# Stabilized Partitioning of Metapopulations Networks

## TL;DR

This paper investigates how removing dispersal connections in metapopulation networks affects their stability, establishing conditions for partitioning into stable sub-networks based on Fiedler values, with broader implications for various spatially discrete systems.

## Contribution

It introduces a mathematical framework to identify dispersal connection removals that ensure network stability, applicable across ecological and non-ecological systems.

## Key findings

- Existence of a lower bound Fiedler value guaranteeing stability.
- Derived necessary and sufficient conditions for network partitioning.
- Illustrated with examples across ecological and other systems.

## Abstract

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.