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.
Highlights
In many natural ecosystems, at least one constituent species evolves quickly enough relative to its population growth that the two effects become interdependent
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 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
Summary
At least one constituent species evolves quickly enough relative to its population growth that the two effects become interdependent This phenomenon can occur when selection forces are tied to such sudden environmental effects as algal blooms or flooding [1], or it can arise from more subtle, population-level effects such as overcrowding or resource depletion [2]. The fitness landscape may have an arbitrarily complex topology, as it can depend on myriad factors ranging from environmental variability [5, 6], to inter- and intraspecific competition [7, 8], to resource depletion [9] These complex landscapes can be broadly classified according to whether they result in stabilizing or disruptive selection. In disruptive selection, the fitness landscape may contain multiple local maxima, in which case the population could have a wide distribution of trait values and occupy multiple distinct niches [11]
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