Red Queens and ESS: the coevolution of evolutionary rates

Using the Unity Game Engine to Develop a 3D Simulated Ecological System Based on a Predator–Prey Model Extended by Gene Evolution

In this paper, we present a novel implementation of an ecosystem simulation. In our previous work, we implemented a 3D environment based on a predator–prey model, but we found that in most cases, regardless of the choice of starting parameters, the simulation quickly led to extinctions. We wanted to achieve system stabilization, long-term operation, and better simulation of reality by incorporating genetic evolution. Therefore we applied the predator–prey model with an evolutional approach. Using the Unity game engine we created and managed a closed 3D ecosystem environment defined by an artificial or real uploaded map. We present some demonstrative runs while gathering data, observing interesting events (such as extinction, sustainability, and behavior of swarms), and analyzing possible effects on the initial parameters of the system. We found that incorporating genetic evolution into the simulation slightly stabilized the system, thus reducing the likelihood of extinction of different types of objects. The simulation of ecosystems and the analysis of the data generated during the simulations can also be a starting point for further research, especially in relation to sustainability. Our system is publicly available, so anyone can customize and upload their own parameters, maps, objects, and biological species, as well as inheritance and behavioral habits, so they can test their own hypotheses from the data generated during its operation. The goal of this article was not to create and validate a model but to create an IT tool for evolutionary researchers who want to test their own models and to present them, for example, as animated conference presentations. The use of 3D simulation is primarily useful for educational purposes, such as to engage students and to increase their interest in biology. Students can learn in a playful way while observing in the graphical scenery how the ecosystem behaves, how natural selection helps the adaptability and survival of species, and what effects overpopulation and competition can have.

Extinction in complex communities as driven by adaptive dynamics

In a complex community, species continuously adapt to each other. On rare occasions, the adaptation of a species can lead to the extinction of others, and even its own. 'Adaptive dynamics' is the standard mathematical framework to describe evolutionary changes in community interactions, and in particular, predict adaptation driven extinction. Unfortunately, most authors implement the equations of adaptive dynamics through computer simulations that require assuming a large number of questionable parameters and fitness functions. In this study, we present analytical solutions to adaptive dynamics equations, thereby clarifying how outcomes depend on any computational input. We develop general formulas that predict equilibrium abundances over evolutionary time scales. Additionally, we predict which species will go extinct next, and when this will happen.

Co-adaptive behavior of interacting populations in a habitat selection game significantly impacts ecosystem functions

Individuals of different interacting populations often adjust to prevailing conditions by changing their behavior simultaneously, with consequences for trophic relationships throughout the system. While we now have a good theoretical understanding of how individuals adjust their behavior, the population dynamical consequences of co-adaptive behaviors are rarely described. Further, mechanistic descriptions of ecosystem functions are based on population models that seldom take behavior into account. Here, we present a model that combines the population dynamics and adaptive behavior of organisms of two populations simultaneously. We explore how the Nash equilibrium of a system - i.e. the optimal behavior of its constituent organisms - can shape population dynamics, and conversely how population dynamics impact the Nash equilibrium of the system. We illustrate this for the case of diel vertical migration (DVM), the daily movement of marine organisms between food-depleted but safe dark depths and more risky nutrition-rich surface waters. DVM represents the archetypal example of populations choosing between a foraging arena (the upper sunlit ocean) and a refuge (the dark depths). We show that population sizes at equilibrium are significantly different if organisms can adapt their behavior, and that optimal DVM behaviors within the community vary significantly if population dynamics are considered. As a consequence, ecosystem function estimates such as trophic transfer efficiency and vertical carbon export differ greatly when fitness seeking behavior is included. Ignoring the role of behavior in multi-trophic population modeling can potentially lead to inaccurate predictions of population biomasses and ecosystem functions.

