Ambush strategy impacts species predominance and coexistence in rock-paper-scissors models

TL;DR

The paper addresses how cognitive ambush decision-making affects biodiversity in spatial cyclic competition. It extends the rock–paper–scissors framework to five species with an Ambush strategy for species 1, controlled by a perception radius $R$ and a local-density threshold $\beta$, and evaluates outcomes via large-scale stochastic lattice simulations across varying mobility $m$. The results show that Ambush disrupts classical spiral patterns, shifts species dominance depending on the fraction of ambushers, and reveals an optimal $\beta$ (around $>0.15$) that balances attack efficiency with persistence, increasing $\rho_1$ and overall density. Importantly, Ambush strategies improve coexistence probabilities, boosting biodiversity by up to $53\%$ at low mobility. Overall, the work links cognitive foraging decisions to ecosystem resilience and extinction risk in spatially structured communities.

Abstract

We investigate the adaptive Ambush strategy in cyclic models following the rules of the spatial rock-paper-scissors game. In our model, individuals of one species possess cognitive abilities to perceive environmental cues and assess the local density of the species they dominate in the spatial competition for natural resources. Based on this assessment, they either initiate a direct attack or, if the local concentration of target individuals does not justify the risk, reposition strategically to prepare an ambush. To quantify the evolutionary consequences of these behavioural strategies, we perform stochastic simulations, analysing emergent spatial patterns and the dependence of species densities on the threshold used by individuals to decide between immediate attack or anticipation. Our findings reveal that, despite being designed to enhance efficiency, cognitive strategies can reduce the abundance of the species due to the constraints of cyclic dominance. We identify an optimal decision threshold: attacking only when the local density of target individuals exceeds 15% provides the best balance between selection risk and long-term persistence. Furthermore, the Ambush strategy benefits low-mobility organisms, increasing coexistence probabilities by up to 53%. These results deepen the understanding of adaptive decision-making in spatial ecology, linking cognitive complexity to ecosystem resilience and extinction risk.

Figures (6)

• Figure 1: Schematic representation of the five-species rock–paper–scissors model. Arrows indicate the dominance relations, where organisms of species $i$ outcompete those of species $i+1$. The two components of the Ambush strategy are highlighted: i) the dashed arrow (Attack) marks movements of species $1$ toward regions with a higher density of species $2$; ii) the dotted arrow (Anticipation) depicts displacements toward areas where species $3$ are more abundant.
• Figure 2: Snapshots of final organims' spatial distribution captured from stochatic simulations of the five-species rock–paper–scissors model with Ambush Strategy. The lattice contains $500^2$ sites and evolves for $5000$ generations, starting with the random initial configurations. Fig. \ref{['fig2a']} shows the scenario where no organism can perform the behavioural movement, while Figs. \ref{['fig2b']}, \ref{['fig2c']}, \ref{['fig2d']}, and \ref{['fig2e']}, the fraction of organisms of species $1$ performing the Ambush strategy is $25\%$, $50\%$, $75\%$ and $100\%$, respectively. Colours follow the scheme of Fig. \ref{['fig1']}, with empty sites represented by white dots.
• Figure 3: Temporal dependence of the species densities for the simulations shown in Fig. \ref{['fig2']}. The black solid line depicts the density of empty spaces, while the pink, green, yellow, purple, and blue lines show the abundance of individuals of species $1$, $2$, $3$, $4$, and $5$, respectively. Figs. \ref{['fig3a']}, \ref{['fig3b']}, \ref{['fig3c']}, \ref{['fig3d']}, and \ref{['fig3e']} show how $\rho_i$ changes in the implementations whose final snapshot is shown in \ref{['fig2a']}, \ref{['fig2b']}, \ref{['fig2c']}, \ref{['fig2d']}, and \ref{['fig2e']}, respectively.
• Figure 4: Changes in the species selection risk due to the Ambush movement strategy in terms of the Attack trigger. The outcomes were averaged from sets of $100$ simulations, starting from different initial conditions in lattices with $500^2$ grid sites, running until $5000$ generations. The error bars show the standard deviation. The colours follow the scheme in Fig.\ref{['fig1']}. The cognitive factor is $\beta=1$, while the interaction parameters are set to $s=r=m=1/3$.
• Figure 5: Changes in the species densities due to the Ambush movement strategy in terms of the Attack trigger. The outcomes were averaged from sets of $100$ simulations, starting from different initial conditions in lattices with $500^2$ grid sites, running until $5000$ generations. The error bars show the standard deviation. The colours follow the scheme in Fig.\ref{['fig1']}. The cognitive factor is $\beta=1$, while the interaction parameters are set to $s=r=m=1/3$.