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 most used measures across these approaches: species interactions measured as constant direct effects (typically used in parametric approaches) and local aggregated effects (typically used in nonparametric approaches). We show two fundamental properties of species interactions that cannot be revealed without bridging these definitions. First, we show that the local aggregated intraspecific effect summarizes all potential pathways through which one species impacts itself, which are likely to be negative even without any constant direct self‐regulation mechanism. This property has implications for the long‐held debate on how communities can be stabilized when little evidence of self‐regulation has been found among higher‐trophic species. Second, we show that a local aggregated interspecific effect between two species is correlated with the constant direct interspecific effect if and only if the population dynamics do not have any higher‐order direct effects. This other property provides a rigorous methodology to detect direct higher‐order effects in the field and experimental data. Overall, our findings illustrate a practical route to gain further insights about non‐equilibrium ecological dynamics and species interactions.

Merging dynamical and structural indicators to measure resilience in multispecies systems

“…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.…”

“…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).…”

Reconstructing large interaction networks from empirical time series data

“…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.…”

Ranking species based on sensitivity to perturbations under non-equilibrium community dynamics

“…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).…”