Evolutionarily stable strategies in stable and periodically fluctuating populations: The Rosenzweig-MacArthur predator-prey model

An evolutionarily stable strategy (ESS) is an evolutionary strategy that, if adapted by a population, cannot be invaded by any deviating (mutant) strategy. The concept of ESS has been extensively studied and widely applied in ecology and evolutionary biology [M. Smith, On Evolution (1972)] but typically on the assumption that the system is ecologically stable. With reference to a Rosenzweig-MacArthur predator-prey model [M. Rosenzweig, R. MacArthur, Am. Nat. 97, 209-223 (1963)], we derive the mathematical conditions for the existence of an ESS when the ecological dynamics have asymptotically stable limit points as well as limit cycles. By extending the framework of Reed and Stenseth [J. Reed, N. C. Stenseth, J. Theoret. Biol. 108, 491-508 (1984)], we find that ESSs occur at values of the evolutionary strategies that are local optima of certain functions of the model parameters. These functions are identified and shown to have a similar form for both stable and fluctuating populations. We illustrate these results with a concrete example.

The Evolutionary Significance of Generalist Viruses with Special Emphasis on Plant Viruses and their Hosts

The host range of a virus is defined as the number of species a virus potentially infects. The specialist virus infects one or few related species while the generalist virus infects several different species, possibly in different families. Origin of generalist viruses from their specialist nature and the expansion of the host range of the generalist virus occur with the host shift event in which the virus encounters and adapts to a new host. Host shift events have resulted in the majority of the newly emerging viral diseases. This review discusses the advantages and disadvantages of generalist over specialist viruses and the unique features of plant viruses and their hosts that result in a higher incidence of generalist viruses in plants.

Getting somewhere with the Red Queen: chasing a biologically modern definition of the hypothesis

The Red Queen hypothesis (RQH) is both familiar and murky, with a scope and range that has broadened beyond its original focus. Although originally developed in the palaeontological arena, it now encompasses many evolutionary theories that champion biotic interactions as significant mechanisms for evolutionary change. As such it de-emphasizes the important role of abiotic drivers in evolution, even though such a role is frequently posited to be pivotal. Concomitant with this shift in focus, several studies challenged the validity of the RQH and downplayed its propriety. Herein, we examine in detail the assumptions that underpin the RQH in the hopes of furthering conceptual understanding and promoting appropriate application of the hypothesis. We identify issues and inconsistencies with the assumptions of the RQH, and propose a redefinition where the Red Queen's reign is restricted to certain types of biotic interactions and evolutionary patterns occurring at the population level.

The Fossil Record of Predator-Prey Arms Races: Coevolution and Escalation Hypotheses

Arms races between predators and prey may be driven by two related processes—escalation and coevolution. Escalation is enemy-driven evolution. In this top-down view of an arms race, the role of prey (with the exception of dangerous prey) is downplayed. In coevolution, two or more species change reciprocally in response to one another; prey are thought to drive the evolution of their predator, and vice versa. In the fossil record, the two processes are most reliably distinguished when the predator-prey system is viewed within the context of the other species that may influence the interaction, thus allowing for a relative ranking of the importance of selective agents. Detailed documentation of the natural history of living predator-prey systems is recommended in order to distinguish the processes in some fossil systems. A geographic view of species interactions and the processes driving their evolution may lead to a more diverse array of testable hypotheses on how predator-prey systems evolve and what constraints interactions impose on the evolution of organisms. Scale is important in evaluating the role of escalation and coevolution in the evolution of species interactions. If short-term reciprocal adaptation (via phenotypic plasticity or selection mosaics among populations) between predator and prey is a common process, then prey are likely to exert some selective pressure over their predators over the short term (on ecological time scales), but in the long run predators may still exert primary “top-down” control in directing evolution. On the scale of evolutionary time, predators of large effect likely control the overall directionality of evolution due to the inequalities of predator and prey in control of resources.

