Conservation and management of natural resources and biodiversity need improved criteria to select functional networks of protected areas. The connectivity within networks due to dispersal is rarely considered, partly because it is unclear how connectivity information can be included in the selection of protected areas. We present a novel and general method that applies eigenvalue perturbation theory (EPT) to select optimum networks of protected areas based on connectivity. At low population densities, characteristic of threatened populations, this procedure selects networks that maximize the growth rate of the overall network. This method offers an improved link between connectivity and metapopulation dynamics. Our framework is applied to connectivities estimated for marine larvae and demonstrates that, for open populations, the best strategy is to protect areas acting as both strong donors and recipients of recruits. It should be possible to implement an EPT framework for connectivity analysis into existing holistic tools for design of protected areas.