  The increasing volume of ecologically and biologically relevant data has
revealed a wide collection of emergent patterns in living systems. Analyzing
different datasets, ranging from metabolic gene-regulatory to species
interaction networks, we find that these networks are sparse, i.e. the
percentage of the active interactions scales inversely proportional to the
system size. This puzzling characteristic has been neither yet considered nor
explained. Herein, we introduce the new concept of explorability, a measure of
the ability of the system to adapt to newly intervening changes. We show that
sparsity is an emergent property resulting from a variational principle aiming
at the optimization of both explorability and dynamical robustness, the
capacity of the system to remain stable after perturbations of the underlying
dynamics. Networks with higher connectivities lead to an incremental difficulty
to find better values for both the explorability and dynamical robustness,
associated with the fine-tuning of the newly added interactions. A relevant
characteristic of our solution is its scale invariance, that is, it remains
optimal when several communities are assembled togheter. Connectivity is also a
key ingredient determining ecosystem stability and our proposed solution
contributes to solving May's celebrated complexity-stability paradox.
