Fungi develop structures that interact with their surroundings and evolve adaptively in the presence of geometrical constraints, finding optimal solutions for complex combinatorial problems. The pathogenic fungus Ophiocordyceps constitutes a perfect model for the study of constrained interactive networks. Modeling these networks is challenging due to the highly coupled physics involved and their interaction with moving boundaries. In this work, we develop a computational phase-field model to elucidate the mechanics of the emerging properties observed in fungal networks. We use a variational approach to derive the equations governing the evolution in time of the mycelium biomass and the nutrients in the medium. We present an extensive testing of our model, reproduce growing and decaying phenomena, and capture spatial and temporal scales. We explore the variables interplay mechanism that leads to different colony morphologies, and explain abrupt changes of patterns observed in the laboratory. We apply our model to simulate analogous processes to the evolution of Ophiocordyceps as it grows through confined geometry and depletes available resources, demonstrating the suitability of the formulation to study this class of biological networks.

真菌开发出与周围环境相互作用的结构，并在存在几何约束的情况下自适应进化，为复杂的组合问题寻找最佳解决方案。病原真菌 Ophiocordyceps 构成了研究受限交互网络的完美模型。由于所涉及的高度耦合物理及其与移动边界的相互作用，对这些网络进行建模具有挑战性。在这项工作中，我们开发了一个计算相场模型来阐明在真菌网络中观察到的新兴特性的机制。我们使用变分方法推导出控制菌丝体生物量和培养基中营养物质随时间演变的方程。我们对我们的模型进行了广泛的测试，重现了增长和衰退的现象，并捕捉了空间和时间尺度。我们探索了导致不同菌落形态的变量相互作用机制，并解释了实验室中观察到的模式的突然变化。我们应用我们的模型来模拟 Ophiocordyceps 进化的类似过程，因为它通过有限的几何形状生长并耗尽可用资源，证明该配方适用于研究此类生物网络。