Emergence and Evolution of Hierarchical Structure in Complex Systems

Abstract

It is well known that many complex systems, both in technology and nature, exhibit hierarchical modularity: smaller modules, each of them providing a certain function, are used within larger modules that perform more complex functions. What is not well understood however is how this hierarchical structure (which is fundamentally a network property) emerges, and how it evolves over time. We propose a modeling framework, referred to as Evo-Lexis, that provides insight to some fundamental questions about evolving hierarchical systems. Evo-Lexis models the most elementary modules of the system as symbols ("sources") and the modules at the highest level of the hierarchy as sequences of those symbols ("targets"). Evo-Lexis computes the optimized adjustment of a given hierarchy when the set of targets changes over time by additions and removals (a process referred to as "incremental design"). In this paper we use computation modeling to show that:-Low-cost and deep hierarchies emerge when the population of target sequences evolves through tinkering and mutation. -Strong selection on the cost of new candidate targets results in reuse of more complex (longer) nodes in an optimized hierarchy. -The bias towards reuse of complex nodes results in an "hourglass architecture" (i.e., few intermediate nodes that cover almost all source-target paths). -With such bias, the core nodes are conserved for relatively long time periods although still being vulnerable to major transitions and punctuated equilibria. -Finally, we analyze the differences in terms of cost and structure between incrementally designed hierarchies and the corresponding "clean-slate" hierarchies which result when the system is designed from scratch after a change.arXiv:1805.04924v2 [cs.NE] 4 Aug 20182. Under what conditions do the emergent hierarchies exhibit the so called "hourglass effect"? Why are few intermediate modules reused much more than others? 3. Do intermediate modules persist during the evolution of hierarchies? Or are there "punctuated equilibria" where the highly reused modules change significantly? 4. Which are the differences in terms of cost and structure between the incrementally designed and the corresponding clean-slate designed hierarchies?The structure of the paper is as follows: In Section 2, we present an overview of Lexis, the static optimization framework that serves as the main building block in Evo-Lexis. 1 In Section 3, we present the components of the Evo-Lexis framework, along with the metrics that we use for the analysis of evolving hierarchies. In Section 4, we evaluate the evolution of hierarchies under different target generation models. Sections 5 and 6 present further analysis regarding the evolvability and major transitions in hierarchies produced using the most full-fledged (MRS) target generation model. Finally, Section 7 focuses on the comparison between clean-slate and incremental design in terms of cost and structure. In Section 8, we review related work in the context of Evo-Lexis. Section 9 discusses the results and p...

Evolution of Hierarchical Structure and Reuse in iGEM Synthetic DNA Sequences

“…(2) In the "expansion phase", the new targets are added incrementally to the current Lexis-DAG by minimizing the marginal cost of adding every new target to the existing hierarchy. We refer to this incremental design algorithm as Inc-Lexis, and it is described in detail [21]. (3) If the number of targets that are present in the system has reached a steady-state threshold, we also remove the batch of oldest targets from the Lexis-DAG.…”

“…From this section on, we compare the results over iGEM with the results gathered from Evo-Lexis in [21]. We refer the reader to [21] for details of the model and parameter settings.…”

“…Previous research in [3,20] has provided some evidence that these synthetic DNA sequences are designed by reusing existing components, and as such, it has a hierarchical organization. In this paper, we investigate how to apply the Evo-Lexis framework in the time series of iGEM sequences, and whether the resulting iGEM hierarchies exhibit the same qualitative properties we observed in [21] which was solely based on abstract target generation models. We ask the following questions in this paper:…”

“…In prior work in [21], we present Evo-Lexis, a modeling framework for the emergence and evolution of hierarchical structure in complex modular systems. There are many hypotheses in the literature regarding the factors that contribute to either the hierarchy or modularity properties.…”

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Many complex systems, both in technology and nature, exhibit hierarchical modularity: smaller modules, each of them providing a certain function, are used within larger modules that perform more complex functions. Previously, we have proposed a modeling framework, referred to as Evo-Lexis [21], that provides insight to some fundamental questions about evolving hierarchical systems. The predictions of the Evo-Lexis model should be tested using real data from evolving systems in which the outputs can be well represented by sequences.

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