Optimal lineage principle for age-structured populations

Synergistic and antagonistic effects of deterministic and stochastic cell-cell variations

By diversifying, cells in a clonal population can together overcome the limits of individuals. Diversity in single-cell growth rates allows the population to survive environmental stresses, such as antibiotics, and grow faster than the undiversified population. These functional cell-cell variations can arise stochastically, from noise in biochemical reactions, or deterministically, by asymmetrically distributing damaged components. While each of the mechanisms is well understood, the effect of the combined mechanisms is unclear. To evaluate the contribution of the deterministic component we developed a mathematical model by mapping the growing population to the Ising model. To analyze the combined effects of stochastic and deterministic contributions we introduced the analytical results of the Ising-mapping into an Euler-Lotka framework. Model results, confirmed by simulations and experimental data, show that deterministic cell-cell variations increase near-linearly with stress. As a consequence, we predict that the gain in population doubling time from cell-cell variations is primarily stochastic at low stress but may cross over to deterministic at higher stresses. Furthermore, we find that while the deterministic component minimizes population damage, stochastic variations antagonize this effect. Together our results may help identifying stress-tolerant pathogenic cells and thus inspire novel antibiotic strategies.

Kobayashi T. Population dynamics models for various forms of adaptation

Adaptability to changing environments is one of the universal characteristics of living organisms. Because individual modes of adaptation are diverse, a unified understanding of these diverse modes is essential to comprehend adaptation. Adaptations can be categorized from at least two perspectives with respect to information. One is the passivity and activity of adaptation and the other is the type of information transmission. In Darwinian natural selection, organisms are selected among randomly generated traits under which individual organisms are passive in the sense that they do not process any environmental information. On the other hand, organisms can also adapt by sensing their environment and changing their traits. This is an active adaptation in that it makes use of environmental information. In terms of information transfer, adaptation through phenotypic heterogeneity, such as bacterial bet-hedging, is intragenerational in which traits are not passed on to the next generation. In contrast, adaptation through genetic diversity is intergenerational. The theory of population dynamics enables us to unify these various modes of adaptations and their properties can be analyzed qualitatively and quantitatively using techniques from quantitative genetics and information thermodynamics. In addition, such methods can be applied to situations where organisms can learn from past experiences and pass them on from generation to generation. In this work, we introduce the unified theory of biological adaptation based on population dynamics and show its potential applications to evaluate the fitness value of information and to analyze experimental lineage tree data. Finally, we discuss future perspectives for its development. This review article is an extended version of the Japanese article in SEIBUTSU BUTSURI Vol. 57, p. 287-290 (2017).

A unified framework for measuring selection on cellular lineages and traits

Intracellular states probed by gene expression profiles and metabolic activities are intrinsically noisy, causing phenotypic variations among cellular lineages. Understanding the adaptive and evolutionary roles of such variations requires clarifying their linkage to population growth rates. Extending a cell lineage statistics framework, here we show that a population's growth rate can be expanded by the cumulants of a fitness landscape that characterize how fitness distributes in a population. The expansion enables quantifying the contribution of each cumulant, such as variance and skewness, to population growth. We introduce a function that contains all the essential information of cell lineage statistics, including mean lineage fitness and selection strength. We reveal a relation between fitness heterogeneity and population growth rate response to perturbation. We apply the framework to experimental cell lineage data from bacteria to mammalian cells, revealing distinct levels of growth rate gain from fitness heterogeneity across environments and organisms. Furthermore, third or higher order cumulants' contributions are negligible under constant growth conditions but could be significant in regrowing processes from growth-arrested conditions. We identify cellular populations in which selection leads to an increase of fitness variance among lineages in retrospective statistics compared to chronological statistics. The framework assumes no particular growth models or environmental conditions, and is thus applicable to various biological phenomena for which phenotypic heterogeneity and cellular proliferation are important.

Cell Cycle Heritability and Localization Phase Transition in Growing Populations

The cell cycle duration is a variable cellular phenotype that underlies long-term population growth and age structures. By analyzing the stationary solutions of a branching process with heritable cell division times, we demonstrate the existence of a phase transition, which can be continuous or first order, by which a nonzero fraction of the population becomes localized at a minimal division time. Just below the transition, we demonstrate the coexistence of localized and delocalized age-structure phases and the power law decay of correlation functions. Above it, we observe the self-synchronization of cell cycles, collective divisions, and the slow "aging" of population growth rates.

