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     

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.     

Unifying evolutionary and thermodynamic information for RNA folding of multiple alignments

Computational methods for determining the secondary structure of RNA sequences from given alignments are currently either based on thermodynamic folding, compensatory base pair substitutions or both. However, there is currently no approach that combines both sources of information in a single optimization problem. Here, we present a model that formally integrates both the energy-based and evolution-based approaches to predict the folding of multiple aligned RNA sequences. We have implemented an extended version of Pfold that identifies base pairs that have high probabilities of being conserved and of being energetically favorable. The consensus structure is predicted using a maximum expected accuracy scoring scheme to smoothen the effect of incorrectly predicted base pairs. Parameter tuning revealed that the probability of base pairing has a higher impact on the RNA structure prediction than the corresponding probability of being single stranded. Furthermore, we found that structurally conserved RNA motifs are mostly supported by folding energies. Other problems (e.g. RNA-folding kinetics) may also benefit from employing the principles of the model we introduce. Our implementation, PETfold, was tested on a set of 46 well-curated Rfam families and its performance compared favorably to that of Pfold and RNAalifold.     

Stochastic tunnels in evolutionary dynamics

We study a situation that arises in the somatic evolution of cancer. Consider a finite population of replicating cells and a sequence of mutations: type 0 can mutate to type 1, which can mutate to type 2. There is no back mutation. We start with a homogeneous population of type 0. Mutants of type 1 emerge and either become extinct or reach fixation. In both cases, they can generate type 2, which also can become extinct or reach fixation. If mutation rates are small compared to the inverse of the population size, then the stochastic dynamics can be described by transitions between homogeneous populations. A "stochastic tunnel" arises, when the population moves from all 0 to all 2 without ever being all 1. We calculate the exact rate of stochastic tunneling for the case when type 1 is as fit as type 0 or less fit. Type 2 has the highest fitness. We discuss implications for the elimination of tumor suppressor genes and the activation of genetic instability. Although our theory is developed for cancer genetics, stochastic tunnels are general phenomena that could arise in many circumstances.     

The evolutionary dynamics of endogenous retroviruses

Endogenous retroviruses (ERVs) are vertically transmitted intragenomic elements derived from integrated retroviruses. ERVs can proliferate within the genome of their host until they either acquire inactivating mutations or are lost by recombinational deletion. We present a model that unifies current knowledge of ERV biology into a single evolutionary framework. The model predicts the possible long-term outcomes of retroviral germline infection and can account for the variable patterns of observed ERV genetic diversity. We hope the model will provide a useful framework for understanding ERV evolution, enabling the testing of evolutionary hypotheses and the estimation of parameters governing ERV proliferation.     

On the dynamics of evolutionary discontinuities

Intraspecific competition and selection in polymorphic populations are considered as gradual, yet highly nonlinear, processes which possibly lead to structurally unstable states in species and ecosystems. Discontinuous genetic and morphological changes may thus occur, which are interpreted as evolutionary “catastrophes,” that is, instantaneous transitions between distant, secularly stable evolutionary branches. It is argued that evolutionary gradualism and saltationism represent complementary modes of macroevolution corresponding respectively to the local and global topographical structure of adaptive surfaces.     

The evolutionary dynamics of self-incompatibility systems

Self-incompatible flowering plants reject pollen that expresses the same mating specificity as the pistil (female reproductive tract). In most plant families, pollen and pistil mating specificities segregate as a single locus, the S locus. In at least two self-incompatibility systems, distinct pollen and pistil specificity genes are embedded in an extensive nonrecombining tract. To facilitate consideration of how new S locus specificities arise in systems with distinct pollen and pistil genes, we present a graphical model for the generation of hypotheses. It incorporates the evolutionary principle that nonreciprocal siring success (cross-pollinations between two plants produce seeds in only one direction) tends to favor the rejecting partner. This model suggests that selection within S-allele specificity classes could accelerate the rate of nonsynonymous (amino acid-changing) substitutions, with periodic selective sweeps removing segregating variation within classes. Accelerated substitution within specificity classes could also promote the origin of new S-allele specificities.     

