Saltatory targeting strategy in rock-paper-scissors models

Abstract: We explore how strategic leaps alter the classic rock-paper-scissors dynamics in spatially structured populations. In our model, individuals can expend energy reserves to jump toward regions with a high density of individuals of the species they dominate in the spatial game. This enables them to eliminate the target organisms and gain new territory, promoting species proliferation. Through stochastic, lattice-based simulations, we show that even when the energy allocated to jumping, as opposed to random walking, is low, there is a significant shift in the cyclic dominance balance. This arises from the increased likelihood of the leaping species successfully acquiring territory. Due to the cyclical nature of the game, the dominant species becomes the one that is superior to the jumping species. We investigate how spatial patterns are affected and calculate the changes in characteristic length scales. Additionally, we quantify how saltatory targeting reshapes spatial correlations and drives shifts in population dominance. Finally, we estimate the coexistence probability and find evidence that this behavioural strategy may promote biodiversity among low-mobility organisms but jeopardise long-term coexistence in the case of high-mobility dispersal. These results underscore the profound impact of novel foraging tactics on community structure and provide concrete parameters for ecologists seeking to incorporate behavioural innovation into ecosystem models.