The Minimal Complexity of Adapting Agents Increases with Fitness

What is the relationship between the complexity and the fitness of evolved organisms, whether natural or artificial? It has been asserted, primarily based on empirical data, that the complexity of plants and animals increases as their fitness within a particular environment increases via evolution by natural selection. We simulate the evolution of the brains of simple organisms living in a planar maze that they have to traverse as rapidly as possible. Their connectome evolves over 10,000s of generations. We evaluate their circuit complexity, using four information-theoretical measures, including one that emphasizes the extent to which any network is an irreducible entity. We find that their minimal complexity increases with their fitness.Author Summary: It has often been asserted that as organisms adapt to natural environments with many independent forces and actors acting over a variety of different time scales, they become more complex. We investigate this question from the point of view of information theory as applied to the nervous systems of simple creatures evolving in a stereotyped environment. We performed a controlled in silico evolution experiment to study the relationship between complexity, as measured using different information-theoretic measures, and fitness, by evolving animats with brains of twelve binary variables over 60,000 generations. We compute the complexity of these evolved networks using three measures based on mutual information and one measure based on the extent to which their brain contain states that are both differentiated and integrated. All measures show the same trend - the minimal complexity at any one fitness level increases as the organisms become more adapted to their environment, that is, as they become fitter. Above this minimum, there exists a large degree of degeneracy in evidence.