Resist or perish: Fate of a microbial population subjected to a periodic presence of antimicrobial

Mutant fate in spatially structured populations on graphs: Connecting models to experiments

In nature, most microbial populations have complex spatial structures that can affect their evolution. Evolutionary graph theory predicts that some spatial structures modelled by placing individuals on the nodes of a graph affect the probability that a mutant will fix. Evolution experiments are beginning to explicitly address the impact of graph structures on mutant fixation. However, the assumptions of evolutionary graph theory differ from the conditions of modern evolution experiments, making the comparison between theory and experiment challenging. Here, we aim to bridge this gap by using our new model of spatially structured populations. This model considers connected subpopulations that lie on the nodes of a graph, and allows asymmetric migrations. It can handle large populations, and explicitly models serial passage events with migrations, thus closely mimicking experimental conditions. We analyze recent experiments in light of this model. We suggest useful parameter regimes for future experiments, and we make quantitative predictions for these experiments. In particular, we propose experiments to directly test our recent prediction that the star graph with asymmetric migrations suppresses natural selection and can accelerate mutant fixation or extinction, compared to a well-mixed population.

The many dimensions of combination therapy: How to combine antibiotics to limit resistance evolution

In combination therapy, bacteria are challenged with two or more antibiotics simultaneously. Ideally, separate mutations are required to adapt to each of them, which is a priori expected to hinder the evolution of full resistance. Yet, the success of this strategy ultimately depends on how well the combination controls the growth of bacteria with and without resistance mutations. To design a combination treatment, we need to choose drugs and their doses and decide how many drugs get mixed. Which combinations are good? To answer this question, we set up a stochastic pharmacodynamic model and determine the probability to successfully eradicate a bacterial population. We consider bacteriostatic and two types of bactericidal drugs-those that kill independent of replication and those that kill during replication. To establish results for a null model, we consider non-interacting drugs and implement the two most common models for drug independence-Loewe additivity and Bliss independence. Our results show that combination therapy is almost always better in limiting the evolution of resistance than administering just one drug, even though we keep the total drug dose constant for a 'fair' comparison. Yet, exceptions exist for drugs with steep dose-response curves. Combining a bacteriostatic and a bactericidal drug which can kill non-replicating cells is particularly beneficial. Our results suggest that a 50:50 drug ratio-even if not always optimal-is usually a good and safe choice. Applying three or four drugs is beneficial for treatment of strains with large mutation rates but adding more drugs otherwise only provides a marginal benefit or even a disadvantage. By systematically addressing key elements of treatment design, our study provides a basis for future models which take further factors into account. It also highlights conceptual challenges with translating the traditional concepts of drug independence to the single-cell level.

Optimizing Antimicrobial Treatment Schedules: Some Fundamental Analytical Results

This work studies fundamental questions regarding the optimal design of antimicrobial treatment protocols, using pharmacodynamic and pharmacokinetic mathematical models. We consider the problem of designing an antimicrobial treatment schedule to achieve eradication of a microbial infection, while minimizing the area under the time-concentration curve (AUC), which is equivalent to minimizing the cumulative dosage. We first solve this problem under the assumption that an arbitrary antimicrobial concentration profile may be chosen, and prove that the ideal concentration profile consists of a constant concentration over a finite time duration, where explicit expressions for the optimal concentration and the time duration are given in terms of the pharmacodynamic parameters. Since antimicrobial concentration profiles are induced by a dosing schedule and the antimicrobial pharmacokinetics, the 'ideal' concentration profile is not strictly feasible. We therefore also investigate the possibility of achieving outcomes which are close to those provided by the 'ideal' concentration profile, using a bolus+continuous dosing schedule, which consists of a loading dose followed by infusion of the antimicrobial at a constant rate. We explicitly find the optimal bolus+continuous dosing schedule, and show that, for realistic parameter ranges, this schedule achieves results which are nearly as efficient as those attained by the 'ideal' concentration profile. The optimality results obtained here provide a baseline and reference point for comparison and evaluation of antimicrobial treatment plans.