PREY ADAPTATION AS A CAUSE OF PREDATOR-PREY CYCLES

We analyze simple models of predator-prey systems in which there is adaptive change in a trait of the prey that determines the rate at which it is captured by searching predators. Two models of adaptive change are explored: (1) change within a single reproducing prey population that has genetic variation for vulnerability to capture by the predator; and (2) direct competition between two independently reproducing prey populations that differ in their vulnerability. When an individual predator's consumption increases at a decreasing rate with prey availability, prey adaptation via either of these mechanisms may produce sustained cycles in both species' population densities and in the prey's mean trait value. Sufficiently rapid adaptive change (e.g., behavioral adaptation or evolution of traits with a large additive genetic variance), or sufficiently low predator birth and death rates will produce sustained cycles or chaos, even when the predator-prey dynamics with fixed prey capture rates would have been stable. Adaptive dynamics can also stabilize a system that would exhibit limit cycles if traits were fixed at their equilibrium values. When evolution fails to stabilize inherently unstable population interactions, selection decreases the prey's escape ability, which further destabilizes population dynamics. When the predator has a linear functional response, evolution of prey vulnerability always promotes stability. The relevance of these results to observed predator-prey cycles is discussed.

Host coevolution alters the adaptive landscape of a virus

The origin of new and complex structures and functions is fundamental for shaping the diversity of life. Such key innovations are rare because they require multiple interacting changes. We sought to understand how the adaptive landscape led to an innovation whereby bacteriophage λ evolved the new ability to exploit a receptor, OmpF, on Escherichia coli cells. Previous work showed that this ability evolved repeatedly, despite requiring four mutations in one virus gene. Here, we examine how this innovation evolved by studying six intermediate genotypes of λ isolated during independent transitions to exploit OmpF and comparing them to their ancestor. All six intermediates showed large increases in their adsorption rates on the ancestral host. Improvements in adsorption were offset, in large part, by the evolution of host resistance, which occurred by reduced expression of LamB, the usual receptor for λ. As a consequence of host coevolution, the adaptive landscape of the virus changed such that selection favouring four of the six virus intermediates became stronger after the host evolved resistance, thereby accelerating virus populations along the path to using the new OmpF receptor. This dependency of viral fitness on host genotype thus shows an important role for coevolution in the origin of the new viral function.

A new dimension: Evolutionary food web dynamics in two dimensional trait space

Species within a habitat are not uniformly distributed. However this aspect of community structure, which is fundamental to many conservation activities, is neglected in the majority of models of food web assembly. To address this issue, we introduce a model which incorporates a second dimension, which can be interpreted as space, into the trait space used in evolutionary food web models. Our results show that the additional trait axis allows the emergence of communities with a much greater range of network structures, similar to the diversity observed in real ecological communities. Moreover, the network properties of the food webs obtained are in good agreement with those of empirical food webs. Community emergence follows a consistent pattern with spread along the second trait axis occurring before the assembly of higher trophic levels. Communities can reach either a static final structure, or constantly evolve. We observe that the relative importance of competition and predation is a key determinant of the network structure and the evolutionary dynamics. The latter are driven by the interaction-competition and predation-between small groups of species. The model remains sufficiently simple that we are able to identify the factors, and mechanisms, which determine the final community state.

Asymmetric ecological conditions favor Red-Queen type of continued evolution over stasis

Four decades ago, Leigh Van Valen presented the Red Queen's hypothesis to account for evolution of species within a multispecies ecological community [Van Valen L (1973) Evol Theory 1(1):1-30]. The overall conclusion of Van Valen's analysis was that evolution would continue even in the absence of abiotic perturbations. Stenseth and Maynard Smith presented in 1984 [Stenseth NC, Maynard Smith J (1984) Evolution 38(4):870-880] a model for the Red Queen's hypothesis showing that both Red-Queen type of continuous evolution and stasis could result from a model with biotically driven evolution. However, although that contribution demonstrated that both evolutionary outcomes were possible, it did not identify which ecological conditions would lead to each of these evolutionary outcomes. Here, we provide, using a simple, yet general population-biologically founded eco-evolutionary model, such analytically derived conditions: Stasis will predominantly emerge whenever the ecological system contains only symmetric ecological interactions, whereas both Red-Queen and stasis type of evolution may result if the ecological interactions are asymmetrical, and more likely so with increasing degree of asymmetry in the ecological system (i.e., the more trophic interactions, host-pathogen interactions, and the like there are [i.e., +/- type of ecological interactions as well as asymmetric competitive (-/-) and mutualistic (+/+) ecological interactions]). In the special case of no between-generational genetic variance, our results also predict dynamics within these types of purely ecological systems.

