Cascade of Complexity in Evolving Predator-Prey Dynamics

Abstract

We simulate an individual-based model that represents both the phenotype and genome of digital organisms with predator-prey interactions.We show how open-ended growth of complexity arises from the invariance of genetic evolution operators with respect to changes in the complexity, and that the dynamics which emerges shows scaling indicative of a non-equilibrium critical point. The mechanism is analogous to the development of the cascade in fluid turbulence.PACS numbers: 87.23.Kg, Experiments on digital organisms represent one of the most accurate and informative methodologies for understanding the process of evolution [1]. Systematic studies on digital organisms are especially informative, because the entire phylogenetic history of a population can be tracked, something that is much more difficultbut not impossible[2]-to do with natural organisms. Experiments on digital organisms can be performed over time scales relevant for evolution, and can capture universal aspects of evolutionary processes, including those relevant to long-term adaptation [3,4], ecological specialization [5,6] and the evolution of complex traits [7].Despite this progress, the way in which evolution leads to ever increasing complexity of organisms remains poorly understood and difficult to capture in simulations and models to date. Is this because these calculations are not sufficiently realistic, extensive, or detailed, or has something fundamental been left out? In this Letter, we argue that two fundamental aspects of evolutionary dynamics, with the character of symmetries, have been omitted, thus causing complexity growth to saturate.The first feature is that the evolutionary dynamics must be invariant with respect to changes in the complexity of the evolving organisms. That is, if there are inhomogeneities which encourage organisms to have a specific complexity, then these will act to prevent the complexity of the system from continually increasing. This invariance is similar in spirit to that which lies at the heart of the Richardson cascade in turbulence [8,9]. Here, a hierarchy of length-scales exists due to a transport of energy by scale-invariant processes between a large length scale and a small length scale. The largest and smallest features of the flow are determined by where the invariance is broken. In the biological case, processes invariant to changes in complexity will allow the dynamics to produce structures of arbitrarily high complexity. We will see below, in an explicit model, the effects of different genetic operations with regard to this invariance criterion. This criterion can also apply to the way that the fitness of an organism is determined in the dynamics, either explicitly or implicitly.The second feature is that there must be some advantage which can only be gained by an organism in the system being more complex than the organisms it competes with. Competitive interactions can drive such a dynamic; for example, if competition can be thought of as one organism setting the environmental problem that the other or...

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