Large Deviation Principle Linking Lineage Statistics to Fitness in Microbial Populations

In exponentially proliferating populations of microbes, the population doubles at a rate less than the average doubling time of a single-cell due to variability at the single-cell level. It is known that the distribution of generation times obtained from a single lineage is, in general, insufficient to determine a population's growth rate. Is there an explicit relationship between observables obtained from a single lineage and the population growth rate? We show that a population's growth rate can be represented in terms of averages over isolated lineages. This lineage representation is related to a large deviation principle that is a generic feature of exponentially proliferating populations. Due to the large deviation structure of growing populations, the number of lineages needed to obtain an accurate estimate of the growth rate depends exponentially on the duration of the lineages, leading to a nonmonotonic convergence of the estimate, which we verify in both synthetic and experimental data sets.

The interplay of phenotypic variability and fitness in finite microbial populations

In isogenic microbial populations, phenotypic variability is generated by a combination of stochastic mechanisms, such as gene expression, and deterministic factors, such as asymmetric segregation of cell volume. Here we address the question: how does phenotypic variability of a microbial population affect its fitness? While this question has previously been studied for exponentially growing populations, the situation when the population size is kept fixed has received much less attention, despite its relevance to many natural scenarios. We show that the outcome of competition between multiple microbial species can be determined from the distribution of phenotypes in the culture using a generalization of the well-known Euler-Lotka equation, which relates the steady-state distribution of phenotypes to the population growth rate. We derive a generalization of the Euler-Lotka equation for finite cultures, which relates the distribution of phenotypes among cells in the culture to the exponential growth rate. Our analysis reveals that in order to predict fitness from phenotypes, it is important to understand how distributions of phenotypes obtained from different subsets of the genealogical history of a population are related. To this end, we derive a mapping between the various ways of sampling phenotypes in a finite population and show how to obtain the equivalent distributions from an exponentially growing culture. Finally, we use this mapping to show that species with higher growth rates in exponential growth conditions will have a competitive advantage in the finite culture.

Lineage EM algorithm for inferring latent states from cellular lineage trees

SUMMARY

Phenotypic variability in a population of cells can work as the bet-hedging of the cells under an unpredictably changing environment, the typical example of which is the bacterial persistence. To understand the strategy to control such phenomena, it is indispensable to identify the phenotype of each cell and its inheritance. Although recent advancements in microfluidic technology offer us useful lineage data, they are insufficient to directly identify the phenotypes of the cells. An alternative approach is to infer the phenotype from the lineage data by latent-variable estimation. To this end, however, we must resolve the bias problem in the inference from lineage called survivorship bias. In this work, we clarify how the survivorship bias distorts statistical estimations. We then propose a latent-variable estimation algorithm without the survivorship bias from lineage trees based on an expectation-maximization (EM) algorithm, which we call lineage EM algorithm (LEM). LEM provides a statistical method to identify the traits of the cells applicable to various kinds of lineage data.

AVAILABILITY AND IMPLEMENTATION

An implementation of LEM is available at https://github.com/so-nakashima/Lineage-EM-algorithm.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Linking lineage and population observables in biological branching processes

Using a population dynamics inspired by an ensemble of growing cells, a set of fluctuation theorems linking observables measured at the lineage and population levels is derived. One of these relations implies specific inequalities comparing the population doubling time with the mean generation time at the lineage or population levels. While these inequalities have been derived before for age-controlled models with negligible mother-daughter correlations, we show that they also hold for a broad class of size-controlled models. We discuss the implications of this result for the interpretation of a recent experiment in which the growth of bacteria strains has been probed at the single-cell level.