The role of biotic forces in driving macroevolution: beyond the Red Queen

A multitude of hypotheses claim that abiotic factors are the main drivers of macroevolutionary change. By contrast, Van Valen's Red Queen hypothesis is often put forward as the sole representative of the view that biotic forcing is the main evolutionary driver. This imbalance of hypotheses does not reflect our current knowledge: theoretical work demonstrates the plausibility of biotically driven long-term evolution, whereas empirical work suggests a central role for biotic forcing in macroevolution. We call for a more pluralistic view of how biotic forces may drive long-term evolution that is compatible with both phenotypic stasis in the fossil record and with non-constant extinction rates. Promising avenues of research include contrasting predictions from relevant theories within ecology and macroevolution, as well as embracing both abiotic and biotic proxies while modelling long-term evolutionary data. By fitting models describing hypotheses of biotically driven macroevolution to data, we could dissect their predictions and transcend beyond pattern description, possibly narrowing the divide between our current understanding of micro- and macroevolution.

The ecology of human fear: survival optimization and the nervous system

We propose a Survival Optimization System (SOS) to account for the strategies that humans and other animals use to defend against recurring and novel threats. The SOS attempts to merge ecological models that define a repertoire of contextually relevant threat induced survival behaviors with contemporary approaches to human affective science. We first propose that the goal of the nervous system is to reduce surprise and optimize actions by (i) predicting the sensory landscape by simulating possible encounters with threat and selecting the appropriate pre-encounter action and (ii) prevention strategies in which the organism manufactures safe environments. When a potential threat is encountered the (iii) threat orienting system is engaged to determine whether the organism ignores the stimulus or switches into a process of (iv) threat assessment, where the organism monitors the stimulus, weighs the threat value, predicts the actions of the threat, searches for safety, and guides behavioral actions crucial to directed escape. When under imminent attack, (v) defensive systems evoke fast reflexive indirect escape behaviors (i.e., fight or flight). This cascade of responses to threat of increasing magnitude are underwritten by an interconnected neural architecture that extends from cortical and hippocampal circuits, to attention, action and threat systems including the amygdala, striatum, and hard-wired defensive systems in the midbrain. The SOS also includes a modulatory feature consisting of cognitive appraisal systems that flexibly guide perception, risk and action. Moreover, personal and vicarious threat encounters fine-tune avoidance behaviors via model-based learning, with higher organisms bridging data to reduce face-to-face encounters with predators. Our model attempts to unify the divergent field of human affective science, proposing a highly integrated nervous system that has evolved to increase the organism's chances of survival.

Chaotic Red Queen coevolution in three-species food chains

Coevolution between two antagonistic species follows the so-called 'Red Queen dynamics' when reciprocal selection results in an endless series of adaptation by one species and counteradaptation by the other. Red Queen dynamics are 'genetically driven' when selective sweeps involving new beneficial mutations result in perpetual oscillations of the coevolving traits on the slow evolutionary time scale. Mathematical models have shown that a prey and a predator can coevolve along a genetically driven Red Queen cycle. We found that embedding the prey-predator interaction into a three-species food chain that includes a coevolving superpredator often turns the genetically driven Red Queen cycle into chaos. A key condition is that the prey evolves fast enough. Red Queen chaos implies that the direction and strength of selection are intrinsically unpredictable beyond a short evolutionary time, with greatest evolutionary unpredictability in the superpredator. We hypothesize that genetically driven Red Queen chaos could explain why many natural populations are poised at the edge of ecological chaos. Over space, genetically driven chaos is expected to cause the evolutionary divergence of local populations, even under homogenizing environmental fluctuations, and thus to promote genetic diversity among ecological communities over long evolutionary time.