Frequent asymmetric migrations suppress natural selection in spatially structured populations

Natural microbial populations often have complex spatial structures. This can impact their evolution, in particular the ability of mutants to take over. While mutant fixation probabilities are known to be unaffected by sufficiently symmetric structures, evolutionary graph theory has shown that some graphs can amplify or suppress natural selection, in a way that depends on microscopic update rules. We propose a model of spatially structured populations on graphs directly inspired by batch culture experiments, alternating within-deme growth on nodes and migration-dilution steps, and yielding successive bottlenecks. This setting bridges models from evolutionary graph theory with Wright-Fisher models. Using a branching process approach, we show that spatial structure with frequent migrations can only yield suppression of natural selection. More precisely, in this regime, circulation graphs, where the total incoming migration flow equals the total outgoing one in each deme, do not impact fixation probability, while all other graphs strictly suppress selection. Suppression becomes stronger as the asymmetry between incoming and outgoing migrations grows. Amplification of natural selection can nevertheless exist in a restricted regime of rare migrations and very small fitness advantages, where we recover the predictions of evolutionary graph theory for the star graph.

Coupled environmental and demographic fluctuations shape the evolution of cooperative antimicrobial resistance

There is a pressing need to better understand how microbial populations respond to antimicrobial drugs, and to find mechanisms to possibly eradicate antimicrobial-resistant cells. The inactivation of antimicrobials by resistant microbes can often be viewed as a cooperative behaviour leading to the coexistence of resistant and sensitive cells in large populations and static environments. This picture is, however, greatly altered by the fluctuations arising in volatile environments, in which microbial communities commonly evolve. Here, we study the eco-evolutionary dynamics of a population consisting of an antimicrobial-resistant strain and microbes sensitive to antimicrobial drugs in a time-fluctuating environment, modelled by a carrying capacity randomly switching between states of abundance and scarcity. We assume that antimicrobial resistance (AMR) is a shared public good when the number of resistant cells exceeds a certain threshold. Eco-evolutionary dynamics is thus characterised by demographic noise (birth and death events) coupled to environmental fluctuations which can cause population bottlenecks. By combining analytical and computational means, we determine the environmental conditions for the long-lived coexistence and fixation of both strains, and characterise a fluctuation-driven AMR eradication mechanism, where resistant microbes experience bottlenecks leading to extinction. We also discuss the possible applications of our findings to laboratory-controlled experiments.

Genus Streptomyces: Recent advances for biotechnological purposes

Actinomycetes are a distinct group of filamentous bacteria. The Streptomyces genus within this group has been extensively studied over the years, with substantial contributions to society and science. This genus is known for its antimicrobial production, as well as antitumor, biopesticide, and immunomodulatory properties. Therefore, the extraordinary plasticity of the Streptomyces genus has inspired new research techniques. The newest way of exploring Streptomyces has comprised the discovery of new natural metabolites and the application of emerging tools such as CRISPR technology in drug discovery. In this narrative review, we explore relevant published literature concerning the ongoing novelties of the Streptomyces genus.

A stochastic analysis of the interplay between antibiotic dose, mode of action, and bacterial competition in the evolution of antibiotic resistance

The use of an antibiotic may lead to the emergence and spread of bacterial strains resistant to this antibiotic. Experimental and theoretical studies have investigated the drug dose that minimizes the risk of resistance evolution over the course of treatment of an individual, showing that the optimal dose will either be the highest or the lowest drug concentration possible to administer; however, no analytical results exist that help decide between these two extremes. To address this gap, we develop a stochastic mathematical model of bacterial dynamics under antibiotic treatment. We explore various scenarios of density regulation (bacterial density affects cell birth or death rates), and antibiotic modes of action (biostatic or biocidal). We derive analytical results for the survival probability of the resistant subpopulation until the end of treatment, the size of the resistant subpopulation at the end of treatment, the carriage time of the resistant subpopulation until it is replaced by a sensitive one after treatment, and we verify these results with stochastic simulations. We find that the scenario of density regulation and the drug mode of action are important determinants of the survival of a resistant subpopulation. Resistant cells survive best when bacterial competition reduces cell birth and under biocidal antibiotics. Compared to an analogous deterministic model, the population size reached by the resistant type is larger and carriage time is slightly reduced by stochastic loss of resistant cells. Moreover, we obtain an analytical prediction of the antibiotic concentration that maximizes the survival of resistant cells, which may help to decide which drug dosage (not) to administer. Our results are amenable to experimental tests and help link the within and between host scales in epidemiological models.

