Single species evolutionary dynamics

Not long after the introduction of evolutionary stable strategy (ESS) concept, it was noticed that dynamic selection did not always lead to the establishment of the ESS. The concept of continuously stable strategy (CSS) was thereafter developed. It was generally accepted that dynamic selection leads to the establishment of an ESS if it is a CSS. Examination of an evolutionary stability concept which is called neighborhood invader strategy (NIS) shows that it may be impossible for an ESS to be established through dynamic selection even if it is a CSS and no polymorphisms occur. We will examine the NIS concept and its implications for two evolutionary game models: root-shoot allocation in plant competition and Lotka–Volterra competition. In the root-shoot model we show that an ESS will be attained through dynamic selection if it is a NIS. Similarly for the Lotka–Volterra model, we show that an ESS will be attained through dynamic selection even if protected dimorphisms occur during the evolutionary process if it is an NIS.     

Red Queens and ESS: the coevolution of evolutionary rates

Summary The Red Queen principle states that a set of interacting species reaches an evolutionary equilibrium at which all their rates of coevolution exactly balance each other. The lag-load model, which is one way of searching for Red Queens, has, by itself, previously predicted that they do not exist. But this model has assumed that infinite maladaptedness is possible. The lag-load model is improved by assuming that once the lag load of all but one species is determined, so is that of the final species. This assumption eliminates the possibility of infinite maladaptedness. Its result is to allow the lag-load model to yield Red Queen coevolution. It does this whether or not speciation and extinction rates are included. Thus the lag-load model is harmonized with the earlier Red Queen model derived from studies of predation.Because of the intercorrelation of phenotypic traits, the predatory model concluded that the eventual stable rate of coevolution must be zero (except for intermittent bursts after some correlation or compromise is successfully broken). Another model that predicts stable coevolutionary rates of zero is that of evolutionarily stable strategies (ESS).Red Queen assumes that the more extreme a phenotypic trait is, the better it is, and that there are no constraints on the growth of such a phenotypic trait value. Such traits are the key to the Red Queen prediction of progressive coevolution. ESS models make no such assumptions. Eliminating unbounded traits from the model of predator-victim evolution changed its prediction from progressive coevolution to stasis. Before this paper, no model had dealt simultaneously with both unbounded and constrained traits.To handle both sorts of phenotypic traits at the same time in the same model, we abandoned lag load as a measure of evolutionary rate (lag loads do not uniquely determine phenotype). Instead, we used the traditional assumption that rate is proportional to the slope of the adaptive landscape. A model, relying on continuous evolutionary game theory, was developed and simulated under various conditions in two or three species sets, with up to five independent traits coevolving simultaneously. The results were: (1) there was always a set of equilibrium densities eventually achieved by coevolution; if the population interaction represented by this stable coevolutionary state is also stable, then the system should persist whether it evolves further or not; (2) whenever traits were present which were unbounded and best at their most extreme values, then a Red Queen emerged; (3) whenever traits were present which were correlated with each other or constrained below infinity, then an ESS emerged; (4) if both types were present, both results occurred: Red Queen in the unbounded traits and ESS in the constrained ones.Because unbounded traits may not exist, the Red Queen may have no domain. But the domain of ESS is real. ESS should lead to the evolutionary pattern called punctuated equilibrium. The changes in design rules which punctuate stasis should lead to an ever-expanding independence of traits from each other, i.e. to more and more refined differentiation. A single set of design rules which governs a set of species is called a fitness-generating function. Such functions may help to define the concepts of adaptive zone and ecological guild.     

Multi-species evolutionary dynamics

Dynamical attainability of an evolutionarily stable strategy (ESS) through the process of mutations and natural selection has mostly been addressed through the use of the continuously stable strategy (CSS) concept for species evolutionary games in which strategies are drawn from a continuum, and by the adaptive trait dynamics method. We address the issue of dynamical attainability of an ESS in coevolving species through the use of the concept of an ESNIS. It is shown that the definition of an ESNIS coalition for coevolving species is not in general equivalent to other definitions for CSS given in the literature. We show under some additional conditions that, in a dynamic system which involves the strategies of a dimorphic ESNIS coalition and at most two strategies that are not members of ESNIS coalition, the ESNIS coalition will emerge as the winner. In addition an ESNIS will be approached because of the invasion structure of strategies in its neighborhood. This proves that under the above conditions an ESNIS has a better chance of being attained than a strategy coalition which is a CSS. The theory developed is applied to a class of coevolutionary game models with Lotka–Volterra type interactions and we show that for such models, an ESS coalition will be dynamically attainable through mutations and natural selection if the ESS coalition is also an ESNIS coalition.Co-ordinating editor: Metz     

