Interplay of structured and random interactions in complex ecosystems dynamics

Abstract Minimal models for complex ecosystems often assume random interactions, whose statistics suffice to predict dynamical and macroecological patterns. However, ecological networks commonly possess a variety of properties, such as hierarchies or functional groups, that structure species interactions. Here, we ask how conclusions from random interaction models are altered by the presence of such community-level network structures. We consider a Lotka-Volterra model where pairwise species interactions combine structure and randomness, and study macroscopic community-level observables, abundance distributions and dynamical regimes. Randomness and structure combine in a surprisingly yet deceptively straightforward way: contributions from each component to community patterns are largely independent. Yet, their interplay has non-trivial consequences, notably out of equilibrium. We conclude that whether interaction structure matters depends on the pattern: when breaking species equivalence, static patterns of species presence and abundance predicted from random interaction models are less robust than the qualitative nature of dynamical regimes. Author summary Ecological communities with many species are a challenge for theoretical ecology, since they harbour many and very diverse interactions. A common approach is to focus on aggregated quantities, such as the abundance of broad taxonomic or functional groups, thus neglecting all the diversity at finer scales. We develop a theoretical framework that combines both ecological structure and fine-grained heterogeneity, which we represent with randomness. We find that structure and randomness contribute to ecosystem properties with effects that can be largely disentangled, allowing a continuous transition between two simple effective descriptions of the community dynamics. Still, they interact in unexpected ways. For instance, we show that species heterogeneity can simplify the dynamics of functional groups, countering the idea that complexity should always destabilize large ecosystems. Data availability statement: The source code used to produce the results and analyses presented in this manuscript is freely available at the GitHub repository: https://github.com/juanelogiral/interplay-structure-randomness.git Competing Interest Statement The authors have declared no competing interest. Footnotes All Figures were revised to improve the understanding of the manuscript. Minor errors corrected and added clarifications throughout the Sections.