Lotka-Volterra predator-prey model with periodically varying carrying capacity

We study the stochastic spatial Lotka-Volterra model for predator-prey interaction subject to a periodically varying carrying capacity. The Lotka-Volterra model with on-site lattice occupation restrictions (i.e., finite local carrying capacity) that represent finite food resources for the prey population exhibits a continuous active-to-absorbing phase transition. The active phase is sustained by the existence of spatiotemporal patterns in the form of pursuit and evasion waves. Monte Carlo simulations on a two-dimensional lattice are utilized to investigate the effect of seasonal variations of the environment on species coexistence. The results of our simulations are also compared to a mean-field analysis in order to specifically delineate the impact of stochastic fluctuations and spatial correlations. We find that the parameter region of predator and prey coexistence is enlarged relative to the stationary situation when the carrying capacity varies periodically. The (quasi-)stationary regime of our periodically varying Lotka-Volterra predator-prey system shows qualitative agreement between the stochastic model and the mean-field approximation. However, under periodic carrying capacity-switching environments, the mean-field rate equations predict period-doubling scenarios that are washed out by internal reaction noise in the stochastic lattice model. Utilizing visual representations of the lattice simulations and dynamical correlation functions, we study how the pursuit and evasion waves are affected by ensuing resonance effects. Correlation function measurements indicate a time delay in the response of the system to sudden changes in the environment. Resonance features are observed in our simulations that cause prolonged persistent spatial correlations. Different effective static environments are explored in the extreme limits of fast and slow periodic switching. The analysis of the mean-field equations in the fast-switching regime enables a semiquantitative description of the (quasi-)stationary state.

Controlling the Mean Time to Extinction in Populations of Bacteria

Populations of ecological systems generally have demographic fluctuations due to birth and death processes. At the same time, they are exposed to changing environments. We studied populations composed of two phenotypes of bacteria and analyzed the impact that both types of fluctuations have on the mean time to extinction of the entire population if extinction is the final fate. Our results are based on Gillespie simulations and on the WKB approach applied to classical stochastic systems, here in certain limiting cases. As a function of the frequency of environmental changes, we observe a non-monotonic dependence of the mean time to extinction. Its dependencies on other system parameters are also explored. This allows the control of the mean time to extinction to be as large or as small as possible, depending on whether extinction should be avoided or is desired from the perspective of bacteria or the perspective of hosts to which the bacteria are deleterious.

Modulation of antibiotic effects on microbial communities by resource competition

Antibiotic treatment significantly impacts the human gut microbiota, but quantitative understanding of how antibiotics affect community diversity is lacking. Here, we build on classical ecological models of resource competition to investigate community responses to species-specific death rates, as induced by antibiotic activity or other growth-inhibiting factors such as bacteriophages. Our analyses highlight the complex dependence of species coexistence that can arise from the interplay of resource competition and antibiotic activity, independent of other biological mechanisms. In particular, we identify resource competition structures that cause richness to depend on the order of sequential application of antibiotics (non-transitivity), and the emergence of synergistic and antagonistic effects under simultaneous application of multiple antibiotics (non-additivity). These complex behaviors can be prevalent, especially when generalist consumers are targeted. Communities can be prone to either synergism or antagonism, but typically not both, and antagonism is more common. Furthermore, we identify a striking overlap in competition structures that lead to non-transitivity during antibiotic sequences and those that lead to non-additivity during antibiotic combination. In sum, our results establish a broadly applicable framework for predicting microbial community dynamics under deleterious perturbations.

Interplay between strain fitness and transmission frequency determines prevalence of antimicrobial resistance

The steep rise of infections caused by bacteria that are resistant to antimicrobial agents threatens global health. However, the association between antimicrobial use and the prevalence of resistance is not straightforward. Therefore, it is necessary to quantify the importance of additional factors that affect this relationship. We theoretically explore how the prevalence of resistance is affected by the combination of three factors: antimicrobial use, bacterial transmission, and fitness cost of resistance. We present a model that combines within-host, between-hosts and between-populations dynamics, built upon the competitive Lotka-Volterra equations. We developed the model in a manner that allows future experimental validation of the findings with single isolates in the laboratory. Each host may carry two strains (susceptible and resistant) that represent the host’s commensal microbiome and are not the target of the antimicrobial treatment. The model simulates a population of hosts who are treated periodically with antibiotics and transmit bacteria to each other. We show that bacterial transmission results in strain co-existence. Transmission disseminates resistant bacteria in the population, increasing the levels of resistance. Counterintuitively, when the cost of resistance is low, high transmission frequencies reduce resistance prevalence. Transmission between host populations leads to more similar resistance levels, increasing the susceptibility of the population with higher antimicrobial use. Overall, our results indicate that the interplay between bacterial transmission and strain fitness affects the prevalence of resistance in a non-linear way. We then place our results within the context of ecological theory, particularly on temporal niche partitioning and metapopulation rescue, and we formulate testable experimental predictions for future research.