Intrinsic and extrinsic noise of gene expression in lineage trees

Cell-to-cell heterogeneity is driven by stochasticity in intracellular reactions and the population dynamics. While these sources are usually studied separately, we develop an agent-based framework that accounts for both factors while tracking every single cell of a growing population. Apart from the common intrinsic variability, the framework also predicts extrinsic noise without the need to introduce fluctuating rate constants. Instead, extrinsic fluctuations are explained by cell cycle fluctuations and differences in cell age. We provide explicit formulas to quantify mean molecule numbers, intrinsic and extrinsic noise statistics in two-colour experiments. We find that these statistics differ significantly depending on the experimental setup used to observe the cells. We illustrate this fact using (i) averages over an isolated cell lineage tracked over many generations as observed in the mother machine, (ii) population snapshots with known cell ages as recorded in time-lapse microscopy, and (iii) snapshots with unknown cell ages as measured from static images or flow cytometry. Applying the method to models of stochastic gene expression and feedback regulation elucidates that isolated lineages, as compared to snapshot data, can significantly overestimate the mean number of molecules, overestimate extrinsic noise but underestimate intrinsic noise and have qualitatively different sensitivities to cell cycle fluctuations.

Fitness response relation of a multitype age-structured population dynamics

We construct a pathwise formulation for a multitype age-structured population dynamics, which involves an age-dependent cell replication and transition of gene- or phenotypes. By employing the formulation, we derive a variational representation of the stationary population growth rate; the representation comprises a tradeoff relation between growth effects and a single-cell intrinsic dynamics described by a semi-Markov process. This variational representation leads to a response relation of the stationary population growth rate, in which statistics on a retrospective history work as the response coefficients. These results contribute to predicting and controlling growing populations based on experimentally observed cell-lineage information.

Making sense of snapshot data: ergodic principle for clonal cell populations

Population growth is often ignored when quantifying gene expression levels across clonal cell populations. We develop a framework for obtaining the molecule number distributions in an exponentially growing cell population taking into account its age structure. In the presence of generation time variability, the average acquired across a population snapshot does not obey the average of a dividing cell over time, apparently contradicting ergodicity between single cells and the population. Instead, we show that the variation observed across snapshots with known cell age is captured by cell histories, a single-cell measure obtained from tracking an arbitrary cell of the population back to the ancestor from which it originated. The correspondence between cells of known age in a population with their histories represents an ergodic principle that provides a new interpretation of population snapshot data. We illustrate the principle using analytical solutions of stochastic gene expression models in cell populations with arbitrary generation time distributions. We further elucidate that the principle breaks down for biochemical reactions that are under selection, such as the expression of genes conveying antibiotic resistance, which gives rise to an experimental criterion with which to probe selection on gene expression fluctuations.

The Effects of Stochasticity at the Single-Cell Level and Cell Size Control on the Population Growth

Establishing a quantitative connection between the population growth rate and the generation times of single cells is a prerequisite for understanding evolutionary dynamics of microbes. However, existing theories fail to account for the experimentally observed correlations between mother-daughter generation times that are unavoidable when cell size is controlled for, which is essentially always the case. Here, we study population-level growth in the presence of cell size control and corroborate our theory using experimental measurements of single-cell growth rates. We derive a closed formula for the population growth rate and demonstrate that it only depends on the single-cell growth rate variability, not other sources of stochasticity. Our work provides an evolutionary rationale for the narrow growth rate distributions often observed in nature: when single-cell growth rates are less variable but have a fixed mean, the population will exhibit an enhanced population growth rate as long as the correlations between the mother and daughter cells' growth rates are not too strong.

Possible roles of mechanical cell elimination intrinsic to growing tissues from the perspective of tissue growth efficiency and homeostasis

