Emergence of robust global modules from local interactions and smooth gradients

Abstract Modular structure and function are ubiquitous in biology, from the scale of ecosystems to the organization of animal bodies and brains. However, the mechanisms of modularity emergence over development remain unclear. Here we introduce the principle of peak selection, a process in which two local interactions self-organize discontinuous module boundaries from a smooth global gradient, unifying the positional hypothesis and the Turing pattern formation hypothesis for morphogenesis. Applied to the brain's grid cell networks, peak selection results in the spontaneous emergence of functionally distinct modules with discretely spaced spatial periods. Applied to ecological systems, a generalization of the process results in discrete systems-level niches. The dynamics exhibits emergent self-scaling to variations in system size and ``topological robustness'' that renders module emergence and module properties insensitive to most parameters. Peak selection substantially ameliorates the fine-tuning requirement of continuous attractor dynamics even within single modules. It makes a detail-independent prediction that grid module period ratios should approximate adjacent integer ratios, furnishing the most accurate match to data to date, with additional predictions to connect physiology, connectomics, and transcriptomics data. In sum, our results indicate that local competitive interactions combined with low-information global gradients can lead to robust global module emergence.