Network Analysis and Maximum Entropy Approaches in Complex Agroforestry Systems

We are developing a network analysis of a multispecies agroforestry system, where interactions between harvest plants (Ilex paraguariensis) and nine tree species form a complex adaptive network. Building upon our validated agent-based model of this system, we analyse the emergent network properties of plant-plant interactions and their evolution over time through network metrics including degree distribution, clustering coefficients, and centrality measures revealing distinct community structures at different developmental stages. The network edges represent physical competition (shading), resource competition, and synergistic interactions mediated through soil quality modifications, capturing the system's complex adaptive behaviour across multiple temporal scales. Maximum entropy principles help quantify the information content of network configurations and predict optimal states, particularly during critical transitions in soil quality regimes. Our analysis reveals distinct network topologies characterized by different clustering patterns and community structures as soil quality regimes evolve. The temporal evolution of these network properties provides early warning signals for transitions and regime shifts. By combining network analysis with maximum entropy methods, we identify optimal management strategies that maximize both network resilience and agricultural productivity balancing complexity and productivity. This work demonstrates how network science tools can illuminate complex ecological interactions and guide sustainable agriculture practices, with implications for both theoretical ecological networks and practical agroforestry management. Keywords: spatial networks, adaptive networks, ecological networks, maximum entropy, sustainability, complex systems, critical transitions, sustainable agriculture.