Minimal branching and fusion morphogenesis approaches biological multi-objective optimality

Abstract: Many biological networks grow by elongation of filaments that can branch and fuse -- typical examples include fungal mycelium or slime mold. These networks must simultaneously perform multiple tasks such as transport, exploration, and robustness under finite resources. Yet, how such multi-task architectures emerge from local growth processes remains poorly understood. Here, we introduce a minimal model of spatial network morphogenesis based solely on stochastic branching, fusion, and stopping, during elongation. Despite the absence of global optimization or feedback, the model generates a broad morphospace from tree-like, to loopy, as well as hybrid architectures. By quantifying multiple functional objectives, we show that (i) these synthetic structures occupy similar regions of performance space than evolved empirical fungal networks, and (ii) that their Pareto front of optimal trade-offs lies close to that of these same fungal networks. Our results show that biological architectures approaching multi-objective optimality can arise from simple local growth rules, and identify branching and fusion as fundamental ingredients shaping the architecture of living transport networks.