Senescence and antibiotic resistance in an age-structured population model

Different theories have been proposed to understand the growing problem of antibiotic resistance of microbial populations. Here we investigate a model that is based on the hypothesis that senescence is a possible explanation for the existence of so-called persister cells which are resistant to antibiotic treatment. We study a chemostat model with a microbial population which is age-structured and show that if the growth rates of cells in different age classes are sufficiently close to a scalar multiple of a common growth rate, then the population will globally stabilize at a coexistence steady state. This steady state persists under an antibiotic treatment if the level of antibiotics is below a certain threshold; if the level exceeds this threshold, the washout state becomes a globally attracting equilibrium.     

Mapping the environmental fitness landscape of a synthetic gene circuit

Gene expression actualizes the organismal phenotypes encoded within the genome in an environment-dependent manner. Among all encoded phenotypes, cell population growth rate (fitness) is perhaps the most important, since it determines how well-adapted a genotype is in various environments. Traditional biological measurement techniques have revealed the connection between the environment and fitness based on the gene expression mean. Yet, recently it became clear that cells with identical genomes exposed to the same environment can differ dramatically from the population average in their gene expression and division rate (individual fitness). For cell populations with bimodal gene expression, this difference is particularly pronounced, and may involve stochastic transitions between two cellular states that form distinct sub-populations. Currently it remains unclear how a cell population's growth rate and its subpopulation fractions emerge from the molecular-level kinetics of gene networks and the division rates of single cells. To address this question we developed and quantitatively characterized an inducible, bistable synthetic gene circuit controlling the expression of a bifunctional antibiotic resistance gene in Saccharomyces cerevisiae. Following fitness and fluorescence measurements in two distinct environments (inducer alone and antibiotic alone), we applied a computational approach to predict cell population fitness and subpopulation fractions in the combination of these environments based on stochastic cellular movement in gene expression space and fitness space. We found that knowing the fitness and nongenetic (cellular) memory associated with specific gene expression states were necessary for predicting the overall fitness of cell populations in combined environments. We validated these predictions experimentally and identified environmental conditions that defined a "sweet spot" of drug resistance. These findings may provide a roadmap for connecting the molecular-level kinetics of gene networks to cell population fitness in well-defined environments, and may have important implications for phenotypic variability of drug resistance in natural settings.     

Bayesian Estimates of Transition Probabilities in Seven Small Lithophytic Orchid Populations: Maximizing Data Availability from Many Small Samples

Predicting population dynamics for rare species is of paramount importance in order to evaluate the likelihood of extinction and planning conservation strategies. However, evaluating and predicting population viability can be hindered from a lack of data. Rare species frequently have small populations, so estimates of vital rates are often very uncertain due to lack of data. We evaluated the vital rates of seven small populations from two watersheds with varying light environment of a common epiphytic orchid using Bayesian methods of parameter estimation. From the Lefkovitch matrices we predicted the deterministic population growth rates, elasticities, stable stage distributions and the credible intervals of the statistics. Populations were surveyed on a monthly basis between 18–34 months. In some of the populations few or no transitions in some of the vital rates were observed throughout the sampling period, however, we were able to predict the most likely vital rates using a Bayesian model that incorporated the transitions rates from the other populations. Asymptotic population growth rate varied among the seven orchid populations. There was little difference in population growth rate among watersheds even though it was expected because of physical differences as a result of differing canopy cover and watershed width. Elasticity analyses of Lepanthes rupestris suggest that growth rate is more sensitive to survival followed by growth, shrinking and the reproductive rates. The Bayesian approach helped to estimate transition probabilities that were uncommon or variable in some populations. Moreover, it increased the precision of the parameter estimates as compared to traditional approaches.     

