Evolutionarily stable mutation rate in a periodically changing environment

Evolution of mutation rate controlled by a neutral modifier is studied for a locus with two alleles under temporally fluctuating selection pressure. A general formula is derived to calculate the evolutionarily stable mutation rate μ(ess) in an infinitely large haploid population, and following results are obtained. (I) For any fluctuation, periodic or random: (1) if the recombination rate r per generation between the modifier and the main locus is 0, μ(ess) is the same as the optimal mutation rate μ(op) which maximizes the long-term geometric average of population fitness; and (2) for any r, if the strength s of selection per generation is very large, μ(ess) is equal to the reciprocal of the average number T of generations (duration time) during which one allele is persistently favored than the other. (II) For a periodic fluctuation in the limit of small s and r, μ(ess)T is a function of sT and rT with properties: (1) for a given sT, μ(ess)T decreases with increasing rT; (2) for sT </= 1, μ(ess)T is almost independent of sT, and depends on rT as μ(ess)T & 1.6 for rT << 1 and μ(ess)T & 6/rT for rT >> 1; and (3) for sT >/= 1, and for a given rT, μ(ess)T decreases with increasing sT to a certain minimum less than 1, and then increases to 1 asymptotically in the limit of large sT. (III) For a fluctuation consisting of multiple Fourier components (i.e., sine wave components), the component with the longest period is the most effective in determining μ(ess) (low pass filter effect). (IV) When the cost c of preventing mutation is positive, the modifier is nonneutral, and μ(ess) becomes larger than in the case of neutral modifier under the same selection pressure acting at the main locus. The value of c which makes μ(ess) equal to μ(op) of the neutral modifier case is calculated. It is argued that this value gives a critical cost such that, so long as the actual cost exceeds this value, the evolution rate at the main locus must be smaller than its mutation rate μ(ess).     

Universal reserve constants and selection criteria in the periodically changing environment

The authors analyse different approaches (geometrical and analytical) to investigate the dynamic of competing populations in changing environment. For the broad range of models a sufficient character of selection is determined: in changing environment one population excludes the others if its productivity is higher with some reserve. In competition models "everybody against everybody" there is a universal reserve constant that is not depended on the number of populations in community. In the models "everybody against one" reserve constant can increase without limits in increasing the number of competitors.     

Population models in a periodically fluctuating environment

Summary We investigate the behavior of population models in the presence of a periodically fluctuating environment. We consider in particular single-species models and models of interspecific competition. It is shown that the fluctuations cause constant equilibrium states to be replaced by periodic equilibrium states, with a shift in the mean value relative to the constant-environment state. It is shown also that the locations of points of exchange of stability may be changed as a result of the fluctuations.     

A mixed strategy model for the emergence and intensification of social learning in a periodically changing natural environment

Based on a population genetic model of mixed strategies determined by alleles of small effect, we derive conditions for the evolution of social learning in an infinite-state environment that changes periodically over time. Each mixed strategy is defined by the probabilities that an organism will commit itself to individual learning, social learning, or innate behavior. We identify the convergent stable strategies (CSS) by a numerical adaptive dynamics method and then check the evolutionary stability (ESS) of these strategies. A strategy that is simultaneously a CSS and an ESS is called an attractive ESS (AESS). For certain parameter sets, a bifurcation diagram shows that the pure individual learning strategy is the unique AESS for short periods of environmental change, a mixed learning strategy is the unique AESS for intermediate periods, and a mixed learning strategy (with a relatively large social learning component) and the pure innate strategy are both AESS's for long periods. This result entails that, once social learning emerges during a transient era of intermediate environmental periodicity, a subsequent elongation of the period may result in the intensification of social learning, rather than a return to innate behavior.     

