The Red Queen and King in finite populations

Asymmetric arms races between predators and prey: a tug of war between the life-dinner principle and the rare-enemy principle

Antagonistic co-evolution can be asymmetric, where one species lags behind another. Asymmetry in a predator-prey context is expressed by the 'life-dinner principle', a classic informal model predicting that prey should be in some sense ahead in this arms race, since prey are running for their lives, while predators lag as they only run for their dinner. The model has undergone surprisingly little theoretical scrutiny. We derive analytical models that show coevolutionary outcomes do not always align with the life-dinner principle. Our results show that other important asymmetries can easily reverse the outcome, especially the rare-enemy principle: predators are usually outnumbered by their prey, sometimes substantially (trophic asymmetry), which can make selection on prey relatively weak. We additionally show that the antagonists typically exhibit different evolutionary responses to a situation where both predator and prey start out as equally fast runners. Although predators sometimes become so efficient that attacks always succeed, attack success often reaches a stable intermediate value. We conclude that the life-dinner principle has some validity as a metaphor, but its effect is of an 'all else being equal' type, which is surprisingly easily overridden by other features of the evolutionary dynamics.

Evolutionary dynamics of hyperbolic language

Models of evolution of simple languages have typically assumed full alignment of the speaker and listeners interests, with perfect understanding representing the optimal outcome for both parties. In more realistic settings, communicating individuals will often desire different outcomes from one another. Previous work has shown that misalignment of speaker-listener interests reduces the maximum informativeness among Nash-equilibrium languages, and that multiple equilibrium languages (with different degrees of informativeness) are supported. We study the stochastic evolutionary dynamics of signaling games in which the alignment of speaker-listener interests can vary. We find that increased misalignment of speaker-listener interests is associated with a decrease in information transmission. Moreover, the most common languages to evolve are typically the most informative languages supportable as static Nash equilibria, suggesting a solution to the 'equilibrium selection problem'. In addition, our dynamics reveal the mechanism by which less informative languages evolve: words that previously signaled intense states come to be used hyperbolically for less intense states, with listeners' interpretation of these newly-ambiguous words evolving downward in response. We ground our results in linguistic data on intensifiers such as so and very, words which have unique dynamics-with constant recycling and innovation that match our theoretical results well.

Divergent paths in the evolutionary history of maternally transmitted clam symbionts

Vertical transmission of bacterial endosymbionts is accompanied by virtually irreversible gene loss that results in a progressive reduction in genome size. While the evolutionary processes of genome reduction have been well described in some terrestrial symbioses, they are less understood in marine systems where vertical transmission is rarely observed. The association between deep-sea vesicomyid clams and chemosynthetic Gammaproteobacteria is one example of maternally inherited symbioses in the ocean. Here, we assessed the contributions of drift, recombination and selection to genome evolution in two extant vesicomyid symbiont clades by comparing 15 representative symbiont genomes (1.017-1.586 Mb) to those of closely related bacteria and the hosts' mitochondria. Our analyses suggest that drift is a significant force driving genome evolution in vesicomyid symbionts, though selection and interspecific recombination appear to be critical for maintaining symbiont functional integrity and creating divergent patterns of gene conservation. Notably, the two symbiont clades possess putative functional differences in sulfide physiology, anaerobic respiration and dependency on environmental vitamin B12, which probably reflect adaptations to different ecological habitats available to each symbiont group. Overall, these results contribute to our understanding of the eco-evolutionary processes shaping reductive genome evolution in vertically transmitted symbioses.

Should we hail the Red King? Evolutionary consequences of a mutualistic lifestyle in genomes of lichenized ascomycetes

The Red Queen dynamic is often brought into play for antagonistic relationships. However, the coevolutionary effects of mutualistic interactions, which predict slower evolution for interacting organisms (Red King), have been investigated to a lesser extent. Lichens are a stable, mutualistic relationship of fungi and cyanobacteria and/or algae, which originated several times independently during the evolution of fungi. Therefore, they represent a suitable system to investigate the coevolutionary effect of mutualism on the fungal genome. We measured substitution rates and selective pressure of about 2000 protein-coding genes (plus the rDNA region) in two different classes of Ascomycota, each consisting of closely related lineages of lichenized and non-lichenized fungi. Our results show that independent lichenized clades are characterized by significantly slower rates for both synonymous and non-synonymous substitutions. We hypothesize that this evolutionary pattern is connected to the lichen life cycle (longer generation time of lichenized fungi) rather than a result of different selection strengths, which is described as the main driver for the Red Kind dynamic. This first empirical evidence of slower evolution in lichens provides an important insight on how biotic cooperative interactions are able to shape the evolution of symbiotic organisms.