A novel approach for combining the metagenome, metaresistome, metareplicome and causal inference to determine the microbes and their antibiotic resistance gene repertoire that contribute to dysbiosis

The use of whole metagenomic data to infer the relative abundance of all its microbes is well established. The same data can be used to determine the replication rate of all eubacterial taxa with circular chromosomes. Despite their availability, the replication rate profiles (metareplicome) have not been fully exploited in microbiome analyses. Another relatively new approach is the application of causal inferencing to analyse microbiome data that goes beyond correlational studies. A novel scalable pipeline called MeRRCI (Metagenome, metaResistome, and metaReplicome for Causal Inferencing) was developed. MeRRCI combines efficient computation of the metagenome (bacterial relative abundance), metaresistome (antimicrobial gene abundance) and metareplicome (replication rates), and integrates environmental variables (metadata) for causality analysis using Bayesian networks. MeRRCI was applied to an infant gut microbiome data set to investigate the microbial community's response to antibiotics. Our analysis suggests that the current treatment stratagem contributes to preterm infant gut dysbiosis, allowing a proliferation of pathobionts. The study highlights the specific antibacterial resistance genes that may contribute to exponential cell division in the presence of antibiotics for various pathogens, namely Klebsiella pneumoniae, Citrobacter freundii, Staphylococcus epidermidis, Veilonella parvula and Clostridium perfringens. These organisms often contribute to the harmful long-term sequelae seen in these young infants.

Evolution in fluctuating environments: A generic modular approach

Evolutionary processes take place in fluctuating environments, where carrying capacities and selective forces vary over time. The fate of a mutant type and the persistence time of polymorphic states were studied in some specific cases of varying environments, but a generic methodology is still lacking. Here, we present such a general analytic framework. We first identify a set of elementary building blocks, a few basic demographic processes like logistic or exponential growth, competition at equilibrium, sudden decline, and so on. For each of these elementary blocks, we evaluate the mean and the variance of the changes in the frequency of the mutant population. Finally, we show how to find the relevant terms of the diffusion equation for each arbitrary combination of these blocks. Armed with this technique one may calculate easily the quantities that govern the evolutionary dynamics, like the chance of ultimate fixation, the time to absorption, and the time to fixation.

Reversion is most likely under high mutation supply when compensatory mutations do not fully restore fitness costs

The dynamics of adaptation, reversion, and compensation have been central topics in microbial evolution, and several studies have attempted to resolve the population genetics underlying how these dynamics occur. However, questions remain regarding how certain features-the evolution of mutators and whether compensatory mutations alleviate costs fully or partially-may influence the evolutionary dynamics of compensation and reversion. In this study, we attempt to explain findings from experimental evolution by utilizing computational and theoretical approaches toward a more refined understanding of how mutation rate and the fitness effects of compensatory mutations influence adaptive dynamics. We find that high mutation rates increase the probability of reversion toward the wild type when compensation is only partial. However, the existence of even a single fully compensatory mutation is associated with a dramatically decreased probability of reversion to the wild type. These findings help to explain specific results from experimental evolution, where compensation was observed in nonmutator strains, but reversion (sometimes with compensation) was observed in mutator strains, indicating that real-world compensatory mutations are often unable to fully alleviate the costs associated with adaptation. Our findings emphasize the potential role of the supply and quality of mutations in crafting the dynamics of adaptation and reversal, with implications for theoretical population genetics and for biomedical contexts like the evolution of antibiotic resistance.

Quantifying the impact of ecological memory on the dynamics of interacting communities

Ecological memory refers to the influence of past events on the response of an ecosystem to exogenous or endogenous changes. Memory has been widely recognized as a key contributor to the dynamics of ecosystems and other complex systems, yet quantitative community models often ignore memory and its implications.

Recent modeling studies have shown how interactions between community members can lead to the emergence of resilience and multistability under environmental perturbations. We demonstrate how memory can be introduced in such models using the framework of fractional calculus. We study how the dynamics of a well-characterized interaction model is affected by gradual increases in ecological memory under varying initial conditions, perturbations, and stochasticity.