Cell competition is a phenomenon originally described as the competition between cell populations with different genetic backgrounds; losing cells with lower fitness are eliminated. With the progress in identification of related molecules, some reports described the relevance of cell mechanics during elimination. Furthermore, recent live imaging studies have shown that even in tissues composed of genetically identical cells, a non-negligible number of cells are eliminated during growth. Thus, mechanical cell elimination (MCE) as a consequence of mechanical cellular interactions is an unavoidable event in growing tissues and a commonly observed phenomenon. Here, we studied MCE in a genetically-homogeneous tissue from the perspective of tissue growth efficiency and homeostasis. First, we propose two quantitative measures, cell and tissue fitness, to evaluate cellular competitiveness and tissue growth efficiency, respectively. By mechanical tissue simulation in a pure population where all cells have the same mechanical traits, we clarified the dependence of cell elimination rate or cell fitness on different mechanical/growth parameters. In particular, we found that geometrical (specifically, cell size) and mechanical (stress magnitude) heterogeneities are common determinants of the elimination rate. Based on these results, we propose possible mechanical feedback mechanisms that could improve tissue growth efficiency and density/stress homeostasis. Moreover, when cells with different mechanical traits are mixed (e.g., in the presence of phenotypic variation), we show that MCE could drive a drastic shift in cell trait distribution, thereby improving tissue growth efficiency through the selection of cellular traits, i.e. intra-tissue "evolution". Along with the improvement of growth efficiency, cell density, stress state, and phenotype (mechanical traits) were also shown to be homogenized through growth. More theoretically, we propose a mathematical model that approximates cell competition dynamics, by which the time evolution of tissue fitness and cellular trait distribution can be predicted without directly simulating a cell-based mechanical model.

Stochastic and information-thermodynamic structures of population dynamics in a fluctuating environment

Adaptation in a fluctuating environment is a process of fueling environmental information to gain fitness. Living systems have gradually developed strategies for adaptation from random and passive diversification of the phenotype to more proactive decision making, in which environmental information is sensed and exploited more actively and effectively. Understanding the fundamental relation between fitness and information is therefore crucial to clarify the limits and universal properties of adaptation. In this work, we elucidate the underlying stochastic and information-thermodynamic structure in this process, by deriving causal fluctuation relations (FRs) of fitness and information. Combined with a duality between phenotypic and environmental dynamics, the FRs reveal the limit of fitness gain, the relation of time reversibility with the achievability of the limit, and the possibility and condition for gaining excess fitness due to environmental fluctuation. The loss of fitness due to causal constraints and the limited capacity of real organisms is shown to be the difference between time-forward and time-backward path probabilities of phenotypic and environmental dynamics. Furthermore, the FRs generalize the concept of the evolutionary stable state (ESS) for fluctuating environment by giving the probability that the optimal strategy on average can be invaded by a suboptimal one owing to rare environmental fluctuation. These results clarify the information-thermodynamic structures in adaptation and evolution.

Aging, mortality, and the fast growth trade-off of Schizosaccharomyces pombe

Replicative aging has been demonstrated in asymmetrically dividing unicellular organisms, seemingly caused by unequal damage partitioning. Although asymmetric segregation and inheritance of potential aging factors also occur in symmetrically dividing species, it nevertheless remains controversial whether this results in aging. Based on large-scale single-cell lineage data obtained by time-lapse microscopy with a microfluidic device, in this report, we demonstrate the absence of replicative aging in old-pole cell lineages of Schizosaccharomyces pombe cultured under constant favorable conditions. By monitoring more than 1,500 cell lineages in 7 different culture conditions, we showed that both cell division and death rates are remarkably constant for at least 50–80 generations. Our measurements revealed that the death rate per cellular generation increases with the division rate, pointing to a physiological trade-off with fast growth under balanced growth conditions. We also observed the formation and inheritance of Hsp104-associated protein aggregates, which are a potential aging factor in old-pole cell lineages, and found that these aggregates exhibited a tendency to preferentially remain at the old poles for several generations. However, the aggregates were eventually segregated from old-pole cells upon cell division and probabilistically allocated to new-pole cells. We found that cell deaths were typically preceded by sudden acceleration of protein aggregation; thus, a relatively large amount of protein aggregates existed at the very ends of the dead cell lineages. Our lineage tracking analyses, however, revealed that the quantity and inheritance of protein aggregates increased neither cellular generation time nor cell death initiation rates. Furthermore, our results demonstrated that unusually large amounts of protein aggregates induced by oxidative stress exposure did not result in aging; old-pole cells resumed normal growth upon stress removal, despite the fact that most of them inherited significant quantities of aggregates. These results collectively indicate that protein aggregates are not a major determinant of triggering cell death in S. pombe and thus cannot be an appropriate molecular marker or index for replicative aging under both favorable and stressful environmental conditions.