Microbial evolution and transitions along the parasite-mutualist continuum

Virtually all plants and animals, including humans, are home to symbiotic microorganisms. Symbiotic interactions can be neutral, harmful or have beneficial effects on the host organism. However, growing evidence suggests that microbial symbionts can evolve rapidly, resulting in drastic transitions along the parasite-mutualist continuum. In this Review, we integrate theoretical and empirical findings to discuss the mechanisms underpinning these evolutionary shifts, as well as the ecological drivers and why some host-microorganism interactions may be stuck at the end of the continuum. In addition to having biomedical consequences, understanding the dynamic life of microorganisms reveals how symbioses can shape an organism's biology and the entire community, particularly in a changing world.

Coevolution fails to maintain genetic variation in a host-parasite model with constant finite population size

Coevolutionary negative frequency-dependent selection has been hypothesized to maintain genetic variation in host and parasites. Despite the extensive literature pertaining to host-parasite coevolution, the temporal dynamics of genetic variation have not been examined in a matching-alleles model (MAM) with a finite population size relative to the expectation under neutral genetic drift alone. The dynamics of the MA coevolution in an infinite population, in fact, suggests that genetic variation in these coevolving populations behaves neutrally. By comparing host heterozygosity to the expectation in a single-species model of neutral genetic drift we find that while this is also largely true in finite populations two additional phenomena arise. First, reciprocal natural selection acting on stochastic perturbations in host and pathogen allele frequencies results in a slight increase or decrease in genetic variation depending on the parameter conditions. Second, following the fixation of an allele in the parasite, selection in the MAM becomes directional, which then rapidly erodes genetic variation in the host. Hence, rather than maintain it, we find that, on average, matching-alleles coevolution depletes genetic variation.

Stochastic evolutionary dynamics of trust games with asymmetric parameters

Trusting in others and reciprocating that trust with trustworthy actions are crucial to successful and prosperous societies. The trust game has been widely used to quantitatively study trust and trustworthiness, involving a sequential exchange between an investor and a trustee. Deterministic evolutionary game theory predicts no trust and no trustworthiness, whereas the behavioral experiments with the one-shot anonymous trust game show that people substantially trust and respond trustworthily. To explain these discrepancies, previous works often turn to additional mechanisms, which are borrowed from other games such as the prisoner's dilemma. Although these mechanisms lead to the evolution of trust and trustworthiness to an extent, the optimal or the most common strategy often involves no trustworthiness. In this paper, we study the impact of asymmetric demographic parameters (e.g., different population sizes) on game dynamics of the trust game. We show that, in a weak-mutation limit, stochastic evolutionary dynamics with the asymmetric parameters can lead to the evolution of high trust and high trustworthiness without any additional mechanisms in well-mixed finite populations. Even full trust and near full trustworthiness can be the most common strategies. These results are qualitatively different from those of the previous works. Our results thereby demonstrate rich evolutionary dynamics of the asymmetric trust game.

How long do Red Queen dynamics survive under genetic drift? A comparative analysis of evolutionary and eco-evolutionary models

Background

Red Queen dynamics are defined as long term co-evolutionary dynamics, often with oscillations of genotype abundances driven by fluctuating selection in host-parasite systems. Much of our current understanding of these dynamics is based on theoretical concepts explored in mathematical models that are mostly (i) deterministic, inferring an infinite population size and (ii) evolutionary, thus ecological interactions that change population sizes are excluded. Here, we recall the different mathematical approaches used in the current literature on Red Queen dynamics. We then compare models from game theory (evo) and classical theoretical ecology models (eco-evo), that are all derived from individual interactions and are thus intrinsically stochastic. We assess the influence of this stochasticity through the time to the first loss of a genotype within a host or parasite population.

Results

The time until the first genotype is lost (“extinction time”), is shorter when ecological dynamics, in the form of a changing population size, is considered. Furthermore, when individuals compete only locally with other individuals extinction is even faster. On the other hand, evolutionary models with a fixed population size and competition on the scale of the whole population prolong extinction and therefore stabilise the oscillations. The stabilising properties of intra-specific competitions become stronger when population size is increased and the deterministic part of the dynamics gain influence. In general, the loss of genotype diversity can be counteracted with mutations (or recombination), which then allow the populations to recurrently undergo negative frequency-dependent selection dynamics and selective sweeps.

Conclusion

Although the models we investigated are equal in their biological motivation and interpretation, they have diverging mathematical properties both in the derived deterministic dynamics and the derived stochastic dynamics. We find that models that do not consider intraspecific competition and that include ecological dynamics by letting the population size vary, lose genotypes – and thus Red Queen oscillations – faster than models with competition and a fixed population size.