Do social learning and conformist bias coevolve? Henrich and Boyd revisited

We studied the coevolution of social learning and conformist bias in a modified version of the Henrich and Boyd [1998. The evolution of conformist transmission and the emergence of between-group differences. Evol. Hum. Behav. 19, 215-241] model that nevertheless preserves its essential features. The convergent stable strategies (CSS) are identified by a numerical adaptive dynamics method and then checked for evolutionary stability. A strategy that is simultaneously a CSS and an ESS is called an attractive evolutionarily stable strategy (AESS). Our main findings are as follows. First, the AESS reliance on social learning is monotone increasing in the fixed interval between environmental changes and monotone decreasing in the quality of environmental information. Second, the AESS strength of conformist bias is monotone non-increasing in the fixed interval between environmental changes and monotone non-decreasing in the quality of environmental information. The first observation is in agreement with Henrich and Boyd (1998), but the second is in direct contradiction. In addition, we conducted Monte Carlo simulations as in Henrich and Boyd (1998), which supported our findings. We believe that the reason for the discrepancy with regard to the strength of conformist bias is that Henrich and Boyd (1998) did not allow a sufficient number of iterations for true convergence to occur. In conclusion, the conditions favoring a heavy reliance on social learning are not the same as those favoring a strong conformist bias.     

Do social learning and conformist bias coevolve? Henrich and Boyd revisited

We studied the coevolution of social learning and conformist bias in a modified version of the Henrich and Boyd [1998. The evolution of conformist transmission and the emergence of between-group differences. Evol. Hum. Behav. 19, 215–241] model that nevertheless preserves its essential features. The convergent stable strategies (CSS) are identified by a numerical adaptive dynamics method and then checked for evolutionary stability. A strategy that is simultaneously a CSS and an ESS is called an attractive evolutionarily stable strategy (AESS). Our main findings are as follows. First, the AESS reliance on social learning is monotone increasing in the fixed interval between environmental changes and monotone decreasing in the quality of environmental information. Second, the AESS strength of conformist bias is monotone non-increasing in the fixed interval between environmental changes and monotone non-decreasing in the quality of environmental information. The first observation is in agreement with Henrich and Boyd (1998), but the second is in direct contradiction. In addition, we conducted Monte Carlo simulations as in Henrich and Boyd (1998), which supported our findings. We believe that the reason for the discrepancy with regard to the strength of conformist bias is that Henrich and Boyd (1998) did not allow a sufficient number of iterations for true convergence to occur. In conclusion, the conditions favoring a heavy reliance on social learning are not the same as those favoring a strong conformist bias.     

ORGANIZATION OF PREDATOR-PREY COMMUNITIES AS AN EVOLUTIONARY GAME

We consider a simple predator-prey model of coevolution. By allowing coevolution both within and between trophic levels the model breaks the traditional dichotomy between coevolution among competitors and coevolution between a prey and its predator. By allowing the diversity of prey and predator species to emerge as a property of the evolutionarily stable strategies (ESS), the model breaks another constraint of most approaches to coevolution that consider as fixed the number of coevolving species. The number of species comprising the ESS is influenced by a parameter that determines the predator's niche breadth. Depending upon the parameter's value the ESS may contain: 1) one prey and one predator species, 2) two prey and one predator, 3) two prey and two predators, 4) three prey and two predators, 5) three prey and three predators, etc. Evolutionarily, these different ESSs all emerge from the same model. Ecologically, however, these ESSs result in very different patterns of community organization. In some communities the predator species are ecologically keystone in that their removal results in extinctions among the prey species. In others, the removal of a predator species has no significant impact on the prey community. These varied ecological roles for the predator species contrasts sharply with the essential evolutionary role of the predators in promoting prey species diversity. The ghost of predation past in which a predator's insignificant ecological role obscures its essential evolutionary role may be a frequent property of communities of predator and prey.     