Origin and number of founders in an introduced insular primate: estimation from nuclear genetic data

Cynomolgus macaques (Macaca fascicularis) were introduced on the island of Mauritius between 400 and 500 years ago and underwent a strong population expansion after a probable initial founding event. However, in practice, little is known of the geographical origin of the individuals that colonized the island, on how many individuals were introduced, and of whether the following demographic expansion erased any signal of this putative bottleneck. In this study, we asked whether the current nuclear genome of the Mauritius population retained a signature that would allow us to answer these questions. Altogether, 21 polymorphic autosomal and sex-linked microsatellites were surveyed from 81 unrelated Mauritius individuals and 173 individuals from putative geographical sources in Southeast Asia: Java, the Philippines islands and the Indochinese peninsula. We found that (i) the Mauritius population was closer to different populations depending on the markers we used, which suggests a possible mixed origin with Java playing most probably a major role; and (ii) the level of diversity was lower than the other populations but there was no clear and consistent bottleneck signal using either summary statistics or full-likelihood methods. However, summary statistics strongly suggest that Mauritius is not at mutation-drift equilibrium and favours an expansion rather than a bottleneck. This suggests that on a short time scale, population decline followed by growth can be difficult to deduce from genetic data based on mutation-drift theory. We then used a simple Bayesian rejection algorithm to estimate the number of founders under different demographic models (exponential, logistic and logistic with lag) and pure genetic drift. This new method uses current population size estimates and expected heterozygosity of Mauritius and source population(s). Our results indicate that a simple exponential growth is unlikely and that, under the logistic models, the population may have expanded from an initial effective number of individuals of 10-15. The data are also consistent with a logistic growth with different lag values, indicating that we cannot exclude past population fluctuation.     

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.     

Modelling the effectiveness of contraception for controlling introduced populations of elephant in South Africa

Re‐introduced African elephant (Loxodonta africana Blumenbach) populations are growing at very high rates in many of southern Africa’s reserves, have attained densities higher than previously thought possible and may be exhibiting irruptive growth. Active management of such populations is necessary to prevent the potentially negative effects on habitat and biodiversity that are associated with elephant overpopulation. One potentially feasible method of elephant management is immunocontraception, but very little is known about the long‐term effectiveness of this method. Using demographic data from three South African elephant populations, we made model projections of the effects of contraception on population growth rates to determine whether contraception may be a feasible management tool for elephant. In comparison with noncontracepted populations, realistic reductions in population growth rate after 20 years of contraception were projected to be up to c. 64%, with 50% being a very feasible target. Through its ability to reduce population growth rates, immunocontraception should be an effective tool for preventing or minimizing irruption in elephants and, perhaps, other introduced ungulate species.     

An agent-based modelling approach to estimate error in gyrodactylid population growth

Comparative studies of gyrodactylid monogeneans on different host species or strains rely upon the observation of growth on individual fish maintained within a common environment, summarised using maximum likelihood statistical approaches. Here we describe an agent-based model of gyrodactylid population growth, which we use to evaluate errors due to stochastic reproductive variation in such experimental studies. Parameters for the model use available fecundity and mortality data derived from previously published life tables of Gyrodactylus salaris, and use a new data set of fecundity and mortality statistics for this species on the Neva stock of Atlantic salmon, Salmo salar. Mortality data were analysed using a mark-recapture analysis software package, allowing maximum-likelihood estimation of daily survivorship and mortality. We consistently found that a constant age-specific mortality schedule was most appropriate for G. salaris in experimental datasets, with a daily survivorship of 0.84 at 13°C. This, however, gave unrealistically low population growth rates when used as parameters in the model, and a schedule of constantly increasing mortality was chosen as the best compromise for the model. The model also predicted a realistic age structure for the simulated populations, with 0.32 of the population not yet having given birth for the first time (pre-first birth). The model demonstrated that the population growth rate can be a useful parameter for comparing gyrodactylid populations when these are larger than 20-30 individuals, but that stochastic error rendered the parameter unusable in smaller populations. It also showed that the declining parasite population growth rate typically observed during the course of G. salaris infections cannot be explained through stochastic error and must therefore have a biological basis. Finally, the study showed that most gyrodactylid-host studies of this type are too small to detect subtle differences in local adaptation of gyrodactylid monogeneans between fish stocks.     

Density-dependent adaptive resistance allows swimming bacteria to colonize an antibiotic gradient

During antibiotic treatment, antibiotic concentration gradients develop. Little is know regarding the effects of antibiotic gradients on populations of nonresistant bacteria. Using a microfluidic device, we show that high-density motile Escherichia coli populations composed of nonresistant bacteria can, unexpectedly, colonize environments where a lethal concentration of the antibiotic kanamycin is present. Colonizing bacteria establish an adaptively resistant population, which remains viable for over 24 h while exposed to the antibiotic. Quantitative analysis of multiple colonization events shows that collectively swimming bacteria need to exceed a critical population density in order to successfully colonize the antibiotic landscape. After colonization, bacteria are not dormant but show both growth and swimming motility under antibiotic stress. Our results highlight the importance of motility and population density in facilitating adaptive resistance, and indicate that adaptive resistance may be a first step to the emergence of genetically encoded resistance in landscapes of antibiotic gradients.     

