Conspecific support in competitive systems as a pattern formation mechanism

The long term properties, like co-existence and extinction, are usually determined by the demographics of the competing species or other competitive advantages. In this paper we consider the effect of conspecific support on the co-existence of species. We show that, even if the competing species have the same demographics and interaction, their co-existence can be destabilized by sufficient level of conspecific support. When considering large number of species the conspecific support destabilizes the co-existance equilibrium, thus producing a pattern of extinction and varied levels of existence. Upscaling the model to continuous space variable leads to model of pattern formation via local self-activation and lateral inhibition.The National Research Foundation of South Africa and the DST/NRF SARChI Chair on Mathematical Models and Methods in Biosciences and Bioengineering.https://aip.scitation.org/journal/apcam2019Mathematics and Applied Mathematic