A phase transition induces chaos in a predator-prey ecosystem with a dynamic fitness landscape

William Gilpin and Marcus W Feldman

PLOS Computational Biology, 2017, vol. 13, issue 7, 1-20

Abstract: In many ecosystems, natural selection can occur quickly enough to influence the population dynamics and thus future selection. This suggests the importance of extending classical population dynamics models to include such eco-evolutionary processes. Here, we describe a predator-prey model in which the prey population growth depends on a prey density-dependent fitness landscape. We show that this two-species ecosystem is capable of exhibiting chaos even in the absence of external environmental variation or noise, and that the onset of chaotic dynamics is the result of the fitness landscape reversibly alternating between epochs of stabilizing and disruptive selection. We draw an analogy between the fitness function and the free energy in statistical mechanics, allowing us to use the physical theory of first-order phase transitions to understand the onset of rapid cycling in the chaotic predator-prey dynamics. We use quantitative techniques to study the relevance of our model to observational studies of complex ecosystems, finding that the evolution-driven chaotic dynamics confer community stability at the “edge of chaos” while creating a wide distribution of opportunities for speciation during epochs of disruptive selection—a potential observable signature of chaotic eco-evolutionary dynamics in experimental studies.Author summary: Evolution is usually thought to occur very gradually, taking millennia or longer in order to appreciably affect a species' survival mechanisms. Conversely, demographic shifts due to predator invasion or environmental change can occur relatively quickly, creating abrupt and lasting effects on a species survival. However, recent studies of ecosystems ranging from the microbiome to oceanic predators have suggested that evolutionary and ecological processes can often occur over comparable timescales—necessitating that the two be addressed within a single, unified theoretical framework. Here, we show that when evolutionary effects are added to a minimal model of two competing species, the resulting ecosystem displays erratic and chaotic dynamics not typically observed in such systems. We then show that these chaotic dynamics arise from a subtle analogy between the evolutionary concept of fitness, and the concept of the free energy in thermodynamical systems. This analogy proves useful for understanding quantitatively how the concept of a changing fitness landscape can confer robustness to an ecosystem, as well as how unusual effects such as history-dependence can be important in complex real-world ecosystems. Our results predict a potential signature of a chaotic past in the distribution of timescales over which new species can emerge during the competitive dynamics, a potential waypoint for future experimental work in closed ecosystems with controlled fitness landscapes.

Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:plo:pcbi00:1005644

DOI: 10.1371/journal.pcbi.1005644

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