  A metapopulations network is a multi-patch habitat system, where populations
live and interact in the habitat patches, and individuals disperse from one
patch to the other via dispersal connections. The loss of dispersal connections
among the habitat patches can impact the stability of the system. In this work,
we determine if there exist(s) set(s) of dispersal connections removal of which
causes partitioning(s) of the metapopulations network into dynamically stable
sub-networks. Our study finds that there exists a lower bound threshold Fiedler
value which guarantees the dynamical stability of the network dynamics.
Necessary and sufficient mathematical conditions for finding partitions that
result in sub-networks with the desired threshold Fiedler values have been
derived and illustrated with examples. Although posed and discussed in the
ecological context, it may be pointed out that such partitioning problems exist
across any spatially discrete but connected dynamical systems with
reaction-diffusion. Non-ecological examples are power distribution grids,
intra-cellular reaction pathway networks and high density nano-fluidic
lab-on-chip applications.