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.     

Plant-Herbivore Interactions and Theory of Coevolution1

Abstract We consider a mathematical model for the coevolution of a plant's defense against herbivores and the herbivore's ability to exploit the plant. The result of coevolution is predicted using the phase portrait of trait value dynamics and contour plots of fitnesses. The following results are derived: (1) The fitnesses of both plant and herbivore are higher at an “armless” state in which both plant and herbivore invest a minimum amount of energy and/or resources in defense and feeding respectively, than at the coevolutionarily stable state (CSS); (2) Perpetual increase in the trait values of both species may occur when the marginal costs of defense and feeding abilities decrease as these abilities increase; (3) If the marginal costs of defense and feeding abilities increase as the abilities increase, there is a coevolutionary equilibrium with finite trait values; (4) There may be more than one coevolutionarily stable state (CSS).     

Sexual conflict over floral receptivity

In flowering plants, the onset and duration of female receptivity vary among species. In several species the receptive structures wilt upon pollination. Here we explore the hypothesis that postpollination wilting may be influenced by pollen and serve as a general means to secure paternity of the pollen donor at the expense of female fitness. Taking a game-theoretical approach, we examine the potential for the evolution of a pollen-borne wilting substance, and for the coevolution of a defense strategy by the recipient plant. The model without defense predicts an evolutionarily stable strategy (ESS) for the production of wilting substance. The ESS value is highest when pollinator visiting rates are intermediate and when the probability that pollen from several donors arrives at the same time is low. This finding has general implications in that it shows that male traits to secure paternity also can evolve in species, such as plants, where mating is not strictly sequential. We further model coevolution of the wilting substance with the timing of stigma receptivity. We assume that pollen-receiving plants can reduce the costs induced by toxic pollen by delaying the onset of stigmatic receptivity. The model predicts a joint ESS, but no female counter-adaptation when the wilting substance is highly toxic. This indicates that toxicity affects the probability that a male manipulative trait stays beneficial (i.e., not countered by female defense) over evolutionary time. We discuss parallels to male induced changes in female receptivity known to occur in animals and the role of harm for the evolution of male manipulative adaptations.     

Measure dynamics on a one-dimensional continuous trait space: theoretical foundations for adaptive dynamics

The measure dynamics approach to modelling single-species coevolution with a one-dimensional trait space is developed and compared to more traditional methods of adaptive dynamics and the Maximum Principle. It is assumed that individual fitness results from pairwise interactions together with a background fitness that depends only on total population size. When fitness functions are quadratic in the real variables parameterizing the one-dimensional traits of interacting individuals, the following results are derived. It is shown that among monomorphisms (i.e. measures supported on a single trait value), the continuously stable strategy (CSS) characterize those that are Lyapunov stable and attract all initial measures supported in an interval containing this trait value. In the cases where adaptive dynamics predicts evolutionary branching, convergence to a dimorphism is established. Extensions of these results to general fitness functions and/or multi-dimensional trait space are discussed.     

COEVOLUTION AS AN EVOLUTIONARY GAME

Coevolution is modeled as a continuous game where the fitness-maximizing strategy of an individual is assumed to be a function of the strategy of other individuals who are also under selection to maximize fitness. An evolutionary stable strategy (ESS) is sought such that no rare alternative strategies can invade the community. The approach can be used to model coevolution because the ESS may be composed of a coalition of more than one strategy. This work, by modeling frequency-dependent selection, extends the approach of Roughgarden (1976) which only considered density-dependent selection. In particular, we show that the coevolutionary model of Rummel and Roughgarden (1985) does contain frequency-dependent selection, and thus, their application of Roughgarden's criterion for evolutionary stability to a model for which it is not applicable leads to the erroneous conclusion that the ecological and evolutionary processes are in conflict. The utility of the game theoretic approach is illustrated by two examples. The first considers an ESS composed of a single strategy, the second an ESS composed of a coalition of two strategies. Evolution occurs on a frequency-dependent adaptive landscape. For this reason, the approach is appropriate for modeling competitive speciation (Rosenzweig, 1978). Also, the game theoretic approach is designed to combine the interplay between the background environment (including the biotic components) and the evolutionary potential of the populations or organisms. The actual application of this theory will require knowledge of both.     