Complex numerical responses to top-down and bottom-up processes in vertebrate populations

Population growth rate is determined in all vertebrate populations by food supplies, and we postulate bottom-up control as the universal primary standard. But this primary control system can be overridden by three secondary controls: top-down processes from predators, social interactions within the species and disturbances. Different combinations of these processes affect population growth rates in different ways. Thus, some relationships between growth rate and density can be hyperbolic or even have multiple nodes. We illustrate some of these in marsupial, ungulate and rabbit populations. Complex interactions between food, predators, environmental disturbance and social behaviour produce the myriad observations of population growth in nature, and we need to develop generalizations to classify populations. Different animal groups differ in the combination of these four processes that affect them, in their growth rates and in their vulnerability to extinction. Because conservation and management of populations depend critically on what factors drive population growth, we need to develop universal generalizations that will relieve us from the need to study every single population before we can make recommendations for management.     

Programming microbial population dynamics by engineered cell-cell communication

A major aim of synthetic biology is to program novel cellular behavior using engineered gene circuits. Early endeavors focused on building simple circuits that fulfill simple functions, such as logic gates, bistable toggle switches, and oscillators. These gene circuits have primarily focused on single-cell behaviors since they operate intracellularly. Thus, they are often susceptible to cell-cell variations due to stochastic gene expression. Cell-cell communication offers an efficient strategy to coordinate cellular behavior at the population level. To this end, we review recent advances in engineering cell-cell communication to achieve reliable population dynamics, spanning from communication within single species to multispecies, from one-way sender-receiver communication to two-way communication in synthetic microbial ecosystems. These engineered systems serve as well-defined model systems to better understand design principles of their naturally occurring counterparts and to facilitate novel biotechnology applications.     

Effective size of fluctuating populations with two sexes and overlapping generations

We derive formulas that can be applied to estimate the effective population size N(e) for organisms with two sexes reproducing once a year and having constant adult mean vital rates independent of age. Temporal fluctuations in population size are generated by demographic and environmental stochasticity. For populations with even sex ratio at birth, no deterministic population growth and identical mean vital rates for both sexes, the key parameter determining N(e) is simply the mean value of the demographic variance for males and females considered separately. In this case Crow and Kimura's generalization of Wright's formula for N(e) with two sexes, in terms of the effective population sizes for each sex, is applicable even for fluctuating populations with different stochasticity in vital rates for males and females. If the mean vital rates are different for the sexes then a simple linear combination of the demographic variances determines N(e), further extending Wright's formula. For long-lived species an expression is derived for N(e) involving the generation times for both sexes. In the general case with nonzero population growth and uneven sex ratio of newborns, we use the model to investigate numerically the effects of different population parameters on N(e). We also estimate the ratio of effective to actual population size in six populations of house sparrows on islands off the coast of northern Norway. This ratio showed large interisland variation because of demographic differences among the populations. Finally, we calculate how N(e) in a growing house sparrow population will change over time.     

Population Dynamics of the Endangered, Long-Lived Perennial Species, Ligularia sibirica

Ligularia sibirica is a relict wetland perennial plant species of the Czech and Slovak Republic. Explaining variation in population growth rate and identifying the causes of that variation is important for effective protection of such an endangered species. Matrix models based on four years of data of 11 populations were used to identify the pattern of variation in the demographic vital rates of this species, and to examine the causes of the variation such as population size and habitat type. Further, the matrix model was used to determine the population growth rate, longevity and risk of extinction of each population and to identify the specific vital rates that most affect population growth rate. The results showed that population growth rates were significantly different between years and populations. Temporal variation was mostly due to variable survival of adult individuals, while spatial variation was mainly driven by fertility of one small currently expanding population. Further, most studied populations of L. sibirica are performing well and only those growing in nitrogen-rich habitats have a high extinction risk. The results also indicate that all populations have low adult mortality, long-lived individuals (61.3?years on average) and some populations also show features of remnant populations (i.e., the persistence of populations in severe conditions in spite of no reproduction). Our results imply that detailed demographic data are needed to understand the long-term prospects of these populations. These data may serve as an early warning system for this species long before an obvious decline occurs in the populations.     