A mixed strategy model for the emergence and intensification of social learning in a periodically changing natural environment

Based on a population genetic model of mixed strategies determined by alleles of small effect, we derive conditions for the evolution of social learning in an infinite-state environment that changes periodically over time. Each mixed strategy is defined by the probabilities that an organism will commit itself to individual learning, social learning, or innate behavior. We identify the convergent stable strategies (CSS) by a numerical adaptive dynamics method and then check the evolutionary stability (ESS) of these strategies. A strategy that is simultaneously a CSS and an ESS is called an attractive ESS (AESS). For certain parameter sets, a bifurcation diagram shows that the pure individual learning strategy is the unique AESS for short periods of environmental change, a mixed learning strategy is the unique AESS for intermediate periods, and a mixed learning strategy (with a relatively large social learning component) and the pure innate strategy are both AESS's for long periods. This result entails that, once social learning emerges during a transient era of intermediate environmental periodicity, a subsequent elongation of the period may result in the intensification of social learning, rather than a return to innate behavior.     

Evolution in a changing environment: a case study with great tit fledging mass

Heritable phenotypic traits under significant and consistent directional selection often fail to show the expected evolutionary response. A potential explanation for this contradiction is that because environmental conditions change constantly, environmental change can mask an evolutionary response to selection. We combined an "animal model" analysis with 36 years of data from a long-term study of great tits (Parus major) to explore selection on and evolution of a morphological trait: body mass at fledging. We found significant heritability of this trait, but despite consistent positive directional selection on both the phenotypic and the additive genetic component of body mass, the population mean phenotypic value declined rather than increased over time. However, the mean breeding value for body mass at fledging increased over time, presumably in response to selection. We show that the divergence between the response to selection observed at the levels of genotype and phenotype can be explained by a change in environmental conditions over time, that is, related both to increased spring temperature before breeding and elevated population density. Our results support the suggestion that measuring phenotypes may not always give a reliable impression of evolutionary trajectories and that understanding patterns of phenotypic evolution in nature requires an understanding of how the environment has itself changed.     

Tropical forests in a changing environment

Understanding and mitigating the impact of an ever-increasing population and global economic activity on tropical forests is one of the great challenges currently facing biologists, conservationists and policy makers. Tropical forests currently face obvious regional changes, both negative and positive, and uncertain global changes. Although deforestation rates have increased to unprecedented levels, natural secondary succession has reclaimed approximately 15% of the area deforested during the 1990s. Governments have also protected 18% of the remaining tropical moist forest; however, unsustainable hunting continues to threaten many keystone mammal and bird species. The structure and dynamics of old-growth forests appear to be rapidly changing, suggesting that there is a pantropical response to global anthropogenic forcing, although the evidence comes almost exclusively from censuses of tree plots and is controversial. Here, I address ongoing anthropogenic change in tropical forests and suggest how these forests might respond to increasing anthropogenic pressure.     

Sexual conflict in a changing environment

Sexual conflict has extremely important consequences for various evolutionary processes including its effect on local adaptation and extinction probability during environmental change. The awareness that the intensity and dynamics of sexual conflict is highly dependent on the ecological setting of a population has grown in recent years, but much work is yet to be done. Here, we review progress in our understanding of the ecology of sexual conflict and how the environmental sensitivity of such conflict feeds back into population adaptivity and demography, which, in turn, determine a population's chances of surviving a sudden environmental change. We link two possible forms of sexual conflict – intralocus and interlocus sexual conflict – in an environmental context and identify major gaps in our knowledge. These include sexual conflict responses to fluctuating and oscillating environmental changes and its influence on the interplay between interlocus and intralocus sexual conflict, among others. We also highlight the need to move our investigations into more natural settings and to investigate sexual conflict dynamics in wild populations.     

Aquatic hyphomycetes in a changing environment

In 1942, Ingold documented an ecologically defined group of fungi, aquatic hyphomycetes, on autumn-shed leaves decaying in streams. They were shown to be vital intermediaries between the nutritionally poor leaf substratum and leaf-eating invertebrates. Research has subsequently emphasized functional aspects such as leaf decomposition and nutritional conditioning by fungi. Structural aspects (community composition) have attracted less attention, partly because of the difficulties of identifying fungal mycelia in situ. Extraction, amplification (PCR, qPCR) and characterization of DNA and RNA, and, more recently, of proteins, allow much greater insights into the presence of fungal taxa, their metabolic status (dead, dormant or active), and their potential and actual participation in decomposition processes. This approach can yield huge amounts of data, and major challenges today are the development and application of suitable bioinformatics techniques. The complexity of data collection and evaluation favour interdisciplinary teams of researchers. Fungi are major players in most ecosystems and are increasingly affected by human impacts. Changing land use, eutrophication/pollution and climate change are among the major factors that affect diversity and ecological functions of aquatic hyphomycetes.     

