Is the addition of higher-order interactions in ecological models increasing the understanding of ecological dynamics?

Abstract

Recent work has shown that higher-order interactions can increase the stability, promote the diversity, and better explain the dynamics of ecological communities. Yet, it remains unclear whether the perceived benefits of adding higher-order terms into population dynamics models come from fundamental principles or a simple mathematical advantage given by the nature of multivariate polynomials. Here, we develop a general method to quantify the mathematical advantage of adding higher-order interactions in ecological models based on the number of free-equilibrium points that can be engineered in a system (i.e., equilibria that can be feasible or unfeasible by tunning model parameters). We apply this method to calculate the number of free-equilibrium points in Lotka-Volterra dynamics. While it is known that Lotka-Volterra models without higherorder interactions only have one free-equilibrium point regardless of the number of parameters, we find that by adding higher-order terms this number increases exponentially with the dimension of the system. Our results suggest that while adding higher-order interactions in ecological models may be good for prediction purposes, they cannot provide additional explanatory power of ecological dynamics if model parameters are not ecologically restricted. 2.

The impact of colonization history on the composition of ecological systems

“…Third, the simulation framework is applicable to LV dynamics with linear functional responses. Extending the calculations to population dynamics models with more complicated functional response will also be an interesting future direction [35,42]. Despite those limitations, the simplicity of our work have allowed us to provide a first-order classification of the conditions modulating the impact of colonization history.…”

Higher order interactions and coexistence theory

“…C9), which suggests that parameter changes in HOIs has the potential to destabilize species coexistence. Hence under restricted parameter space, HOIs could stabilize species coexistence (AlAdwani & Saavedra, 2019). Four-way HOIs could lead to species coexistence across a range of fitness differences, if their direction was positive (appendix Fig.…”

“…It is possible that four-way interactions could be prevalent in species communities, but empirically parameterizing such four-way interactions would be a difficult task (although see Mayfield & Stouffer (2017)). In addition, incorporating four-way HOIs in models parameterized from empirical data might not always provide additional explanatory power (AlAdwani & Saavedra, 2019).…”

Bridging parametric and nonparametric measures of species interactions unveils new insights of non-equilibrium dynamics

“…Importantly, the difference in measures can offer an opportunity to gain further insights about non-equilibrium ecological dynamics and higher-order interactions without modeling them (AlAdwani & Saavedra, 2019). For example, focusing on dynamics and building from the classic complexity-stability debate (May, 1972), it is assumed that a community can be dynamically stable only if most of the constant, direct, intra-specific terms are negative (a ii < 0), i.e., if "the population of each species would by itself be stable" (May, 1972).…”

“…Typically, the parametric approach measures species interactions as constant direct effects, while the nonparametric approach measures them as local aggregated effects (Breiman et al, 2001). Both measures have their own strengths and weaknesses: Within parametric approaches, measures have a mechanistic or phenomenological interpretation of a direct effect between species, but the magnitude and dimension of such parametric measures are model-dependent (Cenci & Saavedra, 2018a;AlAdwani & Saavedra, 2019;Letten & Stouffer, 2019). Instead, within the nonparametric approach, measures can be estimated directly from data, but they are often hard to be biologically interpreted (Sugihara & May, 1990;.…”