. Also, for piecewise continuous-time harvest strategies (i.e., open / closed harvest, and pulse harvest) harvest timing is of crucial importance to annual yield. Optimal timing for harvests coincides with maximal rate of decline in the seasonally fluctuating carrying capacity. For large intrinsic growth rate and small environmental variability several strategies (i.e., constant exploitation rate, linear exploitation rate, and time-dependent harvest) are so effective that M.A.Y. is very close to maximum sustainable yield (M.S.Y.). M.A.Y. of pulse harvest can be even larger than M.S.Y. because in seasonal environments population size varies substantially during the course of the year and how it varies relative to the carrying capacity is what determines the value relative to optimal harvest rate. However, for populations with small intrinsic growth rate but subject to large seasonality none of these strategies is particularly effective with M.A.Y. much lower than M.S.Y. Finding an optimal harvest strategy for this case and to explore harvesting in populations that follow other growth models (e.g., involving predation or age structure) will be an interesting but challenging problem.     

Environmental Uncertainty and Variable Diapause

We analyze a stage-structured model of a population that displays variable diapause in a randomly varying environment. The ruggedness of the environment is measured by the extent of random variation in per-capita reproductive success. We show how variable diapause and environmental characteristics affect the population′s stochastic growth rate. In rugged unpredictable environments, phenotypes that show some tendency to diapause are found to have a higher growth rate than nondiapausing phenotypes. In harsh rugged environments, some tendency to diapause may be all that permits population persistence. Positive serial autocorrelation causes the optimal diapause fraction to decrease, while negative autocorrelation causes that fraction to increase. The structured model behaves very differently from a scalar model for large diapause fractions even in uncorrelated environments, and in many cases predicts a broad optimum. The difference between models is due to the extreme variability of stage structure in populations subject to even small variability when diapause tendency is high.     

Population bottlenecks constrain host microbiome diversity and genetic variation impeding fitness

It is becoming increasingly clear that microbial symbionts influence key aspects of their host’s fitness, and vice versa. This may fundamentally change our thinking about how microbes and hosts interact in influencing fitness and adaptation to changing environments. Here we explore how reductions in population size commonly experienced by threatened species influence microbiome diversity. Consequences of such reductions are normally interpreted in terms of a loss of genetic variation, increased inbreeding and associated inbreeding depression. However, fitness effects of population bottlenecks might also be mediated through microbiome diversity, such as through loss of functionally important microbes. Here we utilise 50 Drosophila melanogaster lines with different histories of population bottlenecks to explore these questions. The lines were phenotyped for egg-to-adult viability and their genomes sequenced to estimate genetic variation. The bacterial 16S rRNA gene was amplified in these lines to investigate microbial diversity. We found that 1) host population bottlenecks constrained microbiome richness and diversity, 2) core microbiomes of hosts with low genetic variation were constituted from subsets of microbiomes found in flies with higher genetic variation, 3) both microbiome diversity and host genetic variation contributed to host population fitness, 4) connectivity and robustness of bacterial networks was low in the inbred lines regardless of host genetic variation, 5) reduced microbial diversity was associated with weaker evolutionary responses of hosts in stressful environments, and 6) these effects were unrelated to Wolbachia density. These findings suggest that population bottlenecks reduce hologenomic variation (combined host and microbial genetic variation). Thus, while the current biodiversity crisis focuses on population sizes and genetic variation of eukaryotes, an additional focal point should be the microbial diversity carried by the eukaryotes, which in turn may influence host fitness and adaptability with consequences for the persistence of populations.     

Mycorrhiza and Phosphate Solubilizing Bacteria: Potential Bioagents for Sustainable Phosphorus Management in Agriculture

Phosphorus (P) is a critical nutrient that plays an essential role in improving soil fertility for optimum plant growth and productivity. It is one of the most deficient macro-nutrients in agricultural soils after nitrogen and is considered inadequate for plant growth and production. To P availability in soils, the farmers are applying huge amounts of synthetic P fertilizers that adversely affect the wider environment, groundwater, soil fertility and microbial population. Many beneficial microbes are known to release and supply soluble P for improving growth and yield of a variety of plants in a sustainable manner in P deficient soils. Thus, inoculation of these microbes, including arbuscular mycorrhizal fungi (AMF) and phosphate solubilizing bacteria (PSB) to soil to enhance crop production without harming the environment, is an alternative approach to chemical fertilizers. The combined role of AMF and PSB in P solubilization is not well understood and the application and mode of action of these microbial groups are often naive due to variation in the environment. Therefore, the current review article would develop a better understanding of the interactive role and mechanisms of AMF and PSB in improving P availability from both organic and inorganic sources in a sustainable crop production system. Finally, the current review would loop out further avenues for researchers interested to commercially produce effective AMF and PSB-based biofertilizers for sustainable management of phosphorus over a wide range of agricultural crops worldwide.     

Pathogen evolution in switching environments: A hybrid dynamical system approach

We propose a hybrid dynamical system approach to model the evolution of a pathogen that experiences different selective pressures according to a stochastic process. In every environment, the evolution of the pathogen is described by a version of the Fisher-Haldane-Wright equation while the switching between environments follows a Markov jump process. We investigate how the qualitative behavior of a simple single-host deterministic system changes when the stochastic switching process is added. In particular, we study the stability in probability of monomorphic equilibria. We prove that in a "constantly" fluctuating environment, the genotype with the highest mean fitness is asymptotically stable in probability while all others are unstable in probability. However, if the probability of host switching depends on the genotype composition of the population, polymorphism can be stably maintained.     