Variability of important vital rates challenges the demographic buffering hypothesis

Selection is assumed to eliminate life-histories showing high variability in vital rates that have the greatest influence on population performance. Therefore, an inverse variability-importance relationship of vital rates is believed to be a universal pattern for diverse life-histories. We tested for such a relationship using multi-year demographic data on a large number of populations of two perennial plant species. Applying different approaches, we first examined the overall variability-importance relationship for the average main vital rates (survival, growth, retrogression, fecundity) per species, and then separately for each population. We found an overall inverse relationship between temporal variation and importance of the average main vital rates for both study species, but these negative species-level correlations were mainly caused by different scales of the examined vital rates. When variability-importance relationships were examined across individual demographic transitions within populations, the abundance of positive and negative correlations depended largely on the method used, and positive correlations were more common after correcting vital rates for sampling variation than when using uncorrected vital rates. Our results cast doubt on the generality of the demographic buffering hypothesis, suggesting that the inverse variability-importance relationship may not be a universal pattern when vital rates are examined for multiple populations of the same plant species.     

New inferences from tree shape: numbers of missing taxa and population growth rates

The relative positions of branching events in a phylogeny contain information about evolutionary and population dynamic processes. We provide new summary statistics of branching event times and describe how these statistics can be used to infer rates of species diversification from interspecies trees or rates of population growth from intraspecies trees. We also introduce a phylogenetic method for estimating the level of taxon sampling in a clade. Different evolutionary models and different sampling regimes can produce similar patterns of branching events, so it is important to consider explicitly the model assumptions involved when making evolutionary inferences. Results of an analysis of the phylogeny of the mosquito-borne flaviviruses suggest that there could be several thousand currently unidentified viruses in this clade.     

Inheritance and state switching of genetic toggle switch in different culture growth phases

Using the gene engineering methods, one can construct simple artificial gene networks with two stable functioning regimes (bistable genetic systems). Such genetic systems make it possible for cells with identical genotype to inherit two alternative phenotypes. The toggle switch is just one of the types of bistable genetic systems. In this work, we investigate the inheritance and switching of toggle switch functioning regimes in the cells at different culture growth phases. It is shown that during transition into the stationary growth phase the inheritance of stable states is disturbed and variations in the toggle-switching rate are more possible in different cells. Also, simultaneous expression of two genes of the system has been experimentally modelled. According to our results, the culture growth phase in this period determines later on the ratio between cell phenotypes in a population.     

The interactive effects of herbivory and mixed mating for the population dynamics of Impatiens capensis

In this study, we examine the demographic consequences of mixed mating and explore the interactive effects of vegetative herbivory and mating system for population dynamics of Impatiens capensis, a species with an obligate mixed mating system (i.e., individuals produce both obligately selfing cleistogamous and facultatively outcrossing chasmogamous flowers). In two natural populations, we followed seeds derived from cleistogamous and chasmogamous flowers subject to different herbivory levels throughout their life cycle. Using a mating system-explicit projection matrix model, we found that mating system types differed in important vital rates. Cleistogamous individuals had higher rates of germination than did chasmogamous individuals, whereas chasmogamous individuals expressed a fecundity advantage over cleistogamous individuals. In addition, population growth was most sensitive to changes in vital rates of cleistogamous individuals, indicating the demographic importance of selfing for these populations. Herbivory also had demographic consequences; a 33%-49% reduction in herbivory caused the population growth rates to increase by 104%-132%, primarily because of effects on vital rates of selfed individuals. Our results not only uncover a novel consequence of mating system expression, that is, mating system influences population dynamics, but also shed light on the role of herbivores in maintaining mixed mating.     