Multicellular organisms universally senesce and must produce rejuvenated progenies in order to transmit life. Although similar age-related deterioration in physiological functions and reproduction is also found in unicellular organisms that divide asymmetrically to produce morphologically distinct aged and younger cells, it has been unclear whether symmetrically dividing microbes—such as fission yeast—exhibit the same traits. Using long-term live-cell microscopy combined with a microfluidic device, we monitor the growth and death of a large number of fission yeast cells and demonstrate the existence of aging-free lineages. These lineages are, however, not immortal, and the probability of death increases as the cells grow more rapidly; thus, the “live fast, die fast” trade-off exists in fission yeast. We further characterize the segregation and inheritance of protein aggregates, which are commonly thought of as “aging factors.” The aging-free lineages bear the aggregate load for some generations with no apparent adverse effects on growth. We also show that there is no threshold amount of protein aggregate above which cells are destined to death in both normal and stressed conditions: protein aggregate is thus not a direct initiation signal for cell death. Our data reveal that protein aggregation might not be an appropriate index for aging and that we should revisit its role in cell physiology.

The genealogical decomposition of a matrix population model with applications to the aggregation of stages

Matrix projection models are a central tool in many areas of population biology. In most applications, one starts from the projection matrix to quantify the asymptotic growth rate of the population (the dominant eigenvalue), the stable stage distribution, and the reproductive values (the dominant right and left eigenvectors, respectively). Any primitive projection matrix also has an associated ergodic Markov chain that contains information about the genealogy of the population. In this paper, we show that these facts can be used to specify any matrix population model as a triple consisting of the ergodic Markov matrix, the dominant eigenvalue and one of the corresponding eigenvectors. This decomposition of the projection matrix separates properties associated with lineages from those associated with individuals. It also clarifies the relationships between many quantities commonly used to describe such models, including the relationship between eigenvalue sensitivities and elasticities. We illustrate the utility of such a decomposition by introducing a new method for aggregating classes in a matrix population model to produce a simpler model with a smaller number of classes. Unlike the standard method, our method has the advantage of preserving reproductive values and elasticities. It also has conceptually satisfying properties such as commuting with changes of units.

Inferring fitness landscapes and selection on phenotypic states from single-cell genealogical data

Recent advances in single-cell time-lapse microscopy have revealed non-genetic heterogeneity and temporal fluctuations of cellular phenotypes. While different phenotypic traits such as abundance of growth-related proteins in single cells may have differential effects on the reproductive success of cells, rigorous experimental quantification of this process has remained elusive due to the complexity of single cell physiology within the context of a proliferating population. We introduce and apply a practical empirical method to quantify the fitness landscapes of arbitrary phenotypic traits, using genealogical data in the form of population lineage trees which can include phenotypic data of various kinds. Our inference methodology for fitness landscapes determines how reproductivity is correlated to cellular phenotypes, and provides a natural generalization of bulk growth rate measures for single-cell histories. Using this technique, we quantify the strength of selection acting on different cellular phenotypic traits within populations, which allows us to determine whether a change in population growth is caused by individual cells’ response, selection within a population, or by a mixture of these two processes. By applying these methods to single-cell time-lapse data of growing bacterial populations that express a resistance-conferring protein under antibiotic stress, we show how the distributions, fitness landscapes, and selection strength of single-cell phenotypes are affected by the drug. Our work provides a unified and practical framework for quantitative measurements of fitness landscapes and selection strength for any statistical quantities definable on lineages, and thus elucidates the adaptive significance of phenotypic states in time series data. The method is applicable in diverse fields, from single cell biology to stem cell differentiation and viral evolution.

Selection is a ubiquitous process in biological populations in which individuals are endowed with heterogeneous reproductive abilities, and it occurs even among genetically homogeneous cells due to the existence of phenotypic noise. Unlike genotypes, which can remain stable for many generations, phenotypic fluctuations at the single cell level are often comparable to cellular generation times. For this reason, quantifying the contribution of specific phenotypic states to cellular fitness remains a major challenge. Here, we develop a method to measure the fitness landscape and selection strength acting on diverse cellular phenotypes by employing a novel conceptual framework in which cellular histories are regarded as a basic unit of selection. With this framework, one can tell quantitatively whether a population adapts to environmental changes by selection or through individual responses. This new analytical approach to genetics reveals the roles of heterogeneous expression patterns and dynamics without directly perturbing genes. Applications in diverse fields including stem cell differentiation and viral evolution are discussed.