Temporal variation can facilitate niche evolution in harsh sink environments

We examine the impact of temporal variation on adaptive evolution in "sink" environments, where a species encounters conditions outside its niche. Sink populations persist because of recurrent immigration from sources. Prior studies have highlighted the importance of demographic constraints on adaptive evolution in sinks and revealed that adaptation is less likely in harsher sinks. We examine two complementary models of population and evolutionary dynamics in sinks: a continuous-state quantitative-genetics model and an individual-based model. In the former, genetic variance is fixed; in the latter, genetic variance varies because of mutation, drift, and sampling. In both models, a population in a constant harsh sink environment can exist in alternative states: local maladaptation (phenotype comparable to immigrants from the source) or adaptation (phenotype near the local optimum). Temporal variation permits transitions between these states. We show that moderate amounts of temporal variation can facilitate adaptive evolution in sinks, permitting niche evolution, particularly for slow or autocorrelated variation. Such patterns of temporal variation may particularly pertain to sinks caused by biotic interactions (e.g., predation). Our results are relevant to the evolutionary dynamics of species' ranges, the fate of exotic invasive species, and the evolutionary emergence of infectious diseases into novel hosts.     

Decomposing Predation: Testing for Parameters that Correlate with Predatory Performance by a Social Bacterium

Predator–prey interactions presumably play major roles in shaping the composition and dynamics of microbial communities. However, little is understood about the population biology of such interactions or how predation-related parameters vary or correlate across prey environments. Myxococcus xanthus is a motile soil bacterium that feeds on a broad range of other soil microbes that vary greatly in the degree to which they support M. xanthus growth. In order to decompose predator–prey interactions at the population level, we quantified five predation-related parameters during M. xanthus growth on nine phylogenetically diverse bacterial prey species. The horizontal expansion rate of swarming predator colonies fueled by prey lawns served as our measure of overall predatory performance, as it incorporates both the searching (motility) and handling (killing and consumption of prey) components of predation. Four other parameters—predator population growth rate, maximum predator yield, maximum prey kill, and overall rate of prey death—were measured from homogeneously mixed predator–prey lawns from which predator populations were not allowed to expand horizontally by swarming motility. All prey species fueled predator population growth. For some prey, predator-specific prey death was detected contemporaneously with predator population growth, whereas killing of other prey species was detected only after cessation of predator growth. All four of the alternative parameters were found to correlate significantly with predator swarm expansion rate to varying degrees, suggesting causal interrelationships among these diverse predation measures. More broadly, our results highlight the importance of examining multiple parameters for thoroughly understanding the population biology of microbial predation.     

Modeling of the forest insect population size: a game theory approach

A game theory model of insect population dynamics is proposed. For the case when the population may be in one of two states: when physiological processes are directed to growth and reproduction, and when physiological processes are directed to the development of defense reactions, outbreaks of mass reproduction of insect populations may occur in conditions when population and environment have the "memory", and the state of population and environment depends on their state at the previous time moment. In the framework of the model, the well known effect of insect phase variation during the outbreak of reproduction is explained.     

Applying population and community ecology theory to advance understanding of belowground biogeochemistry

Approaches to quantifying and predicting soil biogeochemical cycles mostly consider microbial biomass and community composition as products of the abiotic environment. Current numerical approaches then primarily emphasise the importance of microbe–environment interactions and physiology as controls on biogeochemical cycles. Decidedly less attention has been paid to understanding control exerted by community dynamics and biotic interactions. Yet a rich literature of theoretical and empirical contributions highlights the importance of considering how variation in microbial population ecology, especially biotic interactions, is related to variation in key biogeochemical processes like soil carbon formation. We demonstrate how a population and community ecology perspective can be used to (1) understand the impact of microbial communities on biogeochemical cycles and (2) reframe current theory and models to include more detailed microbial ecology. Through a series of simulations we illustrate how density dependence and key biotic interactions, such as competition and predation, can determine the degree to which microbes regulate soil biogeochemical cycles. The ecological perspective and model simulations we present lay the foundation for developing empirical research and complementary models that explore the diversity of ecological mechanisms that operate in microbial communities to regulate biogeochemical processes.     

Evolution of stress response in the face of unreliable environmental signals

Most organisms live in ever-changing environments, and have to cope with a range of different conditions. Often, the set of biological traits that are needed to grow, reproduce, and survive varies between conditions. As a consequence, organisms have evolved sensory systems to detect environmental signals, and to modify the expression of biological traits in response. However, there are limits to the ability of such plastic responses to cope with changing environments. Sometimes, environmental shifts might occur suddenly, and without preceding signals, so that organisms might not have time to react. Other times, signals might be unreliable, causing organisms to prepare themselves for changes that then do not occur. Here, we focus on such unreliable signals that indicate the onset of adverse conditions. We use analytical and individual-based models to investigate the evolution of simple rules that organisms use to decide whether or not to switch to a protective state. We find evolutionary transitions towards organisms that use a combination of random switching and switching in response to the signal. We also observe that, in spatially heterogeneous environments, selection on the switching strategy depends on the composition of the population, and on population size. These results are in line with recent experiments that showed that many unicellular organisms can attain different phenotypic states in a probabilistic manner, and lead to testable predictions about how this could help organisms cope with unreliable signals.