Expanding spatial domains and transient scaling regimes in populations with local cyclic competition

Ambush strategy enhances organisms' performance in rock-paper-scissors games

We study a five-species cyclic system wherein individuals of one species strategically adapt their movements to enhance their performance in the spatial rock-paper-scissors game. Environmental cues enable the awareness of the presence of organisms targeted for elimination in the cyclic game. If the local density of target organisms is sufficiently high, individuals move towards concentrated areas for direct attack; otherwise, they employ an ambush tactic, maximising the chances of success by targeting regions likely to be dominated by opponents. Running stochastic simulations, we discover that the ambush strategy enhances the likelihood of individual success compared to direct attacks alone, leading to uneven spatial patterns characterised by spiral waves. We compute the autocorrelation function and measure how the ambush tactic unbalances the organisms' spatial organisation by calculating the characteristic length scale of typical spatial domains of each species. We demonstrate that the threshold for local species density influences the ambush strategy's effectiveness, while the neighbourhood perception range significantly impacts decision-making accuracy. The outcomes show that long-range perception improves performance by over 60%, although there is potential interference in decision-making under high attack triggers. Understanding how organisms' adaptation their environment enhances their performance may be helpful not only for ecologists, but also for data scientists, aiming to improve artificial intelligence systems.

Spatial dynamics of synergistic coinfection in rock-paper-scissors models

We investigate the spatial dynamics of two-disease epidemics reaching a three-species cyclic model. Regardless of their species, all individuals are susceptible to being infected with two different pathogens, which spread through person-to-person contact. We consider that the simultaneous presence of multiple infections leads to a synergistic amplification in the probability of host mortality due to complications arising from any of the co-occurring diseases. Employing stochastic simulations, we explore the ramifications of this synergistic coinfection on spatial configurations that emerge from stochastic initial conditions. Under conditions of pronounced synergistic coinfection, we identify the emergence of zones inhabited solely by hosts affected by a singular pathogen. At the boundaries of spatial domains dominated by a single disease, interfaces of coinfected hosts appear. The dynamics of these interfaces are shaped by curvature-driven processes and display a scaling behavior reflective of the topological attributes of the underlying two-dimensional space. As the lethality linked to coinfection diminishes, the evolution of the interface network's spatial dynamics is influenced by fluctuations stemming from waves of coinfection that infiltrate territories predominantly occupied by a single disease. Our analysis extends to quantifying the implications of synergistic coinfection at both the individual and population levels Our outcomes show that organisms' infection risk is maximized if the coinfection increases the death due to disease by 30% and minimized as the network dynamics reach the scaling regime, with species populations being maximum. Our conclusions may help ecologists understand the dynamics of epidemics and their impact on the stability of ecosystems.

Locally adaptive aggregation of organisms under death risk in rock-paper-scissors models

We run stochastic simulations of the spatial version of the rock-paper-scissors game, considering that individuals use sensory abilities to scan the environment to detect the presence of enemies. If the local dangerousness level is above a tolerable threshold, individuals aggregate instead of moving randomly on the lattice. We study the impact of the locally adaptive aggregation on the organisms' spatial organisation by measuring the characteristic length scale of the spatial domains occupied by organisms of a single species. Our results reveal that aggregation is beneficial if triggered when the local density of opponents does not exceed 30%; otherwise, the behavioural strategy may harm individuals by increasing the average death risk. We show that if organisms can perceive further distances, they can accurately scan and interpret the signals from the neighbourhood, maximising the effects of the locally adaptive aggregation on the death risk. Finally, we show that the locally adaptive aggregation behaviour promotes biodiversity independently of the organism's mobility. The coexistence probability rises if organisms join conspecifics, even in the presence of a small number of enemies. We verify that our conclusions hold for more complex systems by simulating the generalised rock-paper-scissors models with five and seven species. Our discoveries may be helpful to ecologists in understanding systems where organisms' self-defence behaviour adapts to local environmental cues.

