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.     

Optimal switching to diapause in relation to the onset of winter

A model is presented that specifies optimal switching times for the induction of diapause relative to the onset of winter in a deterministic environment. Fitness is defined as an individual's contribution to the overwintering population in diapause at the time of the first hard frost. The fitness of a nondiapausing female is determined by the switching times of her offspring. If age-specific fecundity and survivorship do not change significantly from generation to generation, the optimal switching time precedes the onset of winter by a constant amount of time equal to the age of first reproduction plus the time to produce one offspring plus the difference in ages between the sensitive age and the diapause age. This result is independent of the time at which the original female began to reproduce. However, if fecundity or survivorship decreases toward the end of the season, the optimal switching time depends upon the time when she began to reproduce and should be more conservative by an amount of time that can be computed. Possible tests of the model are proposed.     

The evolution of bet-hedging adaptations to rare scenarios

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

On the evolution of mutation in changing environments: recombination and phenotypic switching

Phenotypic switching has been observed in laboratory studies of yeast and bacteria, in which the rate of such switching appears to adjust to match the frequency of environmental changes. Among possible mechanisms of switching are epigenetic influences on gene expression and variation in levels of methylation; thus environmental and/or genetic factors may contribute to the rate of switching. Most previous analyses of the evolution of phenotypic switching have compared exponential growth rates of noninteracting populations, and recombination has been ignored. Our genetic model of the evolution of switching rates is framed in terms of a mutation-modifying gene, environments that cause periodic changes in fitness, and recombination between the mutation modifier and the gene under selection. Exact results are obtained for all recombination rates and symmetric fitnesses that strongly generalize earlier results obtained under complete linkage and strong constraints on the relation between fitness and period of switching. Our analytical and numerical results suggest a general principle that recombination reduces the stable rate of switching in symmetric and asymmetric fitness regimes and when the period of switching is random. As the recombination rate increases, it becomes less likely that there is a stable nonzero rate of switching.     

Adaptation to slow environmental change, with apparent anticipation of selection

We investigate a genetic model of a large population of sexual organisms in a changing environment. The organisms are subject to stabilising selection on a quantitative trait, with environmental change causing the fitness optimum to move. When the fitness optimum moves slowly, adaptation to the changing environment occurs by means of reasonably well-separated substitutions at the loci controlling the trait. In this way, the trait generally tracks the moving optimum, but in such a case, the population may exhibit periods of time where the mean trait value overshoots the moving optimal trait value, thereby exhibiting an apparent anticipation of selection. The mechanism underlying this phenomenon is determined from consideration of a simpler model that correctly captures the observed dynamical behaviour. We note that very slow rates of changes of traits are seen in the fossil record and the present work may be relevant to this topic.     

Expected relative fitness and the adaptive topography of fluctuating selection

Wright's adaptive topography describes gene frequency evolution as a maximization of mean fitness in a constant environment. I extended this to a fluctuating environment by unifying theories of stochastic demography and fluctuating selection, assuming small or moderate fluctuations in demographic rates with a stationary distribution, and weak selection among the types. The demography of a large population, composed of haploid genotypes at a single locus or normally distributed phenotypes, can then be approximated as a diffusion process and transformed to produce the dynamics of population size, N, and gene frequency, p, or mean phenotype, . The expected evolution of p or is a product of genetic variability and the gradient of the long-run growth rate of the population, , with respect to p or . This shows that the expected evolution maximizes , the mean Malthusian fitness in the average environment minus half the environmental variance in population growth rate. Thus, as a function of p or represents an adaptive topography that, despite environmental fluctuations, does not change with time. The haploid model is dominated by environmental stochasticity, so the expected maximization is not realized. Different constraints on quantitative genetic variability, and stabilizing selection in the average environment, allow evolution of the mean phenotype to undergo a stochastic maximization of . Although the expected evolution maximizes the long-run growth rate of the population, for a genotype or phenotype the long-run growth rate is not a valid measure of fitness in a fluctuating environment. The haploid and quantitative character models both reveal that the expected relative fitness of a type is its Malthusian fitness in the average environment minus the environmental covariance between its growth rate and that of the population.     

Algorithms for optimization of the transport system in living and artificial cells

An optimization of the transport system in a cell has been considered from the viewpoint of the operations research. Algorithms for an optimization of the transport system of a cell in terms of both the efficiency and a weak sensitivity of a cell to environmental changes have been proposed. The switching of various systems of transport is considered as the mechanism of weak sensitivity of a cell to changes in environment. The use of the algorithms for an optimization of a cardiac cell has been considered by way of example. We received theoretically for a cell of a cardiac muscle that at the increase of potassium concentration in the environment switching of transport systems for this ion takes place. This conclusion qualitatively coincides with experiments. The problem of synthesizing an optimal system in an artificial cell has been stated.     

