Linear Stability Invariant Metapopulations Network Partitioning
Metapopulations is a multi-patch habitat system, where populations live and interact in habitat patches, and individuals disperse from one patch to other via dispersal connections. The loss of dispersal connections among habitat patches can impact negatively on the stability of the system. This paper aims to determine some necessary and sufficient mathematical conditions for an appropriate metapopulations network partitioning (spatial cut) such that populations remain linearly stable in the partitioning induced daughter subnetworks. For that, metapopulations stability analysed and role of the Fiedler value of a metapopulations induced graph Laplacian described first. Our study suggests, sufficiently connected metapopulations network (having the Fiedler value greater than or equal to some threshold level) along with the constrained internal patch dynamics always results in stable metapopulations dynamics around its co-existential equilibrium solution.