How local antipredator response unbalances the rock-paper-scissors model

Antipredator behavior is a self-preservation strategy present in many biological systems, where individuals join the effort in a collective reaction to avoid being caught by an approaching predator. We study a nonhierarchical tritrophic system, whose predator-prey interactions are described by the rock-paper-scissors game rules. We perform a set of spatial stochastic simulations where organisms of one out of the species can resist predation in a collective strategy. The drop in predation capacity is local, which means that each predator faces a particular opposition depending on the prey group size surrounding it. Considering that the interference in a predator action depends on the prey's physical and cognitive ability, we explore the role of a conditioning factor that indicates the fraction of the species apt to perform the antipredator strategy. Because of the local unbalancing of the cyclic predator-prey interactions, departed spatial domains mainly occupied by a single species emerge. Unlike the rock-paper-scissors model with a weak species because of a nonlocal reason, our findings show that if the predation probability of one species is reduced because individuals face local antipredator response, the species does not predominate. Instead, the local unbalancing of the rock-paper-scissors model results in the prevalence of the weak species' prey. Finally, the outcomes show that local unevenness may jeopardize biodiversity, with the coexistence being more threatened for high mobility.

Spatial organisation plasticity reduces disease infection risk in rock-paper-scissors models

We study a three-species cyclic game system where organisms face a contagious disease whose virulence may change by a pathogen mutation. As a responsive defence strategy, organisms' mobility is restricted to reduce disease dissemination in the system. The impact of the collective self-preservation strategy on the disease infection risk is investigated by performing stochastic simulations of the spatial version of the rock-paper-scissors game. Our outcomes show that the mobility control strategy induces plasticity in the spatial patterns with groups of organisms of the same species inhabiting spatial domains whose characteristic length scales depend on the level of dispersal restrictions. The spatial organisation plasticity allows the ecosystems to adapt to minimise the individuals' disease contamination risk if an eventual pathogen alters the disease virulence. We discover that if a pathogen mutation makes the disease more transmissible or less lethal, the organisms benefit more if the mobility is not strongly restricted, thus forming large spatial domains. Conversely, the benefits of protecting against a pathogen causing a less contagious or deadlier disease are maximised if the average size of groups of individuals of the same species is significantly limited, reducing the dimensions of groups of organisms significantly. Our findings may help biologists understand the effects of dispersal control as a conservation strategy in ecosystems affected by epidemic outbreaks.

Effects of species vigilance on coexistence in evolutionary dynamics of spatial rock-paper-scissors game

Recognizing surrounding situations, such as enemy attacks, which can be realized by predator-prey relationships, is one of the common behaviors of the population in ecosystems. In this paper, we explore the relationship between such species' behavior and biodiversity in the spatial rock-paper-scissors game by employing the ecological concept "vigilance." In order to describe the vigilance process, we adopt a multiplex structure where two distinct layers describe virtual and physical interactions. By investigating the process of evolution in species, we also found that species with different vigilance go together. In addition, by utilizing the dynamic time warping method, we found that species with the same vigilance have consistent behavior, but species with different vigilance have diverse behavior. Our findings may lead to broader interpretations of mechanisms promoting biodiversity via vigilance in species ecosystems.

Enhancing coexistence of mobile species in the cyclic competition system by wildlife refuge

We investigate evolving dynamics of cyclically competing species on spatially extended systems with considering a specific region, which is called the "wildlife refuge," one of the institutional ways to preserve species biodiversity. Through Monte-Carlo simulations, we found that the refuge can play not groundbreaking but an important role in species survival. Species coexistence is maintained at a moderate mobility regime, which traditionally leads to the collapse of coexistence, and eventually, the extinction is postponed depending on the competition rate rather than the portion of the refuge. Incorporating the extinction probability and Fourier transform supported our results in both stochastic and analogous ways. Our findings may provide valuable evidence to assist fields of ecological/biological sciences in understanding the presence and construction of refuges for wildlife with associated effects on species biodiversity.

Emerging spatiotemporal patterns in cyclic predator-prey systems with habitats

Three-species cyclic predator-prey systems are known to establish spiral waves that allow species to coexist. In this study, we analyze a structured heterogeneous system which gives one species an advantage to escape predation in an area that we refer to as a habitat and study the effect on species coexistence and emerging spatiotemporal patterns. Counterintuitively, the predator of the advantaged species emerges as dominant species with the highest average density inside the habitat. The species given the advantage in the form of an escape rate has the lowest average density until some threshold value for the escape rate is exceeded, after which the density of the species with the advantage overtakes that of its prey. Numerical analysis of the spatial density of each species as well as of the spatial two-point correlation function for both inside and outside the habitats allow a detailed quantitative discussion. Our analysis is extended to a six-species game that exhibits spontaneous spiral waves, which displays similar but more complicated results.

