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Coexistence of nestedness and modularity in host–pathogen infection networks

Nature Ecology & Evolution volume 4, pages 568–577 (2020)Cite this article

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Abstract

The long-term coevolution of hosts and pathogens in their environment forms a complex web of multi-scale interactions. Understanding how environmental heterogeneity affects the structure of host–pathogen networks is a prerequisite for predicting disease dynamics and emergence. Although nestedness is common in ecological networks, and theory suggests that nested ecosystems are less prone to dynamic instability, why nestedness varies in time and space is not fully understood. Many studies have been limited by a focus on single habitats and the absence of a link between spatial variation and structural heterogeneity such as nestedness and modularity. Here we propose a neutral model for the evolution of host–pathogen networks in multiple habitats. In contrast to previous studies, our study proposes that local modularity can coexist with global nestedness, and shows that real ecosystems are found in a continuum between nested-modular and nested networks driven by intraspecific competition. Nestedness depends on neutral mechanisms of community assembly, whereas modularity is contingent on local adaptation and competition. The structural pattern may change spatially and temporally but remains stable over evolutionary timescales. We validate our theoretical predictions with a longitudinal study of plant–virus interactions in a heterogeneous agricultural landscape.

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Fig. 1: Hypergraph representation of environmentally mediated host–pathogen infections.
Fig. 2: Neutral evolution of infection networks.
Fig. 3: Emergence of host ecotypes depends on habitat diversity.
Fig. 4: Theoretical predictions for the coexistence of nestedness and modularity.
Fig. 5: Modularity of plant–virus infections from 2000 to 2002 in an agricultural landscape in central Spain.
Fig. 6: Seasonal variation of bridgeness and modularity in empirical EPNs.

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Data availability

The network data are available via Dryad at https://doi.org/10.5061/dryad.253hr.

Code availability

For the analysis of nestedness and modularity we used the open-source software packages FALCON (https://github.com/sjbeckett/FALCON) and BiMat (http://bimat.github.io). Network simulation codes will be provided by the authors upon reasonable request.

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Acknowledgements

The authors thank L. Alsedà, J. Sardanyés, T. Lázaro, S. Duran-Nebreda, N. Conde and R. Solé for useful comments and discussions. This work was supported by the Spanish Ministry of Economy and Competitiveness, grant FIS2016-77447-R MINEICO/AEI/ FEDER and the European Union (to S.V.), and by grant RTI2018-094302-B-I00, Plan Estatal de I+D+i, Spanish Ministry of Economy and Competitiveness (to F.G.-A.). B.V. and R.M. were funded by the PR01018-EC-H2020-FET-Open MADONNA project.

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Authors and Affiliations

  1. Evolution of Technology Laboratory, Institute of Evolutionary Biology, CSIC–Universitat Pompeu Fabra, Barcelona, Spain

    Sergi Valverde

  2. European Centre for Living Technology, Venice, Italy

    Sergi Valverde

  3. ICREA–Complex Systems Laboratory, Health and Experimental Science Department, Institute of Evolutionary Biology, CSIC–Universitat Pompeu Fabra, Barcelona, Spain

    Blai Vidiella & Raúl Montañez

  4. Centro de Biotecnología y Genómica de Plantas (CBGP), Universidad Politécnica de Madrid (UPM) and Instituto nacional de Investigación y Tecnología Agraria y Alimentaria (INIA) and E.T.S.I. Agronómica, Alimentaria y de Biosistemas, Campus de Montegancedo, UPM, Madrid, Spain

    Aurora Fraile, Soledad Sacristán & Fernando García-Arenal

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Contributions

S.V. and F.G.-A. designed and coordinated the study, S.V. conceived the theoretical framework and led its development. B.V. and S.V. contributed to the mean-field model. S.V., R.M. and B.V. developed the network analysis, S.S., A.F. and F.G.-A. collected field samples and the plant–virus network data. S.V. generated all the final illustrations and plots. S.V. and F.G.-A. wrote the manuscript. All authors made revisions and approved the final draft.

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Correspondence to Sergi Valverde or Fernando García-Arenal.

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Extended data

Extended Data Fig. 1 Summary of statistics for full and seasonal subnetworks.

From left to right: pathogen richness Np, host richness Nh, ecotype richness Nt, number of habitats C, host habitat specificity Nt/Nh, average species degree k, habitat modularity Qc, average bridgeness B, spectral radius ρ(A) (a quantitative measure of nestedness), and statistical significance of nestedness.

Extended Data Fig. 2 Summary of statistics for habitat subnetworks.

From left to right, relative fraction of species richness Nk/N, local ecotype richness \(N_p^k\), local pathogen species richness \(N_t^k\), and local habitat modularity \(Q_c^k\). For reference, the first row gives the corresponding values in the full network (N0 = N, \(N_p^0 = N_p\), \(N_t^0 = N_t\) and \(Q_c^0 = Q_c = Q_c^1 + Q_c^2 + Q_c^3 + Q_c^4\)).

Extended Data Fig. 3 Exploration of the theoretical morphospace of ecotype-pathogen networks.

Nestedness is an invariant feature of this morphospace, while modularity is not and depends on speciation rates. This can be appreciated in the structure of networks generated for different combinations of pathogen and host speciation rates. The model predicts habitat modularity increases with habitat specificity. For example, (D) is a highly modular network, while (A) is not because only a few host species (blue nodes) in the former network share multiple habitats (green balls). The black line depicts the intersection of average bridgeness and habitat modularity, which separates low and intermediate modular networks (dark green region) from highly modular networks (light green) (see Supplementary Section 5 for details).

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Supplementary Figs. 1–20, discussion and Table 1.

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Valverde, S., Vidiella, B., Montañez, R. et al. Coexistence of nestedness and modularity in host–pathogen infection networks. Nat Ecol Evol 4, 568–577 (2020). https://doi.org/10.1038/s41559-020-1130-9

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