A game-theoretic model for punctuated equilibrium: Species invasion and stasis through coevolution

A general theory of coevolution is developed that combines the ecological effects of species' densities with the evolutionary effects of changing phenotypes. Our approach also treats the evolutionary changes between coevolving species with discreet traits after the appearance of a new species. We apply this approach to habitat selection models where new species first emerge through competitive selection in an isolated habitat. This successful invasion is quickly followed by evolutionary changes in behavior when this species discovers the other habitat, leading to punctuated equilibrium as the final outcome.

The adaptive dynamics of function-valued traits

This study extends the framework of adaptive dynamics to function-valued traits. Such adaptive traits naturally arise in a great variety of settings: variable or heterogeneous environments, age-structured populations, phenotypic plasticity, patterns of growth and form, resource gradients, and in many other areas of evolutionary ecology. Adaptive dynamics theory allows analysing the long-term evolution of such traits under the density-dependent and frequency-dependent selection pressures resulting from feedback between evolving populations and their ecological environment. Starting from individual-based considerations, we derive equations describing the expected dynamics of a function-valued trait in asexually reproducing populations under mutation-limited evolution, thus generalizing the canonical equation of adaptive dynamics to function-valued traits. We explain in detail how to account for various kinds of evolutionary constraints on the adaptive dynamics of function-valued traits. To illustrate the utility of our approach, we present applications to two specific examples that address, respectively, the evolution of metabolic investment strategies along resource gradients, and the evolution of seasonal flowering schedules in temporally varying environments.

Models and data on plant-enemy coevolution

Although coevolution is complicated, in that the interacting species evolve in response to each other, such evolutionary dynamics are amenable to mathematical modeling. In this article, we briefly review models and data on coevolution between plants and the pathogens and herbivores that attack them. We focus on "arms races," in which trait values in the plant and its enemies escalate to more and more extreme values. Untested key assumptions in many of the models are the relationships between costs and benefits of resistance in the plant and the level of resistance, as well as how costs of virulence or detoxification ability in the enemy change with levels of these traits. A preliminary assessment of these assumptions finds only mixed support for the models. What is needed are models that are more closely tailored to particular plant-enemy interactions, as well as experiments that are expressly designed to test existing models.

Host-parasite coevolution in a multilocus gene-for-gene system

This paper examines a mathematical model for the coevolution of parasite virulence and host resistance under a multilocus gene-for-gene interaction. The degrees of parasite virulence and host resistance show coevolutionary cycles for sufficiently small costs of virulence and resistance. Besides these coevolutionary cycles of a longer period, multilocus genotype frequencies show complex fluctuations over shorter periods. All multilocus genotypes are maintained within host and parasite classes having the same number of resistant/virulent alleles and their frequencies fluctuate with approximately equally displaced phases. If either the cost of virulence or the number of resistance loci is larger then a threshold, the host maintains the static polymorphism of singly (or doubly or more, depending on the cost of resistance) resistant genotypes and the parasite remains universally avirulent. In other words, host polymorphism can prevent the invasion of any virulent strain in the parasite. Thus, although assuming an empirically common type of asymmetrical gene-for-gene interaction, both host and parasite populations can maintain polymorphism in each locus and retain complex fluctuations. Implications for the red queen hypothesis of the evolution of sex and the control of multiple drug resistance are discussed.

A model for the coevolution of resistance and virulence in coupled host—parasitoid interactions

A coevolutionary model is developed of the interaction between a host and an internal parasitoid, where the outcome of parasitism depends upon the extent to which individual hosts invest in resistance mechanisms and individual parasitoids in countermeasures (virulence). The host and parasitoid are assumed to have coupled population dynamics (of Nicholson–Bailey form) and to be composed of a series of asexual clones with different levels of resistance and virulence. Investment in resistance and virulence mechanisms is assumed to be costly. The model has two main outcomes. First, if resistance is relatively costly compared to virulence, the host may be selected not to invest in resistance mechanisms despite parasitoid investment in virulence, in effect trading off the risks of parasitism against the savings in costs. A number of cases which appear to correspond to this result have been reported. Second, for most other feasible parameter values, an arms race occurs between host and parasitoid, until effective resistance becomes so costly that the host abandons defence. This abandonment is followed by a reduction in parasitoid virulence and the cycle begins again. These cycles may explain reports of persistent additive genetic variation in resistance and virulence, and may also contribute towards population dynamic stability.