Plastic inducible morphologies are not always adaptive: The importance of time delays in a stochastic environment

Summary We present a mathematical model for predicting the expected fitness of phenotypically plastic organisms experiencing a variable environment. We assume that individuals experience two discrete environments probabilistically in time (as a Markov process) and that there are two different phenotypic states, each yielding the highest fitness in one of the two environments. We compare the expected fitness of a phenotypically fixed individual to that of an individual whose phenotype is induced to produce the better phenotype in each environment with a time lag between experiencing a new environment and realization of the new phenotype. Such time lags are common in organisms where phenotypically plastic, inducible traits have been documented. We find that although plasticity is generally adaptive when time lags are short (relative to the time scale of environmental variability), plasticity can be disadvantageous for longer lag times. Asymmetries in environmental change probabilities and/or the relative fitnesses of each phenotype strongly influence whether plasticity is favoured. In contrast to other models, our model does not require costs for plasticity to be disadvantageous; costs affect the results quantitatively, not qualitatively.     

Adaptation to spatially heterogeneous modifying and adaptive environments

The development of an individual's phenotype is influenced by environmental factors (the modifying environment) which may differ from those factors (the adaptive environment) that decide on the adaptational value of the developed phenotype. The shapes of adaptationally optimal norms of reaction are therefore essentially determined by associations between these two environmental components together with the degree of adaptational sensitivity of the developed phenotypes. Two complementary aspects of optimality are accounted for: (a) environments can be optimal for a given norm of reaction and (b) norms of reaction can be optimal for a given environment. The results are obtained for random distribution of genotypes over environmental conditions and under the physiologically reasonable premise that fitness is a function of the costs of modification and adaptation. It turned out that the associations of adaptive and modifying environments are the primary sources of adaptational optimization. More specifically, it is shown that (i) independence between the two environmental components constitutes an adaptationally optimal environment only for norms of reaction in which all phenotypes are adaptively insensitive; (ii) if costs of modification do not depend on the environment, and if the two environmental components are not associated, adaptationally optimal norms of reaction can always be realized through phenogenetic invariance; (iii) as a rule, adaptively sensitive phenotypes developed under strong environmental associations necessitate phenogenetic plasticity for the optimal norm of reaction; (iv) a norm of reaction which is adaptationally optimal in its adaptationally optimal environment can always be realized through phenogenetic invariance, if costs of modification do not vary with the environment. These results reveal an important role of patterns of adaptive sensitivity of phenotypes, which may even surpass that of shapes of norms of reaction in adaptational processes.     

Quantification and decomposition of environment‐selection relationships

In nature, selection varies across time in most environments, but we lack an understanding of how specific ecological changes drive this variation. Ecological factors can alter phenotypic selection coefficients through changes in trait distributions or individual mean fitness, even when the trait‐absolute fitness relationship remains constant. We apply and extend a regression‐based approach in a population of Soay sheep (Ovis aries) and suggest metrics of environment‐selection relationships that can be compared across studies. We then introduce a novel method that constructs an environmentally structured fitness function. This allows calculation of full (as in existing approaches) and partial (acting separately through the absolute fitness function slope, mean fitness, and phenotype distribution) sensitivities of selection to an ecological variable. Both approaches show positive overall effects of density on viability selection of lamb mass. However, the second approach demonstrates that this relationship is largely driven by effects of density on mean fitness, rather than on the trait‐fitness relationship slope. If such mechanisms of environmental dependence of selection are common, this could have important implications regarding the frequency of fluctuating selection, and how previous selection inferences relate to longer term evolutionary dynamics.     

Offspring fitness and the optimal propagule size in a fluctuating environment

Propagule size is an important maternal effect on offspring fitness and phenotype in birds and other oviparous animals. The performance of propagules often increases with size, but a fluctuating environment may introduce temporal variation in the optimal phenotype. Understanding these mechanisms will provide novel insights into the eco‐evolutionary dynamics of life history strategies in parental reproductive investment. We investigated the interaction between propagule size (measured as egg volume) and environmental conditions on offspring mortality and phenotype in a Norwegian house sparrow population. Increased propagule size reduced offspring mortality in early life, with more pronounced effects under heavy precipitation. However, the optimal propagule size for low offspring mortality until recruitment shifted from large to small as temperature increased. Propagule size had no significant effect on fledgling body mass and tarsus length. These results reveal a potential for eco‐evolutionary dynamics in propagule size, as populations adapt to fluctuating environmental conditions. The ultimate outcome of this dynamic process will also depend on variation in parental fitness and tradeoffs with other life‐history traits, particularly clutch size.     

