Distribution of growth directions in meadows of clonal plants

Clonal growth plants are abundant in both terrestrial and marine ecosystems. Some marine species are particularly important since they provide essential ecosystem services in the shores of all continents except Antarctica. For the appropriate modelization of clonal growth the discretization of the growth direction angle has to be carefully treated to correctly describe the dynamics of the meadow. Specifically, determining the minimum number of growth directions is important to maximize the efficiency of numerical simulations. We show that the presence of neutral modes in the growth direction angle tends to make the distribution of the growth directions uniform in the presence of noise, allowing us to choose the minimal number of discrete angles compatible with the branching. We also show that the formation of spatial patterns induces small differences in the population density within these different growth directions.
We acknowledge financial support from Agencia Estatal de Investigación (AEI, Spain) and Fondo Europeo de Desarrollo Regional under Project SuMaEco Grant No. RTI2018-095441-B-C22 (AEI/FEDER,UE) and the Spanish State Research Agency, through the Maria de Maeztu Program for units of Excellence in R&D (MDM-2017-0711). D.R-R. also acknowledges the fellowship BES-2016-076264 under the FPI program of MINECO, Spain.