The ghost of nestedness in ecological networks

Abstract

Ecologists are fascinated by the prevalence of nestedness in biogeographic and community data, where it is thought to promote biodiversity in mutualistic systems. Traditionally, nestedness has been treated in a binary sense: species and their interactions are either present or absent, neglecting information on abundances and interaction frequencies. Extending nestedness to quantitative data facilitates the study of species preferences, and we propose a new detection method that follows from a basic property of bipartite networks: large dominant eigenvalues are associated with highly nested configurations. We show that complex ecological networks are binary nested, but quantitative preferences are non-nested, indicating limited consumer overlap of favoured resources. The spectral graph approach provides a formal link to local dynamical stability analysis, where we demonstrate that nested mutualistic structures are minimally stable. We conclude that, within the binary constraint of interaction plausibility, species preferences are partitioned to avoid competition, thereby benefiting system-wide resource allocation.

Myosin-driven transport network in plants

“…The modularity of the bipartite network comprising myosins and myosin-binding proteins was assessed using MODULAR software (46), which employs simulated annealing to assign nodes to modules in a way that maximizes the Barber's bipartite modularity index. The nestedness was quantitatively evaluated as the magnitude of the leading eigenvalue of the adjacency matrix (47). The significance of the modularity and nestedness indices was determined by comparing the values obtained for the analyzed network with the values of 200 random bipartite networks with the same degree of distribution.…”

Emergence of structural and dynamical properties of ecological mutualistic networks

“…Nevertheless, the degree of nestedness varies among networks. Recently 5,10 , it has been argued that nestedness increases biodiversity and begets stability, but these results are in conflict with robust theoretical evidences showing that ecological communities with nested interactions are inherently less stable than unstructured ones 12,14,15 and that mutualism could be detrimental to persistence 11,15 . We aim to elucidate general optimization mechanisms underlying network structure and its influence on community dynamics and stability.…”

“…The relatively low abundances of the specialist species make them more vulnerable to extinction and results in correspondingly lower community resilience, as measured by the maximum real part of the eigenvalues of the community matrix community ( Figure 4B). The advantage of having a high total population leading to increased robustness against extinction due to demographic fluctuations, carries with it the cost associated with a lower resilience -the optimized network recovers from perturbations on a longer timescale than its random counterpart 12,14,27 (Figure 4C). …”

“…Here we have shown how binary nested network architecture could emerge as a consequence of an optimization process or variational principle. An interesting unexplored issue is an analysis of emergent quantitative nestedness 12 , i.e. the organization of the interaction intensities in the optimized networks along with a comparison to empirical data in mutualistic networks 12 .…”

“…An interesting unexplored issue is an analysis of emergent quantitative nestedness 12 , i.e. the organization of the interaction intensities in the optimized networks along with a comparison to empirical data in mutualistic networks 12 . The framework proposed here ought to be applicable for investigating the possible driving forces sculpting mutualistic network architectures in a variety of systems ranging from social 28 to economic 29 and other biological 30 (e.g.…”