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Intransitive competition is often projected to be a widespread mechanism of species coexistence in ecological communities. However, it is unknown how much of the coexistence we observe in nature results from this mechanism when species interactions are also stabilized by pairwise niche differences. We combined field-parameterized models of competition among 18 annual plant species with tools from network theory to quantify the prevalence of intransitive competitive relationships. We then analyzed the predicted outcome of competitive interactions with and without pairwise niche differences. Intransitive competition was found for just 15–19% of the 816 possible triplets, and this mechanism was never sufficient to stabilize the coexistence of the triplet when the pair-wise niche differences between competitors were removed. Of the transitive and intransitive triplets, only four were predicted to coexist and these were more similar in multidimensional trait space defined by 11 functional traits than non-coexisting triplets. Our results argue that intransitive competition may be less frequent than recently posed, and that even when it does operate, pairwise niche differences may be key to possible coexistence.

Although mathematical models and laboratory experiments have shown that species interactions can generate chaos, field evidence of chaos in natural ecosystems is rare. We report on a pristine rocky intertidal community located in one of the world’s oldest marine reserves that has displayed a complex cyclic succession for more than 20 y. Bare rock was colonized by barnacles and crustose algae, they were overgrown by mussels, and the subsequent detachment of the mussels returned bare rock again. These processes generated irregular species fluctuations, such that the species coexisted over many generations without ever approaching a stable equilibrium state. Analysis of the species fluctuations revealed a dominant periodicity of about 2 y, a global Lyapunov exponent statistically indistinguishable from zero, and local Lyapunov exponents that alternated systematically between negative and positive values. This pattern indicates that the community moved back and forth between stabilizing and chaotic dynamics during the cyclic succession. The results are supported by a patch-occupancy model predicting similar patterns when the species interactions were exposed to seasonal variation. Our findings show that natural ecosystems can sustain continued changes in species abundances and that seasonal forcing may push these nonequilibrium dynamics to the edge of chaos. Significance The intuitive and popular idea of a balance of nature has been criticized, because species interactions may generate nonequilibrium dynamics, such as oscillations and chaos. However, field evidence of chaos in ecosystems is rare. We report on a coastal community that has displayed striking fluctuations in the abundances of barnacles, mussels, and algae for more than 20 y. Data analysis reveals that these fluctuations reflect a cyclic succession alternating between stabilizing and chaotic dynamics during the species replacement. These results are supported by a simple patch-occupancy model, which predicts very similar dynamics when exposed to seasonal variation. Our findings provide a field demonstration of nonequilibrium coexistence of competing species through a cyclic succession at the edge of chaos.

1. Over 40 years after the introduction of the concept into ecology, intransitive (i.e. non-hierarchical) competition remains overlooked by ecological theory, despite theoretical work showing it could be a major driver of species coexistence. 2. This special feature presents six studies, including models, reviews, experimental studies and large-scale observational studies. Collectively, these studies help to (i) link intransitive competition with short- and long-term coexistence and with other ecological patterns, (ii) evaluate the conditions under which intransitivity is more common and (iii) determine how best to quantify the degree of intransitivity. 3. The studies in this special feature show the generality of intransitive competition in nature, explore interactions between intransitivity and other coexistence mechanisms, and illustrate the effect of environmental conditions (drought, shade, fertility) on intransitivity and coexistence. They also show which metrics best quantify intransitivity and highlight the importance of adopting a more continuous view of competition as varying from strongly transitive to strongly intransitive. The studies also examine relationships between intransitivity and functional diversity and explore the evolution of intransitivity over time. 4. Synthesis. The studies presented here advance the field by integrating intransitive competition into species coexistence and general ecological theory. We also highlight important research gaps that will hopefully inspire the next generation of studies in this topic.

Cooperation and diversity abound in nature despite cooperators risking exploitation from defectors and superior competitors displacing weaker ones. Understanding the persistence of cooperation and diversity is therefore a major problem for evolutionary ecology, especially in the context of well-mixed populations, where the potential for exploitation and displacement is greatest. Here, we demonstrate that a ‘loner effect’, described by economic game theorists, can maintain cooperation and diversity in real-world biological settings. We use mathematical models of public-good-producing bacteria to show that the presence of a loner strain, which produces an independent but relatively inefficient good, can lead to rock–paper–scissor dynamics, whereby cooperators outcompete loners, defectors outcompete cooperators and loners outcompete defectors. These model predictions are supported by our observations of evolutionary dynamics in well-mixed experimental communities of the bacterium Pseudomonas aeruginosa. We find that the coexistence of cooperators and defectors that produce and exploit, respectively, the iron-scavenging siderophore pyoverdine, is stabilized by the presence of loners with an independent iron-uptake mechanism. Our results establish the loner effect as a simple and general driver of cooperation and diversity in environments that would otherwise favour defection and the erosion of diversity.

We describe new ESS models of density regulation driven by genic selection to explain the cyclical dynamics of a social system that exhibits a rock‐paper‐scissors (RPS) set of three alternative strategies. We tracked changes in morph frequency and fitness ofLacerta viviparaand found conspicuous RPS cycles. Morphs ofUtaandLacertaexhibited parallel survival‐performance trade‐offs. Frequency cycles in both species of lizards are driven by genic selection. InLacerta, frequency of each allele in adult cohorts had significant impacts on juvenile recruitment, similar to mutualistic, altruistic, and antagonistic relations of RPS alleles inUta. We constructed evolutionarily stable strategy (ESS) models in which adults impact juvenile recruitment as a function of self versus nonself color recognition. ESS models suggest that the rapid 4‐year RPS cycles exhibited byLacertaare not possible unless three factors are present: behaviors evolve that discriminate self versus nonself morphs at higher rates than random, self‐ versus non‐self‐recognition contributes to density regulation, and context‐dependent mate choice evolves in females, which choose sire genotypes to enhance progeny survival. We suggest genic selection coupled to density regulation is widespread and thus fundamental to theories of social system evolution as well as theories of population regulation in diverse animal taxa.

