Stefano Allesina and Si Tang examine the stability of complex ecosystems, building on Robert May's 1972 work that showed large ecological networks are unlikely to persist. They extend May's findings to different interaction types, finding that predator-prey interactions increase stability, while mutualistic and competitive ones decrease it. Stability is determined by the eigenvalues of the community matrix, with all eigenvalues needing negative real parts for stability. The stability criterion depends on the interaction strength and network structure. For predator-prey interactions, the stability criterion is K < π/(π - 2) ≈ 2.75, while for mutualistic and competitive interactions, it is K < π/(π + 2) ≈ 0.61. Realistic food web structures and nestedness in mutualistic networks reduce stability. Weak interactions can stabilize or destabilize ecosystems depending on the interaction type. The study shows that the arrangement of interactions significantly affects stability, with predator-prey interactions being more stable than random ones. The results apply broadly to ecological systems and other systems of differential equations. The stability of ecosystems is influenced by both network structure and interaction strengths, with realistic structures sometimes reducing stability. The study highlights the importance of interaction types and their arrangement in determining ecosystem stability.Stefano Allesina and Si Tang examine the stability of complex ecosystems, building on Robert May's 1972 work that showed large ecological networks are unlikely to persist. They extend May's findings to different interaction types, finding that predator-prey interactions increase stability, while mutualistic and competitive ones decrease it. Stability is determined by the eigenvalues of the community matrix, with all eigenvalues needing negative real parts for stability. The stability criterion depends on the interaction strength and network structure. For predator-prey interactions, the stability criterion is K < π/(π - 2) ≈ 2.75, while for mutualistic and competitive interactions, it is K < π/(π + 2) ≈ 0.61. Realistic food web structures and nestedness in mutualistic networks reduce stability. Weak interactions can stabilize or destabilize ecosystems depending on the interaction type. The study shows that the arrangement of interactions significantly affects stability, with predator-prey interactions being more stable than random ones. The results apply broadly to ecological systems and other systems of differential equations. The stability of ecosystems is influenced by both network structure and interaction strengths, with realistic structures sometimes reducing stability. The study highlights the importance of interaction types and their arrangement in determining ecosystem stability.