Evolution of migration in a metapopulation

In this paper a general deterministic discrete-time metapopulation model with a finite number of habitat patches is analysed within the framework of adaptive dynamics. We study a general model and prove analytically that (i) if the resident populations state is a fixed point, then the resident strategy with no migration is an evolutionarily stable strategy, (ii) a mutant population with no migration can invade any resident population in a fixed point state, (iii) in the uniform migration case the strategy not to migrate is attractive under small mutational steps so that selection favours low migration. Some of these results have been previously observed in simulations, but here they are proved analytically in a general case. If the resident population is in a two-cyclic orbit, then the situation is different. In the uniform migration case the invasion behaviour depends both on the type of the residents attractor and the survival probability during migration. If the survival probability during migration is low, then the system evolves towards low migration. If the survival probability is high enough, then evolutionary branching can happen and the system evolves to a situation with several coexisting types. In the case of out-of-phase attractor, evolutionary branching can happen with significantly lower survival probabilities than in the in-phase attractor case. Most results in the two-cyclic case are obtained by numerical simulations. Also, when migration is not uniform we observe in numerical simulations in the two-cyclic orbit case selection for low migration or evolutionary branching depending on the survival probability during migration.     

Assessing rapid evolution in a changing environment

Climate change poses a serious threat to species persistence. Effective modelling of evolutionary responses to rapid climate change is therefore essential. In this review we examine recent advances in phylogenetic comparative methods, techniques normally used to study adaptation over long periods, which allow them to be applied to the study of adaptation over shorter time scales. This increased applicability is largely due to the emergence of more flexible models of character evolution and the parallel development of molecular technologies that can be used to assess adaptive variation at loci scattered across the genome. The merging of phylogenetic and population genetic approaches to the study of adaptation has significant potential to advance our understanding of rapid responses to environmental change.     

Oxygen deprivation stress in a changing environment

Past research into flooding tolerance and oxygen shortages inplants has been motivated largely by cultivation problems ofarable crops. Unfortunately, such species are unsuitable forinvestigating the physiological and biochemical basis of anoxia-toleranceas selection has reduced any tolerance of anaerobiosis and anaerobicsoil conditions that their wild ancestors might have possessed.Restoration of anoxia-tolerance to species that have lost thisproperty is served better by physiological and molecular studiesof the mechanisms that are employed in wild species that stillpossess long-term anoxia-tolerance. Case studies developingthese arguments are presented in relation to a selection ofcrop and wild species. The flooding sensitivity and metabolismof maize is compared in relation to rice in its capacity foranaerobic germination. The sensitivity of potato to floodingis related to its disturbed energy metabolism and inabilityto maintain functioning membranes under anoxia and postinoxia.By contrast, long-term anoxia-tolerance in the American cranberry(Vaccinium macrocarpon) and the arctic grass species Deschampsiaberingensis can be related to the provision and utilizationof carbohydrate reserves. Among temperate species, the sweetflag (Acorus calamus) shows a remarkable tolerance of anoxiain both shoots and roots and is also able to mobilize carbohydrateand maintain ATP levels during anoxia as well as preservingmembrane lipids against anoxic and post-anoxic injury. Phragmitesaustralis and Spartina alterniflora, although anoxia-tolerant,are both sulphide-sensitive species which can pre-dispose themto the phenomenon of die-back in stagnant, nutrient-rich water.Glyceria maxima adapts to flooding through phenological adaptationswith a seasonal metabolic tolerance of anoxia confined to winterand spring which, combined with a facility for root aerationand early spring growth, allows rapid colonization of siteswith only shallow flooding. The diversity of responses to floodingin wild plants suggests that, depending on the life strategyand habitat of the species, many different mechanisms may beinvolved in adapting plants to survive periods of inundationand no one mechanism on its own is adequate for ensuring survival. Key words: Anoxia, hypoxia, flooding, Zea mays, Solanum tuberosum, Oryza sativa, Acorus calamus, Phragmites australis, Glyceria maxima, cranberry     