Noise-driven growth rate gain in clonal cellular populations

Cellular populations in both nature and the laboratory are composed of phenotypically heterogeneous individuals that compete with each other resulting in complex population dynamics. Predicting population growth characteristics based on knowledge of heterogeneous single-cell dynamics remains challenging. By observing groups of cells for hundreds of generations at single-cell resolution, we reveal that growth noise causes clonal populations of Escherichia coli to double faster than the mean doubling time of their constituent single cells across a broad set of balanced-growth conditions. We show that the population-level growth rate gain as well as age structures of populations and of cell lineages in competition are predictable. Furthermore, we theoretically reveal that the growth rate gain can be linked with the relative entropy of lineage generation time distributions. Unexpectedly, we find an empirical linear relation between the means and the variances of generation times across conditions, which provides a general constraint on maximal growth rates. Together, these results demonstrate a fundamental benefit of noise for population growth, and identify a growth law that sets a "speed limit" for proliferation.

Fluctuation Relations of Fitness and Information in Population Dynamics

Phenotype switching with and without sensing environment is a common strategy of organisms to survive in a fluctuating environment. Understanding the evolutionary advantages of switching and sensing requires a quantitative evaluation of their fitness gain and its fluctuation together with the conditions for the switching and sensing strategies being adapted to a given environment. In this work, by using a pathwise formulation of the population dynamics, we show that the optimal switching strategy is characterized by a consistency condition for time-forward and backward path probabilities. The formulation also clarifies the underlying information-theoretic aspect of selection as a passive information compression. The loss of fitness by a suboptimal strategy is also shown to satisfy a fluctuation relation, which provides us with the information on how environmental fluctuation impacts the advantages of the optimal strategy. These results are naturally extended to the situation that organisms can use an environmental signal by actively sensing the environment. The fluctuation relations of the fitness gain by sensing are derived in which the multivariate mutual information among the phenotype, the environment, and the signal plays the role to quantify the relevant information in the signal for the fitness gain.

Populations adapt to fluctuating selection using derived and ancestral allelic diversity

Populations can adapt to changing environments by using allelic diversity, yet whether diversity is recently derived or ancestral is often debated. Although evolution could productively use both types of diversity in a changing environment, their relative frequency has not been quantified. We address this question experimentally using budding yeast strains that harbor a tandem repeat containing URA3 gene, which we expose to cyclical selection and counterselection. We characterize and quantify the dynamics of frameshift events in the URA3 gene in eight populations over 12 cycles of selection and find that ancestral alleles account for 10-20% of all adaptive events. Using a general model of fluctuating selection, we determine how these results depend on mutation rates, population sizes, and fluctuation timescales. We quantify the contribution of derived alleles to the adaptation process using the de novo mutation rate along the population's ancestral lineage, a novel measure that is applicable in a wide range of settings. We find that the adaptive dynamics undergoes a sharp transition from selection on ancestral alleles to selection on derived alleles as fluctuation timescales increase. Our results demonstrate that fluctuations can select between different modes of adaptation over evolutionary timescales.

Pathwise thermodynamic structure in population dynamics

We reveal thermodynamic structure in population dynamics with phenotype switching. Mean fitness for a population of organisms is determined by a thermodynamic variational principle described by the large deviation of phenotype-switching dynamics. Owing to this variational principle, a response relation of the mean fitness with respect to changes of environments and phenotype-switching dynamics is represented as a thermodynamic differential form. Furthermore, we discuss the strength of the selection by using the difference between time-forward and time-backward (retrospective) processes.

