Prediction and experimental evidence of different growth phases of the Podospora anserina hyphal network

Abstract The growth of the mycelial network of a filamentous fungus is monotonous, showing an ever increasing complexity with time. The components of the network growth are very simple and based on two mechanisms: the elongation of each hypha, and their multiplication by successive branching. These two mechanisms are sufficient to produce a complex network, and could be localized only at the tips of hyphae. However, branching can be of two types, apical or lateral, depending on its location on the hyphae, therefore imposing the redistribution of the necessary material in the whole mycelium. From an evolutionary point of view, maintaining different branching processes, with its associated cost, is intriguing. We propose in this work to discuss the advantages of each branching type using a new observable for the network growth allowing us to compare growth configurations. For this purpose, we build on experimental observations of the {\it Podospora anserina} thallus growth, enabling us to feed and constrain a lattice-free modeling of this network based on a binary tree. First, we report the set of statistics related to the branches of {\it P. anserina} that we have implemented into the model. Then, we build the density observable, allowing us to discuss the succession of growth phases. We predict that the evolution of the density is not monotonic but presents a marked stationary phase, clearly separating an anterior phase from a posterior one. The time of appearance of this stable region appears to be driven solely by the growth rate. Finally, we show that the density is a good observable to differentiate growth stress.