  Investigating relation between various structural patterns found in
real-world networks and stability of underlying systems is crucial to
understand importance and evolutionary origin of such patterns. We evolve
multiplex networks, comprising of anti-symmetric couplings in one layer,
depicting predator-prey relation, and symmetric couplings in the other,
depicting mutualistic (or competitive) relation, based on stability
maximization through the largest eigenvalue. We find that the correlated
multiplexity emerges as evolution progresses. The evolved values of the
correlated multiplexity exhibit a dependence on the inter-link coupling
strength. Furthermore, the inter-layer coupling strength governs the evolution
of disassortativity property in the individual layers. We provide analytical
understanding to these findings by considering star like networks in both the
layers. The model and tools used here are useful for understanding the
principles governing the stability as well as importance of such patterns in
the underlying networks of real-world systems.