The evolutionary dynamics of direct phenotypic overdominance: emergence possible, loss probable

An evolutionary dynamical system with explicit diploid genetics is used to investigate the likelihood of observing phenotypically overdominant heterozygotes versus heterozygous phenotypes that are intermediate between the homozygotes. In this model, body size evolves in a population with discrete demographic episodes and with competition limiting reproduction. A genotype-phenotype map for body size is used that can generate the two qualitative types of dominance interactions (overdominance versus intermediate dominance). It is written as a single-locus model with one focal locus and parameters summarizing the effects of alleles at other loci. Two types of evolutionarily stable strategy (ESS; continuously stable strategy, CSS) occur. The ESS is generated either (1) by the population ecology; or (2) by a local maximum of the genotype-phenotype map. Overdominant heterozygotes are expected to arise if the population evolves toward the second type of ESS, where nearly maximum body sizes are found. When other loci with partially dominant inheritance also evolve, the location of the maximum in the genotype-phenotype map repeatedly changes. It is unlikely that an evolving population will track these changes; ESSs of the second type now are at best quasi-stationary states of the evolutionary dynamics. Considering the restrictions on its probability, a pattern of phenotypic overdominance is expected to be rare.     

Evolutionary stability in strategic models of single-locus frequency-dependent viability selection

The dynamic stability of an evolutionarily stable strategy (ESS) is analyzed for a diploid species under individual viability selection. An individual's viability depends on the genotypic frequencies at a single autosomal locus through a payoff matrix determined by phenotypic behaviours (i.e. strategies). It is shown that an ESS of this payoff matrix is dynamically stable if there are at most three alleles — an intuitive result that strengthens the importance of static game-theoretic methods in genetic models.Author for correspondence     

A simple model of host-parasite evolutionary relationships. Parasitism: compromise or conflict?

The evolutionary biology of host-parasite relationships are considered here using a simple game-theory model in which hosts play against parasite and vice versa. In this model, the players can choose between two strategies (aggressive or not aggressive) and the utility of the game is envisaged in terms of fitness and selective costs. The game solutions suggest that the two types of confrontation are encountered in symbiotic relationships and thus constitute two Evolutionary Stable Strategies (ESS). These observations lead us to discuss: (i) the status of different kinds of symbiotic relationships (i.e. parasitoidism; parasitism, commensalism and mutualism) related to selective costs and (ii) the position of coevolution in this game theory context.     

Homage to the red queen. I. Coevolution of predators and their victims

In this paper we develop a model to describe the coevolution of a two-species predator-victim ecosystem. Evolution among the predators acts to displace the predators' zero growth isocline, J, to the left, whereas victim evolution has the opposite effect. More important, we show that for many such systems, there is a value of J, J1, at which the rate of predator evolution exactly equals the rate of victim evolution. This value of J turns out to be a coevolutionary steady state (CSS) which is stable to perturbations. It is suggested that this analysis permits qualitative understanding of why certain real world predator-prey systems oscillate, whereas others do not.     

Euthyroid Sick Syndrome as a Prognostic Indicator of COVID-19 Pulmonary Involvement,Associated With Poorer Disease Prognosis and Increased Mortality

ObjectiveThe prevalence of euthyroid sick syndrome (ESS) and its association with the prognosis of COVID-19 and mortality in patients with lung involvement in COVID-19 have not yet been elucidated.MethodsClinical and laboratory data of patients with COVID-19 with or without ESS were collected retrospectively and analyzed on admission. All subjects were admitted to the Department of Internal Diseases and Clinical Pharmacology at Bieganski Hospital between December 2020 and April 2021.ResultsIn total, 310 medical records of patients with COVID-19 were analyzed retrospectively. Among 215 enrolled patients, 82 cases of ESS were diagnosed. The patients with ESS had higher pro-inflammatory factor levels, longer hospitalizations, and a higher risk of requiring high-flow nasal oxygen therapy or intubation than the patients without ESS. The Kaplan-Meier curve indicated that the patients with ESS had a lower probability of survival when computed tomography showed ≤50% parenchymal involvement compared with that in patients without ESS. However, no differences in mortality were noted in those with more than 50% parenchymal involvement. The survival curve showed that ESS was associated with a higher risk of mortality during hospitalization.ConclusionESS is closely associated with a poor prognosis, including longer hospitalizations, more frequent intubation, transfer to the intensive care unit, and a higher mortality rate in patients with COVID-19. ESS is a potential prognostic predictor of survival, regardless of lung involvement in COVID-19.     

