Interaction Strength Is Key to Persistence of Complex Mutualistic Networks
Wei Su
School of Science, Beijing Jiaotong University
Beijing 100044, China
suwei@amss.ac.cn
Lei Guo
Key Laboratory of Systems and Control
Academy of Mathematics and Systems Science
Chinese Academy of Sciences
Beijing 100190, China
lguo@amss.ac.cn
Abstract
The relationship between stability of complex ecosystems and the interactions among species has always been a basic research focus in ecology. In this paper, we rigorously prove two facts about mutualistic ecological networks based on the Lotka–Volterra model of n-species. First, we prove that the dominant eigenvalue of the mutualistic interaction matrix will monotonically increase to infinity as any one of its off-diagonal elements increases to infinity, coinciding with the discoveries by ecologists via simulations. Second, we show that the persistence of mutualistic networks is equivalent to the stability of their interaction matrix. These two results together reveal the fact that the persistence of large mutualistic ecosystems can be guaranteed with proper interaction strengths, though they will eventually be destroyed as the interaction strength between any two species increases.