Evolutionary dynamics of predator-prey systems: an ecological perspective

Evolution takes place in an ecological setting that typically involves interactions with other organisms. To describe such evolution, a structure is needed which incorporates the simultaneous evolution of interacting species. Here a formal framework for this purpose is suggested, extending from the microscopic interactions between individuals--the immediate cause of natural selection, through the mesoscopic population dynamics responsible for driving the replacement of one mutant phenotype by another, to the macroscopic process of phenotypic evolution arising from many such substitutions. The process of coevolution that results from this is illustrated in the context of predator-prey systems. With no more than qualitative information about the evolutionary dynamics, some basic properties of predator-prey coevolution become evident. More detailed understanding requires specification of an evolutionary dynamic; two models for this purpose are outlined, one from our own research on a stochastic process of mutation and selection and the other from quantitative genetics. Much of the interest in coevolution has been to characterize the properties of fixed points at which there is no further phenotypic evolution. Stability analysis of the fixed points of evolutionary dynamical systems is reviewed and leads to conclusions about the asymptotic states of evolution rather different from those of game-theoretic methods. These differences become especially important when evolution involves more than one species.

The dynamical theory of coevolution: a derivation from stochastic ecological processes

In this paper we develop a dynamical theory of coevolution in ecological communities. The derivation explicitly accounts for the stochastic components of evolutionary change and is based on ecological processes at the level of the individual. We show that the coevolutionary dynamic can be envisaged as a directed random walk in the community's trait space. A quantitative description of this stochastic process in terms of a master equation is derived. By determining the first jump moment of this process we abstract the dynamic of the mean evolutionary path. To first order the resulting equation coincides with a dynamic that has frequently been assumed in evolutionary game theory. Apart from recovering this canonical equation we systematically establish the underlying assumptions. We provide higher order corrections and show that these can give rise to new, unexpected evolutionary effects including shifting evolutionary isoclines and evolutionary slowing down of mean paths as they approach evolutionary equilibria. Extensions of the derivation to more general ecological settings are discussed. In particular we allow for multi-trait coevolution and analyze coevolution under nonequilibrium population dynamics.

Coevolution to the edge of chaos: coupled fitness landscapes, poised states, and coevolutionary avalanches

We introduce a broadened framework to study aspects of coevolution based on the NK class of statistical models of rugged fitness landscapes. In these models the fitness contribution of each of N genes in a genotype depends epistatically on K other genes. Increasing epistatic interactions increases the rugged multipeaked character of the fitness landscape. Coevolution is thought of, at the lowest level, as a coupling of landscapes such that adaptive moves by one player deform the landscapes of its immediate partners. In these models we are able to tune the ruggedness of landscapes, how richly intercoupled any two landscapes are, and how many other players interact with each player. All these properties profoundly alter the character of the coevolutionary dynamics. In particular, these parameters govern how readily coevolving ecosystems achieve Nash equilibria, how stable to perturbations such equilibria are, and the sustained mean fitness of coevolving partners. In turn, this raises the possibility that an evolutionary metadynamics due to natural selection may sculpt landscapes and their couplings to achieve coevolutionary systems able to coadapt well. The results suggest that sustained fitness is optimized when landscape ruggedness relative to couplings between landscapes is tuned such that Nash equilibria just tenuously form across the ecosystem. In this poised state, coevolutionary avalanches appear to propagate on all length scales in a power law distribution. Such avalanches may be related to the distribution of small and large extinction events in the record.