Mutation Rules and the Evolution of Sparseness and Modularity in Biological Systems
Tamar Friedlander, Avraham E. Mayo, Tsvi Tlusty, Uri Alon
(Submitted on 18 Feb 2013)
Biological systems show 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). Here, we studied the origin of modularity and sparseness focusing on the nature of the mutation process, rather than variations in the goal. We use simulations of evolution with different mutation rules. We find that commonly used sum-rule mutations, in which interactions are mutated by adding random numbers, do not lead to modularity or sparseness except for 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, lead 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 lead to modular structure; sum-rule mutations do not. Product-rule mutations generate sparseness and modularity because they keep small interaction terms small.