Before revision:  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 dynamicsalways results in stable metapopulations dynamics around its co-existential equilibrium solution .
After revision:  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 .