Our results highlight the implications of memory on several key aspects of community dynamics. In general, memory introduces inertia into the dynamics. This favors species coexistence under perturbation, enhances system resistance to state shifts, mitigates hysteresis, and can affect system resilience both ways depending on the time scale considered. Memory also promotes long transient dynamics, such as long-standing oscillations and delayed regime shifts, and contributes to the emergence and persistence of alternative stable states. Our study highlights the fundamental role of memory in communities, and provides quantitative tools to introduce it in ecological models and analyse its impact under varying conditions.

An ecosystem is said to exhibit ecological memory when its future states do not only depend on its current state but also on its initial state and trajectory. Memory may arise through various mechanisms as organisms adapt to their environment, modify it, and accumulate biotic and abiotic material. It may also emerge from phenotypic heterogeneity at the population level. Despite its commonness in nature, ecological memory and its potential influence on ecosystem dynamics have been so far overlooked in many applied contexts. Here, we use modeling to investigate how memory can influence the dynamics, composition, and stability landscape of communities. We incorporate long-term memory effects into a multi-species model recently introduced to investigate alternative stable states in microbial communities. We assess the impact of memory on key aspects of model behavior and further examine our findings using a model parameterized by empirical data from the human gut microbiota. Our approach for modeling long-term memory and studying its implications has the potential to improve our understanding of microbial community dynamics and ultimately our ability to predict, manipulate, and experimentally design microbial ecosystems. It could also be applied more broadly in the study of systems composed of interacting components.

Kinetics of bactericidal potency with synergistic combination of allicin and selected antibiotics

Synergistic therapy against the resurgence of bacterial pathogenesis is a modern trend for antibacterial chemotherapy. The phytochemical allicin, found in garlic extract is a commendable antimicrobial agent that can be used in synergistic combination with modern antibiotics. Determination of optimal antibacterial combination for the target species is vital for maximizing efficacy, lowering toxicity, total eradication of the bacterial cells and minimization of the risk of resistance generation. In this present investigation, Hill function-based pharmacodynamics models were employed to elaborate various time-kill kinetics parameters. The bactericidal potency of the synergistic combinations of allicin and individual antibiotic was assessed in comparison to their monotherapy application viz. using sole allicin and sole antibiotics (levofloxacin, ciprofloxacin, oxytetracycline, rifaximin, ornidazole and azithromycin) on actively growing Bacillus subtilis and Escherichia coli bacteria. Here, all the synergistic combinations showed significantly better (t-test p-value < 0.05) killing effect and biofilm reduction potential compared to their respective monotherapy application, where the highest killing effect was observed with rifaximin-allicin combination (kill rate was more than 5.5 h^-1). Moreover, the average inhibition potential to protein denaturation by the synergistic combination group was significantly higher (3.4 fold) than the sole antibiotic's group manifests reduction in the dose-related toxicity. The potential of synergism between antibiotics and allicin combination demonstrated greater killing efficiency at significantly lower concentration compared to monotherapy with increased kill rates in all cases.

Population genetics, biofilm recalcitrance, and antibiotic resistance evolution

Biofilms are communities of bacteria forming high-density sessile colonies. Such a lifestyle comes associated with costs and benefits: while the growth rate of biofilms is often lower than that of their free-living counterparts, this cost is readily repaid once the colony is subjected to antibiotics. Biofilms can grow in antibiotic concentrations a thousand times higher than planktonic bacteria. While numerous mechanisms have been proposed to explain biofilm recalcitrance towards antibiotics, little is yet known about their effect on the evolution of resistance. We synthesize the current understanding of biofilm recalcitrance from a pharmacodynamic and a population genetics perspective. Using the pharmacodynamic framework, we discuss the effects of various mechanisms and show that biofilms can either promote or impede resistance evolution.

Stochastic response of bacterial cells to antibiotics: its mechanisms and implications for population and evolutionary dynamics

The effectiveness of antibiotics against bacterial infections has been declining due to the emergence of resistance. Precisely understanding the response of bacteria to antibiotics is critical to maximizing antibiotic-induced bacterial eradication while minimizing the emergence of antibiotic resistance. Cell-to-cell heterogeneity in antibiotic susceptibility is observed across various bacterial species for a wide range of antibiotics. Heterogeneity in antibiotic susceptibility is not always due to the genetic differences. Rather, it can be caused by non-genetic mechanisms such as stochastic gene expression and biased partitioning upon cell division. Heterogeneous susceptibility leads to the stochastic growth and death of individual cells and stochastic fluctuations in population size. These fluctuations have important implications for the eradication of bacterial populations and the emergence of genotypic resistance.

