Minimal branching and fusion morphogenesis approaches biological multi-objective optimality

TL;DR

This paper presents a minimal stochastic model of biological network growth that, without global optimization, produces diverse architectures similar to fungal networks and approaches multi-objective optimality.

Contribution

It introduces a simple local growth model based on branching and fusion that explains the emergence of complex, multi-tasking biological networks.

Findings

Generated structures resemble empirical fungal networks in performance.

Pareto fronts of synthetic and real networks are closely aligned.

Simple local rules can produce near-optimal multi-objective architectures.

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.