Generalised Lotka-Volterra model with hierarchical interactions

Abstract

In the analysis of complex ecosystems it is common to use random interaction coefficients, often assumed to be such that all species are statistically equivalent. In this work we relax this assumption by choosing interactions according to the cascade model, which we incorporate into a generalised Lotka-Volterra dynamical system. These interactions impose a hierarchy in the community. Species benefit more, on average, from interactions with species further below them in the hierarchy than from interactions with those above. Using dynamic mean-field theory, we demonstrate that a strong hierarchical structure is stabilising, but that it reduces the number of species in the surviving community, as well as their abundances. Additionally, we show that increased heterogeneity in the variances of the interaction coefficients across positions in the hierarchy is destabilising. We also comment on the structure of the surviving community and demonstrate that the abundance and probability of survival of a species is dependent on its position in the hierarchy.

10 pages, 6 Figures

References in corpus (4)

• Properties of equilibria and glassy phases of the random Lotka-Volterra model with demographic noise
• Rank abundance relations in evolutionary dynamics of random replicators
• Eigenvalues of random matrices with generalised correlations: a path integral approach
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Cited by in corpus (6)

• Dynamical Mean-Field Theory of Complex Systems on Sparse Directed Networks
• Incorporating Heterogeneous Interactions for Ecological Biodiversity
• Competitive exclusion and Hebbian couplings in random generalised Lotka-Volterra systems
• Topological conditions drive stability in meta-ecosystems
• Exact solution of Dynamical Mean-Field Theory for a linear system with annealed disorder
• Impossible ecologies: Interaction networks and stability of coexistence in ecological communities