Corrigendum: Trait matching without traits: using correspondence analysis to investigate the latent structure of interaction networks

  1. Lisa Nicvert
  2. Hervé Fritz
  3. Stéphane Dray

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Abstract

In the original article, Equation (2) should read D r − 1 P 0 D c − 1 = U D V ⊤  instead of P 0 = U D V ⊤ . The paragraph directly above Equation (2) should thus be reformulated as: ``CA is based on the generalized singular value decomposition of the matrix D r − 1 P 0 D c − 1 , where P 0 = P − r c ⊤  is the double centered matrix of interaction frequencies P ."

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  1. Version published to 10.24072/pcjournal.610
  2. Version published to 10.24072/pcjournal.580
  3. Peer Community in Ecology

    A long-standing issue when studying the structure of species interaction networks is that the data required to build a more mechanistic understanding is often difficult to collect. For example, Bartomeus et al. (2016) have established a Bayesian framework to establish mechanistic links between the traits that species have, and the interactions that these species establish; but what do we feed these models with?

    In practical terms, the sparsity of data on species interactions, and the sparsity of data on species traits, in particular at a biological scale that is relevant to the study of interactions, means that our ability to link species traits to species interactions is severely limited.

    And yet, there are many exciting ecological questions that would greatly benefit from this integration. For example, being able to connect more explicitly the relationship between species niches and species interactions would provide useful guidance towards the unification of the Grinnellian and Eltonian definitions of the ecological niche. In a recent article, Dehling et al. (2025) have suggested that the reconstruction of the Eltonian niche could benefit from the inclusion of spatial data, and indeed from the adoption of spatial modelling tools. Although the various niche definitions are many decades old at this point, we are still attempting to figure out the precise mechanisms to quantify them for real ecological systems.

    The method that Nicvert et al. (2025) suggest is particularly elegant --- by assuming that the network as it is measured will carry within it the signature of species traits, they suggest that correspondence analysis (again, a tool more common in spatial ecology) can identify a latent structure, from which the niche centroid and breadth for the different species can be measured.

    There is immense value in this methodological proposal, as it suddenly opens up the ability to think about the functional diversity of species within a network without using the interactions themselves as the primary data source. And through an analysis of an actual bipartite interaction network, Nicvert et al. (2025) show that the latent structure thus uncovered can be tied to the actual species traits.

    This is, in other words, a convenient shortcut to start conceptualizing relationships between different definitions of the species niche, even in the situation where trait data is not available.
    Nicvert et al. (2025) argue that the latent structure represents latent traits. I am not sure if I agree. Strydom et al. (2023) make a case that (as a co-author!) I find highly convincing: traits are better understood as originating in, or directly influencing, organismal performance. The multiplication of techniques to identify latent variables is not bridging the Raunkiæran shortfall (de Bello et al., 2025). They can provide information about latent structure, but we should exercise great caution when naming them "traits". 

    Semantics notwithstanding, the work of Nicvert et al. (2025) is an important conceptual and methodological advance for network ecology. As they highlight in their conclusion, it opens up the opportunity to measure species overlap and complementarity in the latent space, which may in turn help understand how the interaction niches are partitioned, and contribute to the maintenance of diversity.​​​​​​

    References

    Bartomeus, I., Gravel, D., Tylianakis, J. M., Aizen, M. A., Dickie, I. A., & Bernard-Verdier, M. (2016). A common framework for identifying linkage rules across different types of interactions. Functional Ecology, 30(12), 1894–1903. https://doi.org/10.1111/1365-2435.12666

    de Bello, F., Fischer, F. M., Puy, J., Shipley, B., Verdú, M., Götzenberger, L., Lavorel, S., Moretti, M., Wright, I. J., Berg, M. P., Carmona, C. P., Cornelissen, J. H. C., Dias, A. T. C., Gibb, H., Lepš, J., Madin, J. S., Majeková, M., Pausas, J. G., Segrestin, J., … Garnier, E. (2025). Raunkiæran shortfalls: Challenges and perspectives in trait‐based ecology. Ecological Monographs, 95(2). https://doi.org/10.1002/ecm.70018

    Dehling, D. M., Lai, H. R., & Stouffer, D. B. (2025). Eltonian niche modelling: Applying joint hierarchical niche models to ecological networks. Ecology Letters, 28(6), e70120. https://doi.org/10.1111/ele.70120

    Lisa Nicvert, Hervé Fritz, Stéphane Dray (2025) Trait matching without traits: using correspondence analysis to investigate the latent structure of interaction networks. bioRxiv, ver. 5 peer-reviewed and recommended by PCI Ecology https://doi.org/10.1101/2024.10.22.619454​

    Strydom, T., Bouskila, S., Banville, F., Barros, C., Caron, D., Farrell, M. J., Fortin, M.-J., Mercier, B., Pollock, L. J., Runghen, R., Dalla Riva, G. V., & Poisot, T. (2023). Graph embedding and transfer learning can help predict potential species interaction networks despite data limitations. Methods in Ecology and Evolution, 14(12), 2917–2930. https://doi.org/10.1111/2041-210x.14228​

  4. Version published to 10.1101/2024.10.22.619454 on bioRxiv