α-Rank: Multi-Agent Evaluation by Evolution

We introduce α-Rank, a principled evolutionary dynamics methodology, for the evaluation and ranking of agents in large-scale multi-agent interactions, grounded in a novel dynamical game-theoretic solution concept called Markov-Conley chains (MCCs). The approach leverages continuous-time and discrete-time evolutionary dynamical systems applied to empirical games, and scales tractably in the number of agents, in the type of interactions (beyond dyadic), and the type of empirical games (symmetric and asymmetric). Current models are fundamentally limited in one or more of these dimensions, and are not guaranteed to converge to the desired game-theoretic solution concept (typically the Nash equilibrium). α-Rank automatically provides a ranking over the set of agents under evaluation and provides insights into their strengths, weaknesses, and long-term dynamics in terms of basins of attraction and sink components. This is a direct consequence of the correspondence we establish to the dynamical MCC solution concept when the underlying evolutionary model’s ranking-intensity parameter, α, is chosen to be large, which exactly forms the basis of α-Rank. In contrast to the Nash equilibrium, which is a static solution concept based solely on fixed points, MCCs are a dynamical solution concept based on the Markov chain formalism, Conley’s Fundamental Theorem of Dynamical Systems, and the core ingredients of dynamical systems: fixed points, recurrent sets, periodic orbits, and limit cycles. Our α-Rank method runs in polynomial time with respect to the total number of pure strategy profiles, whereas computing a Nash equilibrium for a general-sum game is known to be intractable. We introduce mathematical proofs that not only provide an overarching and unifying perspective of existing continuous- and discrete-time evolutionary evaluation models, but also reveal the formal underpinnings of the α-Rank methodology. We illustrate the method in canonical games and empirically validate it in several domains, including AlphaGo, AlphaZero, MuJoCo Soccer, and Poker.

The evolutionary game of interspecific mutualism in the multi-species model

Mutualistic interspecific interactions, including Müllerian mimicry and division of labor, are common in nature. In contrast to antagonistic interactions, where faster evolution is favored, mutualism can favor slower evolution under certain conditions. This is called the Red King effect. Since Bergstrom and Lachmann (2003) proposed the Red King effect, it has been investigated only in two-species models. However, biological examples suggest that mutualism can include three or more species. Here, I modeled the evolutionary dynamics of mutualism in communities where involving two or more species, and in which all species mutually interact. Regardless of the number of species in the community, it is possible to derive conditions for stable equilibria. Although nonlinear relationships exist between the evolutionary rates and the evolutionary fate of each species in the multi-species communities, the model suggests that it is possible to predict whether faster evolution is favored or disfavored for the relatively rapidly evolving species; however, it is difficult to predict the evolutionary fate of species that evolve relatively slowly because their evolutionary dynamics are affected by the evolutionary fate of species evolving rapidly.

Social Closure and the Evolution of Cooperation via Indirect Reciprocity

Direct and indirect reciprocity are good candidates to explain the fundamental problem of evolution of cooperation. We explore the conditions under which different types of reciprocity gain dominance and their performances in sustaining cooperation in the PD played on simple networks. We confirm that direct reciprocity gains dominance over indirect reciprocity strategies also in larger populations, as long as it has no memory constraints. In the absence of direct reciprocity, or when its memory is flawed, different forms of indirect reciprocity strategies are able to dominate and to support cooperation. We show that indirect reciprocity relying on social capital inherent in closed triads is the best competitor among them, outperforming indirect reciprocity that uses information from any source. Results hold in a wide range of conditions with different evolutionary update rules, extent of evolutionary pressure, initial conditions, population size, and density.

Eco-evolutionary Red Queen dynamics regulate biodiversity in a metabolite-driven microbial system

The Red Queen Hypothesis proposes that perpetual co-evolution among organisms can result from purely biotic drivers. After more than four decades, there is no satisfactory understanding as to which mechanisms trigger Red Queen dynamics or their implications for ecosystem features such as biodiversity. One reason for such a knowledge gap is that typical models are complicated theories where limit cycles represent an idealized Red Queen, and therefore cannot be used to devise experimental setups. Here, we bridge this gap by introducing a simple model for microbial systems able to show Red Queen dynamics. We explore diverse biotic sources that can drive the emergence of the Red Queen and that have the potential to be found in nature or to be replicated in the laboratory. Our model enables an analytical understanding of how Red Queen dynamics emerge in our setup, and the translation of model terms and phenomenology into general underlying mechanisms. We observe, for example, that in our system the Red Queen offers opportunities for the increase of biodiversity by facilitating challenging conditions for intraspecific dominance, whereas stasis tends to homogenize the system. Our results can be used to design and engineer experimental microbial systems showing Red Queen dynamics.