Global modules robustly emerge from local interactions and smooth gradients

Modular structure and function are ubiquitous in biology, from the organization of animal brains and bodies to the scale of ecosystems. However, the mechanisms of modularity emergence from non-modular precursors remain unclear. Here we introduce the principle of peak selection, a process by which purely local interactions and smooth gradients can drive the self-organization of discrete global modules. The process combines strengths of the positional and Turing pattern-formation mechanisms into a model for morphogenesis. Applied to the grid-cell system of the brain, peak selection results in the self-organization of functionally distinct modules with discretely spaced spatial periods. Applied to ecological systems, it results in discrete multispecies niches and synchronous spawning across geographically distributed coral colonies. The process exhibits self-scaling with system size and 'topological robustness'¹, which renders module emergence and module properties insensitive to most parameters. Peak selection ameliorates the fine-tuning requirement for continuous attractor dynamics in single grid-cell modules and it makes a detail-independent prediction that grid module period ratios should approximate adjacent integer ratios, providing a highly accurate match to the available data. Predictions for grid cells at the transcriptional, connectomic and physiological levels promise to elucidate the interplay of molecules, connectivity and function emergence in brains.