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In ectothermic organisms, it is hypothesized that metabolic rates mediate influences of temperature on the ecological and evolutionary processes governing biodiversity. However, it is unclear how and to what extent the influence of temperature on metabolism scales up to shape large-scale diversity patterns. In order to clarify the roles of temperature and metabolism, new theory is needed. Here, we establish such theory and model eco-evolutionary dynamics of trophic networks along a broad temperature gradient. In the model temperature can influence, via metabolism, resource supply, consumers' vital rates and mutation rate. Mutation causes heritable variation in consumer body size, which diversifies and governs consumer function in the ecological network. The model predicts diversity to increase with temperature if resource supply is temperature-dependent, whereas temperature-dependent consumer vital rates cause diversity to decrease with increasing temperature. When combining both thermal dependencies, a unimodal temperature-diversity pattern evolves, which is reinforced by temperature-dependent mutation rate. Studying coexistence criteria for two consumers showed that these outcomes are owing to temperature effects on mutual invasibility and facilitation. Our theory shows how and why metabolism can influence diversity, generates predictions useful for understanding biodiversity gradients and represents an extendable framework that could include factors such as colonization history and niche conservatism.

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.

Interspecific mutualisms have been playing a central role in the functioning of all ecosystems since the early history of life. Yet the theory of coevolution of mutualists is virtually nonexistent, by contrast with well-developed coevolutionary theories of competition, predator-prey and host-parasite interactions. This has prevented resolution of a basic puzzle posed by mutualisms: their persistence in spite of apparent evolutionary instability. The selective advantage of 'cheating', that is, reaping mutualistic benefits while providing fewer commodities to the partner species, is commonly believed to erode a mutualistic interaction, leading to its dissolution or reciprocal extinction. However, recent empirical findings indicate that stable associations of mutualists and cheaters have existed over long evolutionary periods. Here, we show that asymmetrical competition within species for the commodities offered by mutualistic partners provides a simple and testable ecological mechanism that can account for the long-term persistence of mutualisms. Cheating, in effect, establishes a background against which better mutualists can display any competitive superiority. This can lead to the coexistence and divergence of mutualist and cheater phenotypes, as well as to the coexistence of ecologically similar, but unrelated mutualists and cheaters.

Explaining the emergence of cooperative behaviours in a selfish world remains a major challenge for sociobiology. The iterated prisoner's dilemma offers a well-studied metaphor with which to explore theoretically the evolution of cooperation by reciprocation. Our current understanding is that 'tit-for-tat' should be the very first step (if not the aim) of evolution towards cooperation, but that mobility of the players in space seems to raise a devastating obstacle to the spread of tit-for-tat, by allowing egoists to exploit cooperation and escape retaliation. The second point is based on models that represent mobility only implicitly (in terms of travelling costs) and assume random interactions. Here we develop a more explicit theory of spatial iterated games: individual mobility is represented in terms of a diffusion process and interactions--defined locally--are inherently non-random. Our model reveals the existence of critical levels of individual mobility allowing for the evolution of cooperation. In fact, tit-for-tat can spread and take over among mobile players even when originating from extreme rarity. The dynamics of invasion of tit-for-tat develop as a travelling wave which propagates the cooperative strategy through space. Significant mobility is required to make the pioneering moves of cooperators towards the front of invasion less hazardous; it also contributes to neutralizing those defectors who may intrude the core of a cluster of cooperative players.