The one-third law of evolutionary dynamics

Evolutionary game dynamics in finite populations provide a new framework for studying selection of traits with frequency-dependent fitness. Recently, a "one-third law" of evolutionary dynamics has been described, which states that strategy A fixates in a B-population with selective advantage if the fitness of A is greater than that of B when A has a frequency 13. This relationship holds for all evolutionary processes examined so far, from the Moran process to games on graphs. However, the origin of the "number"13 is not understood. In this paper we provide an intuitive explanation by studying the underlying stochastic processes. We find that in one invasion attempt, an individual interacts on average with B-players twice as often as with A-players, which yields the one-third law. We also show that the one-third law implies that the average Malthusian fitness of A is positive.     

The evolutionary dynamics of grammar acquisition

Grammar is the computational system of language. It is a set of rules that specifies how to construct sentences out of words. Grammar is the basis of the unlimited expressibility of human language. Children acquire the grammar of their native language without formal education simply by hearing a number of sample sentences. Children could not solve this learning task if they did not have some pre-formed expectations. In other words, children have to evaluate the sample sentences and choose one grammar out of a limited set of candidate grammars. The restricted search space and the mechanism which allows to evaluate the sample sentences is called universal grammar. Universal grammar cannot be learned; it must be in place when the learning process starts. In this paper, we design a mathematical theory that places the problem of language acquisition into an evolutionary context. We formulate equations for the population dynamics of communication and grammar learning. We ask how accurate children have to learn the grammar of their parents' language for a population of individuals to evolve and maintain a coherent grammatical system. It turns out that there is a maximum error tolerance for which a predominant grammar is stable. We calculate the maximum size of the search space that is compatible with coherent communication in a population. Thus, we specify the conditions for the evolution of universal grammar.     

Stochastic evolutionary dynamics of direct reciprocity

Evolutionary game theory is the study of frequency-dependent selection. The success of an individual depends on the frequencies of strategies that are used in the population. We propose a new model for studying evolutionary dynamics in games with a continuous strategy space. The population size is finite. All members of the population use the same strategy. A mutant strategy is chosen from some distribution over the strategy space. The fixation probability of the mutant strategy in the resident population is calculated. The new mutant takes over the population with this probability. In this case, the mutant becomes the new resident. Otherwise, the existing resident remains. Then, another mutant is generated. These dynamics lead to a stationary distribution over the entire strategy space. Our new approach generalizes classical adaptive dynamics in three ways: (i) the population size is finite; (ii) mutants can be drawn non-locally and (iii) the dynamics are stochastic. We explore reactive strategies in the repeated Prisoner''s Dilemma. We perform ‘knock-out experiments’ to study how various strategies affect the evolution of cooperation. We find that ‘tit-for-tat’ is a weak catalyst for the emergence of cooperation, while ‘always cooperate’ is a strong catalyst for the emergence of defection. Our analysis leads to a new understanding of the optimal level of forgiveness that is needed for the evolution of cooperation under direct reciprocity.     

Stochastic evolutionary dynamics on two levels

We consider a population that is subdivided into groups. Individuals reproduce proportional to their fitness. When a group reaches a certain size it has a probability to split into two groups while another group is eliminated. In this stochastic process, the number of groups is constant, while the total population size fluctuates between well-defined bounds. We calculate the fixation probability of newly introduced mutants under constant selection. We show that the described population structure acts as a suppressor of selection compared to an unstructured population of the same size. The maximum suppression of selection is obtained, when the number of groups equals the number of individuals per group. We also study opposing selection on two or more levels by analysing the evolutionary dynamics of hierarchically embedded Moran processes.     

The evolutionary dynamics of the lexical matrix

The lexical matrix is an integral part of the human language system. It provides the link between word form and word meaning. A simple lexical matrix is also at the center of any animal communication system, where it defines the associations between form and meaning of animal signals. We study the evolution and population dynamics of the lexical matrix. We assume that children learn the lexical matrix of their parents. This learning process is subject to mistakes: (i) children may not acquire all lexical items of their parents (incomplete learning); and (ii) children might acquire associations between word forms and word meanings that differ from their parents’ lexical items (incorrect learning). We derive an analytic framework that deals with incomplete learning. We calculate the maximum error rate that is compatible with a population maintaining a coherent lexical matrix of a given size. We calculate the equilibrium distribution of the number of lexical items known to individuals. Our analytic investigations are supplemented by numerical simulations that describe both incomplete and incorrect learning, and other extensions.     