Environmental change, phenotypic plasticity, and genetic compensation

When a species encounters novel environmental conditions, some phenotypic characters may develop differently than in the ancestral environment. Most environmental perturbations of development are likely to reduce fitness, and thus selection would usually be expected to favor genetic changes that restore the ancestral phenotype. I propose the term "genetic compensation" to refer to this form of adaptive evolution. Genetic compensation is a subset of genetic accommodation and the reverse of genetic assimilation. When genetic compensation has occurred along a spatial environmental gradient, the mean trait values of populations in different environments may be more similar in the field than when representatives of the same populations are raised in a common environment (i.e., countergradient variation). If compensation is complete, genetic divergence between populations may be cryptic, that is, not detectable in the field. Here I apply the concept of genetic compensation to three examples involving carotenoid-based sexual coloration and then use these and other examples to discuss the concept in a broader context. I show that genetic compensation may lead to a cryptic form of reproductive isolation between populations evolving in different environments, may explain some puzzling cases in which heritable traits exposed to strong directional selection fail to show the expected evolutionary response, and may complicate efforts to monitor populations for signs of environmental deterioration.     

Interspecific Competition, Environmental Gradients, Gene Flow, and the Coevolution of Species' Borders

Darwin viewed species range limits as chiefly determined by an interplay between the abiotic environment and interspecific interactions. Haldane argued that species' ranges could be set intraspecifically when gene flow from a species' populous center overwhelms local adaptation at the periphery. Recently, Kirkpatrick and Barton have modeled Haldane's process with a quantitative genetic model that combines density-dependent local population growth with dispersal and gene flow across a linear environmental gradient in optimum phenotype. To address Darwin's ideas, we have extended the Kirkpatrick and Barton model to include interspecific competition and the frequency-dependent selection that it generates, as well as stabilizing selection on a quantitative character. Our model includes local population growth, movements over space, natural selection, and gene flow. It simultaneously addresses the evolution of character displacement and species borders. It reproduces the Kirkpatrick and Barton single-species result that limited ranges can be produced with sufficiently steep environmental gradients and strong dispersal. Further, in the absence of environmental gradients or barriers to dispersal, interspecific competition will not limit species ranges at evolutionary equilibrium. However, interspecific competition can interact with environmental gradients and gene flow to generate limited ranges with much less extreme gradient and dispersal parameters than in the single-species case. Species display character displacement in sympatry, yet the reduction in competition that results from this displacement does not necessarily allow the two species to become sympatric everywhere. When species meet, competition reduces population densities in the region of overlap, which, in turn, intensifies the asymmetry in gene flow from center to margin. This reduces the ability of each species to adapt to local physical conditions at their range limits. If environmental gradients are monotonic but not linear, the transition zone between species at coevolutionary equilibrium occurs where the environmental gradient is steepest. If productivity gradients are also introduced into the model, then patterns similar to Rapoport's rule emerge. Interacting species respond to climate change, as it affects the optimal phenotype over space, by a combination of range shifts and local evolution in mean phenotype, while solitary species respond solely by range shifts. Finally, we compare empirical estimates for intrinsic growth rates and diffusion coefficients for several species to those needed by the single-species model to produce a stable limited range. These empirical values are generally insufficient to produce limited ranges in the model suggesting a role for interspecific interactions.     

Adaptation to an extraordinary environment by evolution of phenotypic plasticity and genetic assimilation

Adaptation to a sudden extreme change in environment, beyond the usual range of background environmental fluctuations, is analysed using a quantitative genetic model of phenotypic plasticity. Generations are discrete, with time lag τ between a critical period for environmental influence on individual development and natural selection on adult phenotypes. The optimum phenotype, and genotypic norms of reaction, are linear functions of the environment. Reaction norm elevation and slope (plasticity) vary among genotypes. Initially, in the average background environment, the character is canalized with minimum genetic and phenotypic variance, and no correlation between reaction norm elevation and slope. The optimal plasticity is proportional to the predictability of environmental fluctuations over time lag τ. During the first generation in the new environment the mean fitness suddenly drops and the mean phenotype jumps towards the new optimum phenotype by plasticity. Subsequent adaptation occurs in two phases. Rapid evolution of increased plasticity allows the mean phenotype to closely approach the new optimum. The new phenotype then undergoes slow genetic assimilation, with reduction in plasticity compensated by genetic evolution of reaction norm elevation in the original environment.     

