2021
DOI: 10.1111/oik.08060
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Bridging parametric and nonparametric measures of species interactions unveils new insights of non‐equilibrium dynamics

Abstract: A central theme in ecological research is to understand how species interactions contribute to community dynamics. Species interactions are the basis of parametric (model‐driven) and nonparametric (model‐free) approaches in theoretical and empirical work. However, despite their different interpretations across these approaches, these measures have occasionally been used interchangeably, limiting our opportunity to use their differences to gain new insights about ecological systems. Here, we revisit two of the … Show more

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Cited by 13 publications
(15 citation statements)
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“…Thus, these previous results indicate that it may be possible to merge concepts from dynamical and structural stability also under a nonparametric approach. In this sense, we believe that our study may also add to the unification of parametric and nonparametric approaches (Song & Saavedra, 2020) and could be expanded to be used with different types of empirical data.…”
Section: Discussionmentioning
confidence: 90%
See 1 more Smart Citation
“…Thus, these previous results indicate that it may be possible to merge concepts from dynamical and structural stability also under a nonparametric approach. In this sense, we believe that our study may also add to the unification of parametric and nonparametric approaches (Song & Saavedra, 2020) and could be expanded to be used with different types of empirical data.…”
Section: Discussionmentioning
confidence: 90%
“…It is important to note that, under our framework, we cannot increase the relative strength of interspecific interactions beyond a certain limit in order to guarantee dynamical stability. Thus, we assume that every species in our theoretical systems (see Resilience in theoretical ecological systems ) is self‐regulated, including predators in antagonistic systems (Barabás et al., 2017; Song & Saavedra, 2020).…”
Section: Methodsmentioning
confidence: 99%
“…Theoretically, the interaction coefficients can be extracted from Jacobians by scaling abundances (with a specific assumption regarding the governing equation, e.g., Ricker or generalised Lotka‐Volterra model), but we do not recommend this procedure, as scaling of abundance is numerically unstable unless abundance can be precisely determined. Therefore, there is an urgent need to bridge the two types of interaction measures in theory, for example, theoretical analysis conducted by Song and Saavedra (2021), or to develop novel network theory established on interaction Jacobian networks that are empirically more available.…”
Section: Resultsmentioning
confidence: 99%
“…These studies often rely on the assumption of a population dynamics model under a stable equilibrium to which the community returns after a small perturbation on abundances. Under this assumption, information on the Jacobian matrix—the matrix containing the local effects of each species on the growth rate of other species and itself (Song & Saavedra, 2021)—can be used to partition the recovery rate of the community into its constituent species (Arnoldi et al ., 2018, Ives et al ., 1999, Medeiros et al ., 2021). A community slightly displaced from equilibrium will asymptotically return along the direction spanned by the leading eigenvector of the Jacobian matrix, that is, the eigenvector associated with the leading (i.e., largest) eigenvalue (Dakos, 2018, Patterson et al ., 2021, Strogatz, 2018).…”
Section: Introductionmentioning
confidence: 99%