Antipredator behavior in the rock-paper-scissors model

When faced with an imminent risk of predation, many animals react to escape consumption. Antipredator strategies are performed by individuals acting as a group to intimidate predators and minimize the damage when attacked. We study the antipredator prey response in spatial tritrophic systems with cyclic species dominance using the rock-paper-scissors game. The impact of the antipredator behavior is local, with the predation probability reducing exponentially with the number of prey in the predator's neighborhood. In contrast to the standard Lotka-Volterra implementation of the rock-paper-scissors model, where no spiral waves appear, our outcomes show that the antipredator behavior leads to spiral patterns from random initial conditions. The results show that the predation risk decreases exponentially with the level of antipredator strength. Finally, we investigate the coexistence probability and verify that antipredator behavior may jeopardize biodiversity for high mobility. Our findings may help biologists to understand ecosystems formed by species whose individuals behave strategically to resist predation.

Structured environments foster competitor coexistence by manipulating interspecies interfaces

Natural environments, like soils or the mammalian gut, frequently contain microbial consortia competing within a niche, wherein many species contain genetically encoded mechanisms of interspecies competition. Recent computational work suggests that physical structures in the environment can stabilize local competition between species that would otherwise be subject to competitive exclusion under isotropic conditions. Here we employ Lotka-Volterra models to show that interfacial competition localizes to physical structures, stabilizing competitive ecological networks of many species, even with significant differences in the strength of competitive interactions between species. Within a limited range of parameter space, we show that for stable communities the length-scale of physical structure inversely correlates with the width of the distribution of competitive fitness, such that physical environments with finer structure can sustain a broader spectrum of interspecific competition. These results highlight the potentially stabilizing effects of physical structure on microbial communities and lay groundwork for engineering structures that stabilize and/or select for diverse communities of ecological, medical, or industrial utility.

Performance of weak species in the simplest generalization of the rock-paper-scissors model to four species

We investigate the problem of the predominance and survival of "weak" species in the context of the simplest generalization of the spatial stochastic rock-paper-scissors model to four species by considering models in which one, two, or three species have a reduced predation probability. We show, using lattice based spatial stochastic simulations with random initial conditions, that if only one of the four species has its probability reduced, then the most abundant species is the prey of the "weakest" (assuming that the simulations are large enough for coexistence to prevail). Also, among the remaining cases, we present examples in which "weak" and "strong" species have similar average abundances and others in which either of them dominates-the most abundant species being always a prey of a weak species with which it maintains a unidirectional predator-prey interaction. However, in contrast to the three-species model, we find no systematic difference in the global performance of weak and strong species, and we conjecture that a similar result will hold if the number of species is further increased. We also determine the probability of single species survival and coexistence as a function of the lattice size, discussing its dependence on initial conditions and on the change to the dynamics of the model which results from the extinction of one of the species.

The effect of habitats and fitness on species coexistence in systems with cyclic dominance

Cyclic dominance between species may yield spiral waves that are known to provide a mechanism enabling persistent species coexistence. This observation holds true even in presence of spatial heterogeneity in the form of quenched disorder. In this work we study the effects on spatio-temporal patterns and species coexistence of structured spatial heterogeneity in the form of habitats that locally provide one of the species with an advantage. Performing extensive numerical simulations of systems with three and six species we show that these structured habitats destabilize spiral waves. Analyzing extinction events, we find that species extinction probabilities display a succession of maxima as function of time, that indicate a periodically enhanced probability for species extinction. Analysis of the mean extinction time reveals that as a function of the parameter governing the advantage of one of the species a transition between stable coexistence and unstable coexistence takes place. We also investigate how efficiency as a predator or a prey affects species coexistence.

Predominance of the weakest species in Lotka-Volterra and May-Leonard formulations of the rock-paper-scissors model

We revisit the problem of the predominance of the "weakest" species in the context of Lotka-Volterra and May-Leonard formulations of a spatial stochastic rock-paper-scissors model in which one of the species has its predation probability reduced by 0<P_{w}<1. We show that, despite the different population dynamics and spatial patterns, these two formulations lead to qualitatively similar results for the late time values of the relative abundances of the three species (as a function of P_{w}), as long as the simulation lattices are sufficiently large for coexistence to prevail-the "weakest" species generally having an advantage over the others (specially over its predator). However, for smaller simulation lattices, we find that the relatively large oscillations at the initial stages of simulations with random initial conditions may result in a significant dependence of the probability of species survival on the lattice size.