Potential unsatisfiability of cyclic constraints on stochastic biological networks biases selection towards hierarchical architectures

Temporal, Structural, and Functional Heterogeneities Extend Criticality and Antifragility in Random Boolean Networks

Most models of complex systems have been homogeneous, i.e., all elements have the same properties (spatial, temporal, structural, functional). However, most natural systems are heterogeneous: few elements are more relevant, larger, stronger, or faster than others. In homogeneous systems, criticality-a balance between change and stability, order and chaos-is usually found for a very narrow region in the parameter space, close to a phase transition. Using random Boolean networks-a general model of discrete dynamical systems-we show that heterogeneity-in time, structure, and function-can broaden additively the parameter region where criticality is found. Moreover, parameter regions where antifragility is found are also increased with heterogeneity. However, maximum antifragility is found for particular parameters in homogeneous networks. Our work suggests that the "optimal" balance between homogeneity and heterogeneity is non-trivial, context-dependent, and in some cases, dynamic.

Evolution of resilience in protein interactomes across the tree of life

Phenotype robustness to environmental fluctuations is a common biological phenomenon. Although most phenotypes involve multiple proteins that interact with each other, the basic principles of how such interactome networks respond to environmental unpredictability and change during evolution are largely unknown. Here we study interactomes of 1,840 species across the tree of life involving a total of 8,762,166 protein-protein interactions. Our study focuses on the resilience of interactomes to network failures and finds that interactomes become more resilient during evolution, meaning that interactomes become more robust to network failures over time. In bacteria, we find that a more resilient interactome is in turn associated with the greater ability of the organism to survive in a more complex, variable, and competitive environment. We find that at the protein family level proteins exhibit a coordinated rewiring of interactions over time and that a resilient interactome arises through gradual change of the network topology. Our findings have implications for understanding molecular network structure in the context of both evolution and environment.

Linking structure and function in food webs: maximization of different ecological functions generates distinct food web structures

Trophic interactions are central to ecosystem functioning, but the link between food web structure and ecosystem functioning remains obscure. Regularities (i.e. consistent patterns) in food web structure suggest the possibility of regularities in ecosystem functioning, which might be used to relate structure to function. We introduce a novel, genetic algorithm approach to simulate food webs with maximized throughput (a proxy for ecosystem functioning) and compare the structure of these simulated food webs to real empirical food webs using common metrics of food web structure. We repeat this analysis using robustness to secondary extinctions (a proxy for ecosystem resilience) instead of throughput to determine the relative contributions of ecosystem functioning and ecosystem resilience to food web structure. Simulated food webs that maximized robustness were similar to real food webs when connectance (i.e. levels of interaction across the food web) was high, but this result did not extend to food webs with low connectance. Simulated food webs that maximized throughput or a combination of throughput and robustness were not similar to any real food webs. Simulated maximum-throughput food webs differed markedly from maximum-robustness food webs, which suggests that maximizing different ecological functions can generate distinct food web structures. Based on our results, food web structure would appear to have a stronger relationship with ecosystem resilience than with ecosystem throughput. Our genetic algorithm approach is general and is well suited to large, realistically complex food webs. Genetic algorithms can incorporate constraints on structure and can generate outputs that can be compared directly to empirical data. Our method can be used to explore a range of maximization or minimization hypotheses, providing new perspectives on the links between structure and function in ecological systems.