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

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

Early life of fathers affects offspring fitness in a wild rodent

Intergenerational fitness effects on offspring due to the early life of the parent are well studied from the standpoint of the maternal environment, but intergenerational effects owing to the paternal early life environment are often overlooked. Nonetheless, recent laboratory studies in mammals and ecologically relevant studies in invertebrates predict that paternal effects can have a major impact on the offspring's phenotype. These nongenetic, environment‐dependent paternal effects provide a mechanism for fathers to transmit environmental information to their offspring and could allow rapid adaptation. We used the bank vole Myodes glareolus, a wild rodent species with no paternal care, to test the hypothesis that a high population density environment in the early life of fathers can affect traits associated with offspring fitness. We show that the protein content in the diet and/or social environment experienced during the father's early life (prenatal and weaning) influence the phenotype and survival of his offspring and may indicate adaptation to density‐dependent costs. Furthermore, we show that experiencing multiple environmental factors during the paternal early life can lead to a different outcome on the offspring phenotype than stimulated by experience of a single environmental factor, highlighting the need to study developmental experiences in tandem rather than independent of each other.     

Development and evolution of adaptive polyphenisms

Phenotypic plasticity is the primitive character state for most if not all traits. Insofar as developmental and physiological processes obey the laws of chemistry and physics, they will be sensitive to such environmental variables as temperature, nutrient supply, ionic environment, and the availability of various macro- and micronutrients. Depending on the effect this phenotypic plasticity has on fitness, evolution may proceed to select either for mechanisms that buffer or canalize the phenotype against relevant environmental variation or for a modified plastic response in which some ranges of the phenotypic variation are adaptive to particular environments. Phenotypic plasticity can be continuous, in which case it is called a reaction norm, or discontinuous, in which case it is called a polyphenism. Although the morphological discontinuity of some polyphenisms is produced by discrete developmental switches, most polyphenisms are due to discontinuities in the environment that induce only portions of what is in reality a continuous reaction norm. In insect polyphenisms, the environmental variable that induces the alternative phenotype is a token stimulus that serves as a predictor of, but is not itself, the environment to which the polyphenism is an adaptation. In all cases studied so far, the environmental stimulus alters the endocrine mechanism of metamorphosis by altering either the pattern of hormone secretion or the pattern of hormone sensitivity in different tissues. Such changes in the patterns of endocrine interactions result in the execution of alternative developmental pathways. The spatial and temporal compartmentalization of endocrine interactions has produced a developmental mechanism that enables substantial localized changes in morphology that remain well integrated into the structure and function of the organism.     

How stress selects for reversible phenotypic plasticity

Stress occurring in periods shorter than life span strongly selects for reversible phenotypic plasticity, for maximum reliability of stress indicating cues and for minimal response delays. The selective advantage of genotypes that are able to produce adaptive reversible plastic phenotypes is calculated by using the concept of environmental tolerance. Analytic expressions are given for optimal values of mode and breadth of tolerance functions for stress induced and non-induced phenotypes depending on (1) length of stress periods, (2) response delay for switching into the induced phenotype, (3) response delay for rebuilding the non-induced phenotype, (4) intensity of stress, i.e. mean value of the stress inducing environment, (5) coefficient of variation of the stress environment and (6) completeness of information available to the stressed organism. Adaptively reversible phenotypic plastic traits will most probably affect fitness in a way that can be described by simultaneous reversible plasticity in mode and breadth of tolerance functions.     

Evolution and maintenance of the environmental component of the phenotypic variance: benefit of plastic traits under changing environments

How environmental variances in quantitative traits are influenced by variable environments is an important problem in evolutionary biology. In this study, the evolution and maintenance of phenotypic variance in a plastic trait under stabilizing selection are investigated. The mapping from genotypic value to phenotypic value of the quantitative trait is approximated by a linear reaction norm, with genotypic effects on its phenotypic mean and sensitivity to environment. The environmental deviation is assumed to be decomposed into environmental quality, which interacts with genotypic value, and residual developmental noise, which is independent of genotype. Environmental quality and the optimal phenotype of stabilizing selection are allowed to randomly fluctuate in both space and time, and individuals migrate equally before development and reproduction among different niches. Analyses show that phenotypic plasticity is adaptive within variable environments if correlations have become established between the optimal phenotype and environmental quality in space and/or time. The evolved plasticity increases with variances in optimal phenotypes and correlations between optimal phenotype and environmental quality; this further induces increases in mean fitness and the environmental variance in the trait. Under certain circumstances, however, the environmental variance may decrease with increase in variation in environmental quality.