Basins of distinct asymptotic states in the cyclically competing mobile five species game

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.

Correlation between the formation of new competing group and spatial scale for biodiversity in the evolutionary dynamics of cyclic competition

Securing space for species breeding is important in the evolution and maintenance of life in ecological sciences, and an increase in the number of competing species may cause frequent competition and conflict among the population in securing such spaces in a given area. In particular, for cyclically competing species, which can be described by the metaphor of rock-paper-scissors game, most of the previous works in microscopic frameworks have been studied with the initially given three species without any formation of additional competing species, and the phase transition of biodiversity via mobility from coexistence to extinction has never been changed by a change of spatial scale. In this regard, we investigate the relationship between spatial scales and species coexistence in the spatial cyclic game by considering the emergence of a new competing group by mutation. For different spatial scales, our computations reveal that coexistence can be more sensitive to spatial scales and may require larger spaces for frequencies of interactions. By exploiting the calculation of the coexistence probability from Monte-Carlo simulations, we obtain that certain interaction ranges for coexistence can be affected by both spatial scales and mobility, and spatial patterns for coexistence can appear in different ways. Since the issue of spatial scale is important for species survival as competing populations increase, we expect our results to have broad applications in the fields of social and ecological sciences.

The effect of territorial awareness in a three-species cyclic predator-prey model

Recognizing territories is essential to decide behavior of population either human or animals, and interaction between groups or individuals according to the territorial awareness is universal. Understanding various mechanisms which affect on such species behaviors can be possible by evolutionary games, and in particular, the rock–paper–scissors (RPS) game has been played a key role as a paradigmatic model to explore biodiversity from microbiota to societies. Among paramount mechanisms in systems of RPS, the role of intraspecific interaction has been recently noted in terms of promoting biodiversity. Since intraspecific interaction is defined by an invasive reaction between individuals in the same group, the interaction may be also sensitive to the territorial awareness. To explore how territorial awareness-based intraspecific interaction can affect species biodiversity, we endow species with the mechanism in the classic RPS game. By means of the Monte-Carlo method, we find the phenomenon that the presence of species’ territorial awareness has an impact on intraspecific interaction which ultimately affects species biodiversity. At the same time, we also find that territorial awareness can play a significant role to the average waiting time for extinction which is numerically elucidated by exploiting the quantity: interface width statistic. Unlike prior research that concentrated solely on the relationship between interaction frequency and species diversity, our results shed lights on the important role of territorial awareness in models of RPS, and they reveal fascinating evolutionary outcomes in structured populations that are a unique consequence of such awareness behavior.

Robust coexistence with alternative competition strategy in the spatial cyclic game of five species

Alternative strategy is common in animal populations to promote reproductive fitness by obtaining resources. In spatial dynamics of cyclic competition, reproduction can occur when individuals obtain vacant rooms and, in this regard, empty sites should be resources for reproduction which can be induced by interspecific competition. In this paper, we study the role of alternative competition in the spatial system of cyclically competing five species by utilizing rock-paper-scissors-lizard-spock game. From Monte-Carlo simulations, we found that strong alternative competition can lead to the reemergence of coexistence of five species regardless of mobility, which is never reported in previous works under the symmetric competition structure. By investigating the coexistence probability, we also found that coexistence alternates by passing certain degrees of alternative competition in combination with mobility. In addition, we provided evidences in the opposite scenario by strengthening spontaneous competition, which exhibits the reemergence of coexistence similarly. Our findings may suggest more comprehensive perspectives to interpret mechanisms for biodiversity by alternative strategies in spatially extended systems than previously reported.

Three-species competition with non-deterministic outcomes

Theoretical and experimental research studies have shown that ecosystems governed by non-transitive competition networks tend to maintain high levels of biodiversity. The theoretical body of work, however, has mainly focused on competition networks in which the outcomes of competition events are predetermined and hence deterministic, and where all species are identical up to their competitive relationships, an assumption that may limit the applicability of theoretical results to real-life situations. In this paper, we aim to probe the robustness of the link between biodiversity and non-transitive competition by introducing a three-dimensional winning probability parameter space, making the outcomes of competition events in a three-species in silico ecosystem uncertain. While two degenerate points in this parameter space have been the subject of previous studies, we investigate the remaining settings, which equip the species with distinct competitive abilities. We find that the impact of this modification depends on the spatial dimension of the system. When the system is well mixed, it collapses to monoculture, as is also the case in the non-transitive deterministic setting. In one dimension, chaotic patterns emerge, which tend to maintain biodiversity, and a power law relates the time that species manage to coexist to the degree of uncertainty regarding competition event outcomes. In two dimensions, the formation of spiral wave patterns ensures that biodiversity is maintained for moderate degrees of uncertainty, while considerable deviations from the non-transitive deterministic setting have strong negative effects on species coexistence. It can hence be concluded that non-transitive competition can still produce coexistence when the assumption of deterministic competition is abandoned. When the system collapses to monoculture, one observes a "survival of the strongest" law, as the species that has the highest probability of defeating its competitors has the best odds to become the sole survivor.

Multistability in the cyclic competition system

Cyclically competition models have been successful to gain an insight of biodiversity mechanism in ecosystems. There are, however, still limitations to elucidate complex phenomena arising in real competition. In this paper, we report that a multistability occurs in a simple rock-paper-scissor cyclically competition model by assuming that intraspecific competition depends on the logistic growth of each species density. This complex stability is absent in any cyclically competition model, and we investigate how the proposed intraspecific competition affects biodiversity in the existing society of three species through macroscopic and microscopic approaches. When the system is multistable, we show basins of the asymptotically stable heteroclinic cycle and stable attractors to demonstrate how the survival state is determined by initial densities of three species. Also, we find that the multistability is associated with a subcritical Hopf bifurcation. This surprising finding will give an opportunity to interpret rich dynamical phenomena in ecosystems which may occur in cyclic competition systems with different types of interactions.

Asymmetric interplay leads to robust coexistence by means of a global attractor in the spatial dynamics of cyclic competition

In the past decade, there have been many efforts to understand the species interplay with biodiversity in cyclic games within the macro and microscopic levels. In this direction, mobility and intraspecific competition have been found to be the main factors promoting coexistence in spatially extended systems. In this paper, we explore the relevant effect of asymmetric competitions coupled with mobility on the coexistence of cyclically competing species. By examining the coexistence probability, we have found that mobility can facilitate coexistence in the limited cases of asymmetric competition and can be well predicted by the basin structure of the deterministic system. In addition, it is found that mobility can have beneficial and harmful effects on coexistence when all competitions occur asymmetrically. We also found that the coexistence in the spatial dynamics ultimately becomes a global attractor. We hope to provide insights into the associated effects of asymmetric interplays on species coexistence in a spatially extended system and understand the biodiversity of asymmetrically competitive species under more complex competition structures.

Changes in political party systems arising from conflict and transfer among political parties

Conflict that arises between two groups of different paradigms is an inevitable phenomenon, and a representative example of the conflict among different groups is a conflict phenomenon caused by competition among political parties. In this paper, we study the dynamical behavior of a political party system. Considering three major political parties, we investigate how political party systems can be changed by employing a mathematical model. By considering the transfer mechanism of recruitment as well as conflict of competition between political parties, we found that all parties are likely to coexist when both the competition and transfer between the parties are weak, or if either mechanism can occur at a relatively low level. Otherwise, a political party system is changed to a single-party system. In addition, we found that when a party system was changed into a single-party system, it appeared to be either bistable or multistable, and has been elucidate by linear stability analysis. Our results may provide insights to understand mechanisms how political party systems can be changed by conflict and transfer.