Population and evolutionary dynamics of phage therapy

Following a sixty-year hiatus in western medicine, bacteriophages (phages) are again being advocated for treating and preventing bacterial infections. Are attempts to use phages for clinical and environmental applications more likely to succeed now than in the past? Will phage therapy and prophylaxis suffer the same fates as antibiotics--treatment failure due to acquired resistance and ever-increasing frequencies of resistant pathogens? Here, the population and evolutionary dynamics of bacterial-phage interactions that are relevant to phage therapy and prophylaxis are reviewed and illustrated with computer simulations.     

Avian influenza virus exhibits rapid evolutionary dynamics

Influenza A viruses from wild aquatic birds, their natural reservoir species, are thought to have reached a form of stasis, characterized by low rates of evolutionary change. We tested this hypothesis by estimating rates of nucleotide substitution in a diverse array of avian influenza viruses (AIV) and allowing for rate variation among lineages. The rates observed were extremely high, at >10(-3) substitutions per site, per year, with little difference among wild and domestic host species or viral subtypes and were similar to those seen in mammalian influenza A viruses. Influenza A virus therefore exhibits rapid evolutionary dynamics across its host range, consistent with a high background mutation rate and rapid replication. Using the same approach, we also estimated that the common ancestors of the hemagglutinin and neuraminidase sequences of AIV arose within the last 3,000 years, with most intrasubtype diversity emerging within the last 100 years and suggestive of a continual selective turnover.     

Allele dynamics plots for the study of evolutionary dynamics in viral populations

Phylodynamic techniques combine epidemiological and genetic information to analyze the evolutionary and spatiotemporal dynamics of rapidly evolving pathogens, such as influenza A or human immunodeficiency viruses. We introduce 'allele dynamics plots' (AD plots) as a method for visualizing the evolutionary dynamics of a gene in a population. Using AD plots, we propose how to identify the alleles that are likely to be subject to directional selection. We analyze the method's merits with a detailed study of the evolutionary dynamics of seasonal influenza A viruses. AD plots for the major surface protein of seasonal influenza A (H3N2) and the 2009 swine-origin influenza A (H1N1) viruses show the succession of substitutions that became fixed in the evolution of the two viral populations. They also allow the early identification of those viral strains that later rise to predominance, which is important for the problem of vaccine strain selection. In summary, we describe a technique that reveals the evolutionary dynamics of a rapidly evolving population and allows us to identify alleles and associated genetic changes that might be under directional selection. The method can be applied for the study of influenza A viruses and other rapidly evolving species or viruses.     

Success-biased social learning: Cultural and evolutionary dynamics

Success bias is a social learning strategy whereby learners tend to acquire the cultural variants of successful individuals. I develop a general model of success-biased social learning for discrete cultural traits with stochastic payoffs, and investigate its dynamics when only two variants are present. I find that success bias inherently favors rare variants, and consequently performs worse than unbiased imitation (i.e. random copying) when success payoffs are at least mildly stochastic and the optimal variant is common. Because of this weakness, success bias fails to replace unbiased imitation in an evolutionary model when selection is fairly weak or when the environment is relatively stable, and sometimes fails to invade at all. I briefly discuss the optimal strength of success bias, the complicated nature of defining success in social learning contexts, and the value of variant frequency as an important source of information to social learners. I conclude with predictions regarding the prevalence of success bias in different behavioral domains.     

How genomic and developmental dynamics affect evolutionary processes

Evolutionary genetics is concerned with natural selection and neutral drift, to the virtual exclusion of almost everything else. In its current focus on DNA variation, it reduces phenotypes to symbols. Varying phenotypes, however, are the units of evolution, and, if we want a comprehensive theory of evolution, we need to consider both the internal and external evolutionary forces that shape the development of phenotypes. Genetic systems are redundant, modular and subject to a variety of genomic mechanisms of "turnover" (transposition, gene conversion, unequal crossingover, slippage and so on). As such the construction and spread of novel combinations of modules by turnover, in particular within gene promoters, contributes significantly to the evolution of phenotypes. Furthermore, redundancy, turnover and modularity lead to ever more complex networks of genetic interactions and ever more functions for a given module. The significant interaction between genomic turnover and natural selection leads to a molecular coevolution between interacting modules and hence facilitates the establishment of biological novelties.