On a multi-type growth-fragmentation process modelling the mycelial network of a filamentous fungus

schedule le vendredi 19 mars 2021 de 11h00 à 12h00

Organisé par : Quentin Berger, Nathanaël Enriquez, Thierry Lévy et Shen Lin

Intervenant : Milica Tomasevic (Polytechnique)
Lieu : Zoom : https://zoom.us/j/98589875776?pwd=Q2JCYU5FN25uNUZLdDJ4Uk9zU2Mxdz09

Sujet : On a multi-type growth-fragmentation process modelling the mycelial network of a filamentous fungus

Résumé :

Filamentous fungi form a very large family of species that play an important role in different ecosystems. In this talk, we will present a stochastic bi-type growth-fragmentation model for the expansion of the network of filaments of a filamentous fungus. Motivated by the identification of simple descriptors that characterize the growth of the network, we will study the longtime behaviour of the corresponding mean measure (or first moment semigroup). In addition, we will obtain a law of large numbers that relates the long term behaviour of the stochastic process to the limiting distribution of the mean measure. In the particular model we consider, which depends on only 3 parameters, all the quantities needed to describe this asymptotic behaviour are explicit, which paves the way for parameter inference based on data collected in lab experiments. 
The talk is based on a joint work with V. Bansaye (CMAP) and A. Véber (MAP5) and it is part of the NEMATIC project on "Growing and branching networks: Analysis, modelling and simulation of multiscale spatial exploration, spreading and morphogenesis under constraints". In particular, when it comes to the understanding of the mechanisms of growth of the mycelial network and to modelling choices, we profited from the interactions with F. Chapeland-Leclerc, G. Ruprich-Robert et E. Herbert (LIED, Univ. de Paris).