Perceptual classification in a rapidly changing environment

Humans and monkeys can learn to classify perceptual information in a statistically optimal fashion if the functional groupings remain stable over many hundreds of trials, but little is known about categorization when the environment changes rapidly. Here, we used a combination of computational modeling and functional neuroimaging to understand how humans classify visual stimuli drawn from categories whose mean and variance jumped unpredictably. Models based on optimal learning (Bayesian model) and a cognitive strategy (working memory model) both explained unique variance in choice, reaction time, and brain activity. However, the working memory model was the best predictor of performance in volatile environments, whereas statistically optimal performance emerged in periods of relative stability. Bayesian and working memory models predicted decision-related activity in distinct regions of the prefrontal cortex and midbrain. These findings suggest that perceptual category judgments, like value-guided choices, may be guided by multiple controllers.     

Periodic solutions of population models in a periodically fluctuating environment.

A periodically fluctuating environment is assumed in a population-modeling process that generates nonautonomous difference equations. The existence and uniqueness of periodic solutions are studied. A sufficient condition for existence and a necessary condition for uniqueness are obtained. Stability of the periodic solutions is investigated. Several numerical examples are given to illustrate the basic results, and a brief discussion is presented.     

Sex and adaptation in a changing environment.

In this study we consider a mathematical model of a sexual population that lives in a changing environment. We find that a low rate of environmental change can produce a very large increase in genetic variability. This may help to explain the high levels of heritability observed in many natural populations. We also study asexuality and find that a modest rate of environmental change can be very damaging to an asexual population, while leaving a sexual population virtually unscathed. Furthermore, in a changing environment, the advantages of sexuality over asexuality can be much greater than suggested by most previous studies. Our analysis applies in the case of very large populations, where stochastic forces may be neglected.     

Human choice behaviour in a frequently changing environment

The present experiment provided a replication in humans of an experimental procedure that has been used frequently with nonhumans to investigate choice behaviour in a changing environment. Six volunteers played a computer game, which required tracking of a moving balloon on two simultaneously available response panels for monetary reinforcers. Each of the 15 sessions randomly arranged the following concurrent variable-interval reinforcement schedules, which were in effect until six reinforcers had been obtained: 27:1, 9:1, 3:1, 1:1, 1:3, 1:9, and 1:27. Although many aspects of human performance appeared to be qualitatively similar to that of nonhumans on this procedure, such as the rapid preference shifts towards the within-session reinforcer ratios and the presence of local effects of reinforcers, values of sensitivity to reinforcement were very variable in the present study, as commonly reported in human choice studies. Future variations and refinements of the experimental methods are needed to explore how this variability may be reduced.     

An evolutionary tipping point in a changing environment

Populations can persist in directionally changing environments by evolving. Quantitative genetic theory aims to predict critical rates of environmental change beyond which populations go extinct. Here, we point out that all current predictions effectively assume the same specific fitness function. This function causes selection on the standing genetic variance of quantitative traits to become increasingly strong as mean trait values depart from their optima. Hence, there is no bound on the rate of evolution and persistence is determined by the critical rate of environmental change at which populations cease to grow. We then show that biologically reasonable changes to the underlying fitness function can impose a qualitatively different extinction threshold. In particular, inflection points caused by weakening selection create local extrema in the strength of selection and thus in the rate of evolution. These extrema can produce evolutionary tipping points, where long‐run population growth rates drop from positive to negative values without ever crossing zero. Generic early‐warning signs of tipping points are found to have little power to detect imminent extinction, and require hard‐to‐gather data. Furthermore, we show how evolutionary tipping points produce evolutionary hysteresis, creating extinction debts.