Modification speed and radius of higher-order interactions alter the oscillatory dynamics in an agent-based model

TL;DR

This study demonstrates that higher-order interactions (HOIs) implemented as an interaction modification in an agent-based model can drastically alter oscillatory population dynamics without necessarily changing mean abundances. By modeling three-species intransitive competition where species $C$ modifies the $A$–$B$ interaction within a radius $R_{\mathrm{HOI}}$ and with a temporal speed $\omega$, the authors show that HOI parameters shape oscillation strength, captured via Monte Carlo Singular Spectrum Analysis (MC-SSA) and quantified with VMEOF, while Sobol sensitivity indicates mean abundances are mostly unaffected by $\omega$ and $R_{\mathrm{HOI}}$ and are primarily controlled by $\beta$. Positive HOI strength $\beta$ enhances oscillations, whereas larger radii disperse the modification, dampening temporal effects; slow modification ($\omega$ small) shifts behavior toward HOI-free dynamics. The work highlights the importance of spatio-temporal scales in HOIs for ecosystem stability, revealing dynamics that go beyond traditional pairwise or simpler HOI models and underscoring the need to consider HOI geometry in ecological predictions.

Abstract

Understanding the population dynamics of ecological systems is crucial for predicting shifts in biodiversity and ensuring the protection of these systems. Established models often focus on pairwise species interactions, yet recent studies have highlighted the importance of higher-order interactions (HOIs) in shaping community structure and function. In this study, we investigate the effects of HOIs in an agent-based model with three species engaged in intransitive competition. We introduce an HOI where one species modifies the competition between the other two. We explore the impact of the strength, radius of influence, and speed of this interaction modification on species abundances and oscillations thereof. Our results show that these abundances are not only greatly impacted by the strength, but also by the radius and speed of the interaction modification. A deeper investigation demonstrates that the changes in the oscillations are caused by the interaction modification itself, and not the change in pairwise interaction strength caused by the HOI. These results emphasize the importance of considering the spatio-temporal scales of higher-order interactions when assessing ecosystem stability, highlighting that such interactions can introduce complex dynamical behaviors that go beyond the predictions of traditional pairwise or simpler higher-order models

Figures (8)

• Figure 1: Graph of the competition model. The circles indicate the three species $A$, $B$ and $C$. The red arrows indicate the pairwise competition interactions. The blue arrow between species $C$ and the interaction between species $A$ and $B$ indicates that species $C$ modifies the competition between species $A$ and $B$.
• Figure 2: Any interaction between red ($A$) and green ($B$) agents is modified if it occurs in the neighbourhood of a blue ($C$) agent. The half-green, half-red circle represents the grid cell where agents of species $B$ and $A$ meet and interact. The blue circle represents an agent of the modifier species $C$. (a) No modification happens, since the interaction occurs outside of radius of modification of the agent of species $C$. (b) The interaction is modified when it occurs within the radius of modification of an agent of species $C$.
• Figure 3: A visualisation of the modification caused by species $C$ in the ABM with $R_{\mathrm{HOI}} = 3$. The three species $A$, $B$, and $C$ are shown in red, green and blue, respectively. Lighter regions are the cells at which an interaction between $A$ and $B$ is modified. The lighter the grid cell, the more intense the modification. Only a 50 x 50 subgrid of the entire 200 x 200 grid is shown here for clarity.
• Figure 4: Boxplots of the effect of the HOI strength ($\beta$), modification speed ($\omega$) and modification radius ($R_{\mathrm{HOI}}$) on the mean abundance of species $A$ ((a) and (d)), species $B$ ((b) and (e)) and species $C$ ((c) and (f)), for positive modification ((a)-(c)) and negative modification ((d)-(f)).
• Figure 5: The effect of the modification strength $\beta$ on the mean abundances of species $A$, $B$ and $C$. The (very small) error bars represent the 95% confidence interval of the mean population abundance. The results are shown for (a)-(c) $R_{\mathrm{HOI}} = 3$, (d)-(f) $R_{\mathrm{HOI}} = 10$ and (g)-(i) $R_{\mathrm{HOI}} = 100$, for species $A$, $B$ and $C$ in the first, second and third column. The results are shown for $\omega$ in $\{1, 0.1, 0.01, 0.001\}$.