Population-specific demography and invasion potential in medfly

Biological invasions are constantly gaining recognition as a significant component of global change. The Mediterranean fruit fly (medfly) constitutes an ideal model species for the study of biological invasions due to its (1) almost cosmopolitan geographic distribution, (2) huge economic importance, and (3) well-documented invasion history. Under a common garden experimental set up, we tested the hypothesis that medfly populations obtained from six global regions [Africa (Kenya), Pacific (Hawaii), Central America (Guatemala), South America (Brazil), Extra-Mediterranean (Portugal), and Mediterranean (Greece)] have diverged in important immature life-history traits such as preadult survival and developmental times. We also tested the hypothesis that medfly populations from the above regions exhibit different population growth rates. For this purpose, data on the life history of immatures were combined with adult survival and reproduction data derived from an earlier study in order to calculate population parameters for the above six populations. Our results clearly show that medfly populations worldwide exhibit significant differences in preadult survival, developmental rates of immatures and important population parameters such as the intrinsic rate of increase. Therefore, geographically isolated medfly populations may share different invasion potential, since population growth rates could influence basic population processes that operate mostly during the last two stages of an invasion event, such as establishment and spread. Our findings provide valuable information for designing population suppression measures and managing invasiveness of medfly populations worldwide.     

Effects of antibiotic resistance alleles on bacterial evolutionary responses to viral parasites

Antibiotic resistance has wide-ranging effects on bacterial phenotypes and evolution. However, the influence of antibiotic resistance on bacterial responses to parasitic viruses remains unclear, despite the ubiquity of such viruses in nature and current interest in therapeutic applications. We experimentally investigated this by exposing various Escherichia coli genotypes, including eight antibiotic-resistant genotypes and a mutator, to different viruses (lytic bacteriophages). Across 960 populations, we measured changes in population density and sensitivity to viruses, and tested whether variation among bacterial genotypes was explained by their relative growth in the absence of parasites, or mutation rate towards phage resistance measured by fluctuation tests for each phage. We found that antibiotic resistance had relatively weak effects on adaptation to phages, although some antibiotic-resistance alleles impeded the evolution of resistance to phages via growth costs. By contrast, a mutator allele, often found in antibiotic-resistant lineages in pathogenic populations, had a relatively large positive effect on phage-resistance evolution and population density under parasitism. This suggests costs of antibiotic resistance may modify the outcome of phage therapy against pathogenic populations previously exposed to antibiotics, but the effects of any co-occurring mutator alleles are likely to be stronger.     

Phenotypic Diversification of Microbial Pathogens—Cooperating and Preparing for the Future

Recent studies revealed an amazing phenotypic heterogeneity between genetically identical individual cells within populations of microbial pathogens. During the course of an infection, subpopulations occur, which differ in certain virulence-relevant factors, stress adaptation functions or physiological and metabolic abilities. The mechanisms driving this heterogeneity are divergent reactions of the pathogens to differences in host tissue microenvironments. In addition, certain genetic regulatory circuits with positive feedback loops and stochastic differences in gene expression can generate endogenous fluctuations in regulatory components leading to bistable expression of virulence-associated functions. Here, we focus on the occurrence of phenotypic heterogeneity in populations of well-studied examples of pathogens, which enables cooperative, social behavior where a subpopulation of producers shares fitness- and/or virulence-relevant goods and traits with non-producers. We further highlight that this strategy allows preadaptation of a subgroup of cells to recurrent and thus predictable changes of the environment that they encounter during the different stages of the infection. The diversity within bacterial communities has a significant influence on the survival of the pathogens within their hosts and the progression of the disease.     

Evolution and population dynamics in stochastic environments

Inter-generational temporal variability of the environment is important in the evolution and adaptation of phenotypic traits. We discuss a population-dynamic approach which plays a central role in the analysis of evolutionary processes. The basic principle is that the phenotypes with the greatest long-term average growth rate will dominate the entire population. The calculation of longterm average growth rates for populations under temporal stochasticity can be highly cumbersome. However, for a discrete non-overlapping population, it is identical to the geometric mean of the growth rates (geometric mean fitness), which is usually different from the simple arithmetic mean of growth rates. Evolutionary outcomes based on geometric mean fitness are often very different from the predictions based on the usual arithmetic mean fitness. In this paper we illustrate the concept of geometric mean fitness in a few simple models. We discuss its implications for the adaptive evolution of phenotypes, e.g. foraging under predation risks and clutch size. Next, we present an application: the risk-spreading egg-laying behaviour of the cabbage white butterfly, and develop a two-patch population dynamic model to show how the optimal solution diverges from the ssual arithmetic mean approach. The dynamics of these stochastic models cannot be predicted from the dynamics of simple deterministic models. Thus the inclusion of stochastic factors in the analyses of populations is essential to the understanding of not only population dynamics, but also their evolutionary dynamics.