Mutation Rules and the Evolution of Sparseness and Modularity in Biological Systems

TL;DR

This paper investigates how mutation rules influence the development of sparseness and modularity in biological systems, finding that product-rule mutations naturally promote these features, unlike sum-rule mutations.

Contribution

The study demonstrates that mutation rules, specifically product-rule mutations, are key to evolving sparseness and modularity, providing a new perspective beyond connection costs or goal variations.

Findings

Product-rule mutations lead to natural sparseness in systems.

Product-rule mutations promote modularity when goals are modular.

Sum-rule mutations do not generally produce sparseness or modularity.

Abstract

Biological systems exhibit two structural features on many levels of organization: sparseness, in which only a small fraction of possible interactions between components actually occur; and modularity - the near decomposability of the system into modules with distinct functionality. Recent work suggests that modularity can evolve in a variety of circumstances, including goals that vary in time such that they share the same subgoals (modularly varying goals), or when connections are costly. Here, we studied the origin of modularity and sparseness focusing on the nature of the mutation process, rather than on connection cost or variations in the goal. We use simulations of evolution with different mutation rules. We found that commonly used sum-rule mutations, in which interactions are mutated by adding random numbers, do not lead to modularity or sparseness except for in special situations. In contrast, product-rule mutations in which interactions are mutated by multiplying by random numbers - a better model for the effects of biological mutations - led to sparseness naturally. When the goals of evolution are modular, in the sense that specific groups of inputs affect specific groups of outputs, product-rule mutations also lead to modular structure; sum-rule mutations do not. Product-rule mutations generate sparseness and modularity because they tend to reduce interactions, and to keep small interaction terms small.