1. Indirect biotic interactions—such as intransitive competition—are increasingly recognized as being important in shaping ecological patterns in natural systems. Over long time-scales, such indirect interactions may affect the evolution of species phenotypes, which in turn can modify these interactions, thereby begetting ecoevolutionary feedbacks. If indirect intransitive interactions can emerge in situ during lineage diversification, they could profoundly affect species' phenotypic diversity, temporal stability, and subsequent diversification rates. 2. We address these questions by investigating the conditions under which indirect intransitive competition can emerge from a lineage diversifying in sympatry. We use an adaptive dynamics model to study the ecological and evolutionary properties of this lineage under different scenarios where competition for resources between phenotypes varies in strength and (a)symmetry. 3. Results show that weak-intransitive competition can emerge during the sympatric diversification of a single lineage. \"Weak-intransitivity\" here refers to situations where species interactions are not perfectly transitive, that is, there is no strict hierarchy in species competitive abilities. The strength of such weak-intransitivity increases when the competition between phenotypes increases in strength and asymmetry. The strength of intransitivity also correlates with other system properties. We notably found that the strength of intransitivity increases with the number of phenotypes, and that greater intransitivity correlates with the evolution of greater functional trait divergences between phenotypes, greater resistance to invasion by new phenotypes but lower resistance to disturbances as well as slower evolutionary rates. 4. Synthesis. This theoretical exploration of the evolution of intransitive competition provides the first formal bridge between the ecological and evolutionary aspects of intransitive competition. We show that, when competitive interactions are strong enough, weak-intransitive competition is more likely to emerge through adaptive diversification than from a random community assembly. Intransitive competition is, therefore, not only restricted to between-species interactions but can also function as a regulator of diversification within species, thereby affecting lineage functional diversity, and ecological and evolutionary stability.

In simple dyadic games such as rock, paper, scissors (RPS), people exhibit peculiar sequential dependencies across repeated interactions with a stable opponent. These regularities seem to arise from a mutually adversarial process of trying to outwit their opponent. What underlies this process, and what are its limits? Here, we offer a novel framework for formally describing and quantifying human adversarial reasoning in the rock, paper, scissors game. We first show that this framework enables a precise characterization of the complexity of patterned behaviors that people exhibit themselves, and appear to exploit in others. This combination allows for a quantitative understanding of human opponent modeling abilities. We apply these tools to an experiment in which people played 300 rounds of RPS in stable dyads. We find that although people exhibit very complex move dependencies, they cannot exploit these dependencies in their opponents, indicating a fundamental limitation in people's capacity for adversarial reasoning. Taken together, the results presented here show how the rock, paper, scissors game allows for precise formalization of human adaptive reasoning abilities.

Game spaces in which an organism must repeatedly compete with an opponent for mutually exclusive outcomes are critical methodologies for understanding decision-making under pressure. In the non-transitive game rock, paper, scissors (RPS), the only technique that guarantees the lack of exploitation is to perform randomly in accordance with mixed-strategy. However, such behavior is thought to be outside bounded rationality and so decision-making can become deterministic, predictable, and ultimately exploitable. This review identifies similarities across economics, neuroscience, nonlinear dynamics, human, and animal cognition literatures, and provides a taxonomy of RPS strategy. RPS strategies are discussed in terms of (a) whether the relevant computations require sensitivity to item frequency, the cyclic relationships between responses, or the outcome of the previous trial, and (b) whether the strategy is framed around the self or other. The negative implication of this taxonomy is that despite the differences in cognitive economy and recursive thought, many of the identified strategies are behaviorally isomorphic. This makes it difficult to infer strategy from behavior. The positive implication is that this isomorphism can be used as a novel design feature in furthering our understanding of the attribution, agency, and acquisition of strategy in RPS and other game spaces.

Predictability is a hallmark of poor-quality decision-making during competition. One source of predictability is the strong association between current outcome and future action, as dictated by the reinforcement learning principles of win-stay and lose-shift. We tested the idea that predictability could be reduced during competition by weakening the associations between outcome and action. To do this, participants completed a competitive zero-sum game in which the opponent from the current trial was either replayed (opponent repeat) thereby strengthening the association, or, replaced (opponent change) by a different competitor thereby weakening the association. We observed that win-stay behavior was reduced during opponent change trials but lose-shiftbehavior remained reliably predictable. Consistent with the group data, the number of individuals who exhibited predictable behavior following wins decreased for opponent change relative to opponent repeat trials. Our data show that future actions are more under internal control following positive relative to negative outcomes, and that externally breaking the bonds between outcome and action via opponent association also allows us to become less prone to exploitation.

Cooperative behavior is widely spread in microbial populations. An example is the expression of an extracellular protease by the lactic acid bacterium Lactococcus lactis , which degrades milk proteins into free utilizable peptides that are essential to allow growth to high cell densities in milk. Cheating, protease-negative strains can invade the population and drive the protease-positive strain to extinction. By using multiple experimental approaches, as well as modeling population dynamics, we demonstrate that the persistence of the proteolytic trait is determined by the fraction of the generated peptides that can be captured by the cell before diffusing away from it. The mechanism described is likely to be relevant for the evolutionary stability of many extracellular substrate-degrading enzymes.