Modular network evolution under selection for robustness to noise

Abstract

Real networks often exhibit modularity, which is defined as the degree to which a network can be decomposed into several subnetworks. The question of how a modular network arises is still open to discussion. The leading hypothesis is that high modularity evolves under multiple goals, which are decomposable to subproblems, as well as under the evolutionary constraint that selection prefers sparse links in a network. In the present study, we investigate an alternative evolutionary constraint entailing increased robustness to noise. To examine this, we present noise-interfused network models involving an analytically solvable linear system and biologically inspired nonlinear systems. The models demonstrate that it is possible to evolve a modular network under both modularly changing goal orientations and enhancing robustness to noise, thereby reducing sensitivity to noise. By performing theoretical analyses of linear systems, it is shown that the evolutionary constraint enforces the establishment of well-balanced noise sensitivities of multiple noise sources and leads to a modular network underlying a modular structure in goals. Moreover, computer simulations confirm that the presented mechanisms of modular network evolution are robust to variations of nonlinearity in network functions. Our findings suggest a positive role for the presence of noise in network evolution.

The genetics of phenotypic plasticity. XVI. Interactions among traits and the flow of information

“…Models of (Leclerc ; Burda et al ; Friedlander et al. ; Ikemoto and Sekiyama ) and data about (Proulx et al. ; Winterbach et al ) genetic and metabolic networks provide parallel evidence for selection to shorten and simplify information pathways.…”

“…Models of (Leclerc 2008;Burda et al 2010;Friedlander et al 2013;Ikemoto and Sekiyama 2014) and data about (Proulx et al 2005;Winterbach et al 2013) genetic and metabolic networks provide parallel evidence for selection to shorten and simplify information pathways. Actual networks tend to be sparse and modular as compared to randomly generated networks.…”

‘Evolutionary poker’: an agent‐based model of interactome emergence and epistasis tested against Lenski's long‐term E. coli experiments

“…The emergence of modularity has received less research than the emergence of networks (e.g. Ikemoto & Sekiyama, 2014; Kashtan & Alon, 2005) and, once again, tends to be information‐theoretical rather than based on biological principles or mechanisms (Root‐Bernstein & Dillon, 1997; Simon, 1981). Part of the difficulty is historical.…”

Estimating optimal sparseness of developmental gene networks using a semi-quantitative model

“…Biologically, however, the gene networks are known to be sparsely connected [1]. It has been shown that robustness to expression noise is positively correlated with network modularity [2]. Since a high modularity implies low connections between modules, the networks can be maintained to be sparse in noisy environments.…”