Quantifying selective pressures driving bacterial evolution using lineage analysis

Organisms use a variety of strategies to adapt to their environments and maximize long-term growth potential, but quantitative characterization of the benefits conferred by the use of such strategies, as well as their impact on the whole population's rate of growth, remains challenging. Here, we use a path-integral framework that describes how selection acts on lineages -i.e. the life-histories of individuals and their ancestors- to demonstrate that lineage-based measurements can be used to quantify the selective pressures acting on a population. We apply this analysis to E. coli bacteria exposed to cyclical treatments of carbenicillin, an antibiotic that interferes with cell-wall synthesis and affects cells in an age-dependent manner. While the extensive characterization of the life-history of thousands of cells is necessary to accurately extract the age-dependent selective pressures caused by carbenicillin, the same measurement can be recapitulated using lineage-based statistics of a single surviving cell. Population-wide evolutionary pressures can be extracted from the properties of the surviving lineages within a population, providing an alternative and efficient procedure to quantify the evolutionary forces acting on a population. Importantly, this approach is not limited to age-dependent selection, and the framework can be generalized to detect signatures of other trait-specific selection using lineage-based measurements. Our results establish a powerful way to study the evolutionary dynamics of life under selection, and may be broadly useful in elucidating selective pressures driving the emergence of antibiotic resistance and the evolution of survival strategies in biological systems.

Non-equilibrium physics and evolution--adaptation, extinction, and ecology: a key issues review

Evolutionary dynamics in nature constitute an immensely complex non-equilibrium process. We review the application of physical models of evolution, by focusing on adaptation, extinction, and ecology. In each case, we examine key concepts by working through examples. Adaptation is discussed in the context of bacterial evolution, with a view toward the relationship between growth rates, mutation rates, selection strength, and environmental changes. Extinction dynamics for an isolated population are reviewed, with emphasis on the relation between timescales of extinction, population size, and temporally correlated noise. Ecological models are discussed by focusing on the effect of spatial interspecies interactions on diversity. Connections between physical processes--such as diffusion, turbulence, and localization--and evolutionary phenomena are highlighted.

Neutral null models for diversity in serial transfer evolution experiments

Evolution experiments with microorganisms coupled with genome-wide sequencing now allow for the systematic study of population genetic processes under a wide range of conditions. In learning about these processes in natural, sexual populations, neutral models that describe the behavior of diversity and divergence summaries have played a pivotal role. It is therefore natural to ask whether neutral models, suitably modified, could be useful in the context of evolution experiments. Here, we introduce coalescent models for polymorphism and divergence under the most common experimental evolution assay, a serial transfer experiment. This relatively simple setting allows us to address several issues that could affect diversity patterns in evolution experiments, whether selection is operating or not: the transient behavior of neutral polymorphism in an experiment beginning from a single clone, the effects of randomness in the timing of cell division and noisiness in population size in the dilution stage. In our analyses and discussion, we emphasize the implications for experiments aimed at measuring diversity patterns and making inferences about population genetic processes based on these measurements.

Evolution in microbes

This review presents a broad survey of experimental microbial evolution, covering diverse topics including trade-offs, epistasis, fluctuating conditions, spatial dynamics, cooperation, aging, and stochastic switching. Emphasis is placed on examples that highlight key conceptual points or address theoretical predictions. Experimental evolution is discussed from two points of view. First, population trajectories are described as adaptive walks on a fitness landscape, whose genetic structure can be probed by experiments. Second, populations are viewed from a physiological perspective, and their nongenetic heterogeneity is examined. Bringing together these two viewpoints remains a major challenge for the future.

Microfluidic chemostat for measuring single cell dynamics in bacteria

We designed a microfluidic chemostat consisting of 600 sub-micron trapping/growth channels connected to two feeding channels. The microchemostat traps E. coli cells and forces them to grow in lines for over 50 generations. Excess cells, including the mother cells captured at the start of the process, are removed from both ends of the growth channels by the media flow. With the aid of time-lapse microscopy, we have monitored dynamic properties such as growth rate and GFP expression at the single-cell level for many generations while maintaining a population of bacteria of similar age. We also use the microchemostat to show how the population responds to dynamic changes in the environment. Since more than 100 individual bacterial cells are aligned and immobilized in a single field of view, the microchemostat is an ideal platform for high-throughput intracellular measurements. We demonstrate this capability by tracking with sub-diffraction resolution the movements of fluorescently tagged loci in more than one thousand cells on a single device. The device yields results comparable to conventional agar microscopy experiments with substantial increases in throughput and ease of analysis.