Taming the diffusion approximation through a controlling-factor WKB method

The diffusion approximation (DA) is widely used in the analysis of stochastic population dynamics, from population genetics to ecology and evolution. The DA is an uncontrolled approximation that assumes the smoothness of the calculated quantity over the relevant state space and fails when this property is not satisfied. This failure becomes severe in situations where the direction of selection switches sign. Here we employ the WKB (Wentzel-Kramers-Brillouin) large-deviations method, which requires only the logarithm of a given quantity to be smooth over its state space. Combining the WKB scheme with asymptotic matching techniques, we show how to derive the diffusion approximation in a controlled manner and how to produce better approximations, applicable for much wider regimes of parameters. We also introduce a scalable (independent of population size) WKB-based numerical technique. The method is applied to a central problem in population genetics and evolution, finding the chance of ultimate fixation in a zero-sum, two-types competition.

Adapt or Perish: Evolutionary Rescue in a Gradually Deteriorating Environment

We investigate the evolutionary rescue of a microbial population in a gradually deteriorating environment, through a combination of analytical calculations and stochastic simulations. We consider a population destined for extinction in the absence of mutants, which can survive only if mutants sufficiently adapted to the new environment arise and fix. We show that mutants that appear later during the environment deterioration have a higher probability to fix. The rescue probability of the population increases with a sigmoidal shape when the product of the carrying capacity and of the mutation probability increases. Furthermore, we find that rescue becomes more likely for smaller population sizes and/or mutation probabilities if the environment degradation is slower, which illustrates the key impact of the rapidity of environment degradation on the fate of a population. We also show that our main conclusions are robust across various types of adaptive mutants, including specialist and generalist ones, as well as mutants modeling antimicrobial resistance evolution. We further express the average time of appearance of the mutants that do rescue the population and the average extinction time of those that do not. Our methods can be applied to other situations with continuously variable fitnesses and population sizes, and our analytical predictions are valid in the weak-to-moderate mutation regime.

Mathematical basis for the assessment of antibiotic resistance and administrative counter-strategies

Diversity as well as temporal and spatial changes of the proportional abundances of different antibiotics (cycling, mixing or combinations thereof) have been hypothesised to be an effective administrative control strategy in hospitals to reduce the prevalence of antibiotic-resistant pathogens in nosocomial or community-acquired infections. However, a rigorous assessment of the efficacy of these control strategies is lacking. The main purpose here is to present a mathematical framework for the assessment of control stategies from a processual stance. To this end, we adopt diverse measures of heterogeneity and diversity of proportional abundances based on the concept of entropy from other fields and adapt them to the needs in assessing the impact of variations in antibiotic consumption on antibiotic resistance. Thereby, we derive a family of diversity measures whose members exhibit different degrees of complexity. Most important, we extent these measures such that they account for the assessment of temporal changes in heterogeneity including otherwise undetected diversity-invariant permutations of antibiotics consumption and prevalence of resistant pathogens. We apply a correlation analysis for the assessment of associations between changes of heterogeneities on the antibiotics and on the pathogen side. As a showcase, which serves as a proof-of-principle, we apply the derived methods to records of antibiotic consumption and prevalence of antibiotic-resistant germs from University Hospital Dresden (cf. supplement “DiebnerEtAl_Data-Supplement”). Besides the quantification of heterogeneities of antibiotics consumption and antibiotic resistance, we show that a reduction of prevalence of antibiotic-resistant germs correlates with a temporal change of similarity with respect to the first observation of antibiotics consumption, although heterogeneity remains approximately constant. Although an interventional study is pending, our mathematical framework turns out to be a viable concept for the assessment and optimisation of control strategies intended to reduce antibiotic resistance.

Population Dynamics in a Changing Environment: Random versus Periodic Switching

Environmental changes greatly influence the evolution of populations. Here, we study the dynamics of a population of two strains, one growing slightly faster than the other, competing for resources in a time-varying binary environment modeled by a carrying capacity switching either randomly or periodically between states of abundance and scarcity. The population dynamics is characterized by demographic noise (birth and death events) coupled to a varying environment. We elucidate the similarities and differences of the evolution subject to a stochastically and periodically varying environment. Importantly, the population size distribution is generally found to be broader under intermediate and fast random switching than under periodic variations, which results in markedly different asymptotic behaviors between the fixation probability of random and periodic switching. We also determine the detailed conditions under which the fixation probability of the slow strain is maximal.