Modulating biodiversity through higher-order interactions and intraspecific competition in rock-paper-scissors dynamics

Abstract

Understanding the mechanisms that govern species coexistence and biodiversity represents a fundamental challenge in ecology. This study extends the classic rock-paper-scissors model by introducing a context-dependent higher-order interaction mechanism where intraspecific competition is dynamically regulated by local resource availability. Crucially, our quantitative analysis reveals that higher-order interactions significantly modulate the system's structural organization: Enhanced strength of higher-order interactions leads to a decrease in spatial wavelength, resulting in the formation of more compact species domains. However, this structural change makes the system more sensitive to mobility, shifting the extinction threshold to lower values. These findings highlight the dual role of resource-mediated higher-order regulation: it promotes local pattern formation but alters the system's resilience to dispersal, providing new theoretical perspectives for biodiversity conservation.

Figures (10)

• Figure 1: (a) Schematic diagram of the extended RPS model with intraspecific competition. Species $A$ (red), $B$ (blue), and $C$ (green) are engaged in cyclic dominance interactions. Based on the fundamental structure of a classic RPS system, each species can have intraspecific competition, which occurs depending on the food quantity and is determined by higher-level regulatory parameters dynamically. For details, refer to the model equation. (b) Geometric illustration of the local interaction neighborhood. The central adjacent pair represents the interacting individuals. $E$ represents any species or empty sites. The surrounding squares show the six unique nearest neighbors used to calculate the local resource abundance $\rho$, justifying the denominator in Eq. (\ref{['eqn:rate_P']}).
• Figure 2: Characteristic snapshots with different combinations of $M$ and $\delta$ at the 180000 time step. Panels from tops to bottoms are considered with different $M$: $M = 10^{-5}$, $10^{-4}$, and $10^{-3}$, respectively. In each row, panels from left to right are obtained with different $\delta$: $\delta=0$, $-0.3$, and $-1$, respectively. The colors red, blue, and green represent species $A$, $B$, and $C$, respectively. These snapshots illustrate the typical spatial patterns arising after long-term evolution under different combinations of species mobility and the strength of high-order interactions. The overall survival patterns are similar to those in the classic model. A remarkable point is that, even if a single species dominates the system, the spatial system is not fully occupied by the species; instead, it survives with emerging empty sites.
• Figure 3: Temporal evolution of species densities under different combinations of mobility $M$ and high-order interaction parameter $\delta$. Panels (a-c) show the time series of the densities for $M=10^{-5}$ and $\delta=0$, $-0.3$, $-1$ respectively; panels (d-f) correspond to $M=10^{-4}$ and $\delta=0$, $-0.3$, $-1$; panels (g-i) correspond to $M=10^{-3}$ and $\delta=0$, $-0.3$, $-1$. In each panel, red, blue, and green lines represent the densities of species $A$, $B$, and $C$, respectively, while the black line indicates the fraction of empty sites. The dynamical trajectories reveal the coexistence or extinction outcomes for each parameter set, consistent with the spatial patterns shown in Fig. \ref{['fig:2']}.
• Figure 4: Characteristic snapshots for $\delta=0$ and $M=10^{-4}$ at various time steps: (a) $1$, (b) $150$, (c) $2,950$, (d) $9,850$, (e) $19,000$, and (f) $180,000$. The color information is the same in Fig. \ref{['fig:2']}. The initial random distribution (a) gradually develops into characteristic spiral wave patterns (b-f) as the system evolves.
• Figure 5: Characteristic snapshots for $\delta=-0.3$ and $M=10^{-4}$ at various time steps: (a) 1, (b) 150, (c) 2,950, (d) 9,850, (e) 19,000, and (f) 180,000. The color information is the same in Fig. \ref{['fig:2']}.The initial random distribution (a) gradually develops into characteristic spiral wave patterns (b-f) as the system evolves.