The influence of predator--prey population dynamics on the long-term evolution of food web structure

We develop a set of equations to describe the population dynamics of many interacting species in food webs. Predator-prey interactions are nonlinear, and are based on ratio-dependent functional responses. The equations account for competition for resources between members of the same species, and between members of different species. Predators divide their total hunting/foraging effort between the available prey species according to an evolutionarily stable strategy (ESS). The ESS foraging behaviour does not correspond to the predictions of optimal foraging theory. We use the population dynamics equations in simulations of the Webworld model of evolving ecosystems. New species are added to an existing food web due to speciation events, whilst species become extinct due to coevolution and competition. We study the dynamics of species-diversity in Webworld on a macro-evolutionary time-scale. Coevolutionary interactions are strong enough to cause continuous overturn of species, in contrast to our previous Webworld simulations with simpler population dynamics. Although there are significant fluctuations in species diversity because of speciation and extinction, very large-scale extinction avalanches appear to be absent from the dynamics, and we find no evidence for self-organized criticality.     

Accurate Simulation and Detection of Coevolution Signals in Multiple Sequence Alignments

Background

While the conserved positions of a multiple sequence alignment (MSA) are clearly of interest, non-conserved positions can also be important because, for example, destabilizing effects at one position can be compensated by stabilizing effects at another position. Different methods have been developed to recognize the evolutionary relationship between amino acid sites, and to disentangle functional/structural dependencies from historical/phylogenetic ones.

Methodology/Principal Findings

We have used two complementary approaches to test the efficacy of these methods. In the first approach, we have used a new program, MSAvolve, for the in silico evolution of MSAs, which records a detailed history of all covarying positions, and builds a global coevolution matrix as the accumulated sum of individual matrices for the positions forced to co-vary, the recombinant coevolution, and the stochastic coevolution. We have simulated over 1600 MSAs for 8 protein families, which reflect sequences of different sizes and proteins with widely different functions. The calculated coevolution matrices were compared with the coevolution matrices obtained for the same evolved MSAs with different coevolution detection methods. In a second approach we have evaluated the capacity of the different methods to predict close contacts in the representative X-ray structures of an additional 150 protein families using only experimental MSAs.

Conclusions/Significance

Methods based on the identification of global correlations between pairs were found to be generally superior to methods based only on local correlations in their capacity to identify coevolving residues using either simulated or experimental MSAs. However, the significant variability in the performance of different methods with different proteins suggests that the simulation of MSAs that replicate the statistical properties of the experimental MSA can be a valuable tool to identify the coevolution detection method that is most effective in each case.     

Detecting coevolving positions in a molecule: why and how to account for phylogeny

Positions in a molecule that share a common constraint do not evolve independently, and therefore leave a signature in the patterns of homologous sequences. Exhibiting such positions with a coevolution pattern from a sequence alignment has great potential for predicting functional and structural properties of molecules through comparative analysis. This task is complicated by the existence of additional correlation sources, leading to false predictions. The nature of the data is a major source of noise correlation: sequences are taken from individuals with different degrees of relatedness, and who therefore are intrinsically correlated. This has led to several method developments in different fields that are potentially confusing for non-expert users interested in these methodologies. It also explains why coevolution detection methods are largely unemployed despite the importance of the biological questions they address. In this article, I focus on the role of shared ancestry for understanding molecular coevolution patterns. I review and classify existing coevolution detection methods according to their ability to handle shared ancestry. Using a ribosomal RNA benchmark data set, for which detailed knowledge of the structure and coevolution patterns is available, I demonstrate and explain why taking the underlying evolutionary history of sequences into account is the only way to extract the full coevolution signal in the data. I also evaluate, using rigorous statistical procedures, the best approaches to do so, and discuss several important biological aspects to consider when performing coevolution analyses.