Evolution of cooperation on reinforcement-learning driven-adaptive networks.

Complex networks are widespread in real-world environments across diverse domains. Real-world networks tend to form spontaneously through interactions between individual agents. Inspired by this, we design an evolutionary game model in which agents participate in a prisoner's dilemma game (PDG) with their neighboring agents. Agents can autonomously modify their connections with neighbors using reinforcement learning to avoid unfavorable environments. Interestingly, our findings reveal some remarkable results. Exploiting reinforcement learning-based adaptive networks improves cooperation when juxtaposed with existing PDGs performed on homogeneous networks. At the same time, the network's topology evolves from homogeneous to heterogeneous states. This change occurs as players gain experience from past games and become more astute in deciding whether to join PDGs with their current neighbors or disconnect from the least profitable neighbors. Instead, they seek out more favorable environments by establishing connections with second-order neighbors with higher rewards. By calculating the degree distribution and modularity of the adaptive network in a steady state, we confirm that the adaptive network follows a power law and has a clear community structure, indicating that the adaptive network is similar to networks in the real world. Our study reports a new phenomenon in evolutionary game theory on networks. It proposes a new perspective to generate scale-free networks, which is generating scale-free networks by the evolution of homogeneous networks rather than typical ways of network growth and preferential connection. Our results provide new aspects to understanding the network structure, the emergence of cooperation, and the behavior of actors in nature and society.

Exploring inbreeding dynamics by considering reproductive bound and polygyny.

Inbreeding is a clinically significant measure of a population dependent on human social structures including the population size or the cultural traits. Here, we propose an expanded and elaborate model to analyze the inbreeding within a population where explicit polygyny and inbreeding bounds are taken into account. Unlike the models presented so far, we implemented biologically realistic assumptions that there is the disproportionate probability of males to reproduce (polygyny) and female reproduction is bounded. Using the proposed model equations, we changed the parameters that represent the polygyny degree, the female reproductive bound correlated to the mutation rate, and the total population size. The disappearance of the polygyny that numerous human societies experienced results in the long-lasting effect of the decreasing inbreeding coefficient. Decreased female reproductive bound correlated with a higher mutation rate reveals similar results. After the effect of each factor is analyzed, we modeled the dynamics of the inbreeding coefficient throughout an imaginary human population where polygyny disappears and late marriage becomes prevalent. In this group, the population size gradually and exponentially increases reflecting the traits of prehistoric human society and rising agricultural productivity. To observe how late and less marriage, the feature of the modern developed society, affects the inbreeding dynamics, the female reproductive bound and the population size were assumed to decrease after the population upsurge. The model can explain the decreasing trend of the prehistoric inbreeding coefficient of the actual human population and predict how the trend will be shifted when traits of modern societies continue.

Reinforcement learning relieves the vaccination dilemma.

The main goal of this paper is to study how a decision-making rule for vaccination can affect epidemic spreading by exploiting the Bush-Mosteller (BM) model, one of the methodologies in reinforcement learning in artificial intelligence (AI), which can realize the systematic process of learning in humans, on complex networks. We consider the BM model with two stages-vaccination and epidemiological processes-and address two independent rules about fixed loss consideration and average payoff of neighbors to update agent's vaccination behavior for various stimuli, such as loss of payoffs and environments during the vaccination process. Higher sensitivity not only favors higher vaccination coverage rates but also delays the transition point in relative vaccination costs when transitioning from full vaccination (inoculation level 1) to incomplete vaccination (inoculation level less than 1). Extensive numerical simulations demonstrate that the vaccination dilemma can be overcome to some extent, and the distribution of the intended vaccination probabilities in both independent rules is either normal or skewed when different parameters are considered. Since AI is contributing to many fields, we expect that our BM-empowered learning can ultimately resolve the vaccination dilemma.

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.

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.

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.

Nonlinear dynamics with Hopf bifurcations by targeted mutation in the system of rock-paper-scissors metaphor.

The role of mutation, which is an error process in gene evolution, in systems of cyclically competing species has been studied from various perspectives, and it is regarded as one of the key factors for promoting coexistence of all species. In addition to naturally occurring mutations, many experiments in genetic engineering have involved targeted mutation techniques such as recombination between DNA and somatic cell sequences and have studied genetic modifications through loss or augmentation of cell functions. In this paper, we investigate nonlinear dynamics with targeted mutation in cyclically competing species. In different ways to classic approaches of mutation in cyclic games, we assume that mutation may occur in targeted individuals who have been removed from intraspecific competition. By investigating each scenario depending on the number of objects for targeted mutation analytically and numerically, we found that targeted mutation can lead to persistent coexistence of all species. In addition, under the specific condition of targeted mutation, we found that targeted mutation can lead to emergences of bistable states for species survival. Through the linear stability analysis of rate equations, we found that those phenomena are accompanied by Hopf bifurcation which is supercritical. Our findings may provide more global perspectives on understanding underlying mechanisms to control biodiversity in ecological/biological sciences, and evidences with mathematical foundations to resolve social dilemmas such as a turnover of group members by resigning with intragroup conflicts in social sciences.

Emergence of oscillatory coexistence with exponentially decayed waiting times in a coupled cyclic competition system.

Interpatch migration between two environments is generally considered as a spatial concept and can affect species biodiversity in each patch by inducing flux of population such as inflow and outflow quantities of species. In this paper, we explore the effect of interpatch migration, which can be generally considered as a spatial concept and may affect species biodiversity between two different patches in the perspective of the macroscopic level by exploiting the coupling of two systems, where each patch is occupied by cyclically competing three species who can stably coexist by exhibiting periodic orbits. For two simple scenarios of interpatch migration either single or all species migration, we found that two systems with independently stable coexisting species in each patch are eventually synchronized, and oscillatory behaviors of species densities in two patches become identical, i.e., the synchronized coexistence emerges. In addition, we find that, whether single or all species interpatch migration occurs, the waiting time for the synchronization is exponentially decreasing as the coupling strength is intensified. Our findings suggest that the synchronized behavior of species as a result of migration between different patches can be easily predicted by the coupling of systems and additional information such as waiting times and sensitivity of initial densities.

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.

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.

Biodiversity in the cyclic competition system of three species according to the emergence of mutant species.

Understanding mechanisms which promote or hinder existing ecosystems are important issues in ecological sciences. In addition to fundamental interactions such as competition and migration among native species, existing ecosystems can be easily disturbed by external factors, and the emergence of new species may be an example in such cases. The new species which does not exist in a current ecosystem can be regarded as either alien species entered from outside or mutant species born by mutation in existing normal species. Recently, as existing ecosystems are getting influenced by various physical/chemical external factors, mutation due to anthropogenic and environmental factors can occur more frequently and is thus attracting much attention for the maintenance of ecosystems. In this paper, we consider emergences of mutant species among self-competing three species in the cyclic dominance. By defining mutation as the birth of mutant species, we investigate how mutant species can affect biodiversity in the existing ecosystem. Through microscopic and macroscopic approaches, we have found that the society of existing normal species can be disturbed by mutant species either the society is maintained accompanying with the coexistence of all species or jeopardized by occupying of mutant species. Due to the birth of mutant species, the existing society may be more complex by constituting two different groups of normal and mutant species, and our results can be contributed to analyze complex ecosystems of many species. We hope our findings may propose a new insight on mutation in cyclic competition systems of many species.

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.

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.

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

We study the dynamics of cyclic competing mobile five species on spatially extended systems originated from asymmetric initial populations and investigate the basins for the three possible asymptotic states, coexistence of all species, existences of only two independent species, and the extinction. Through extensive numerical simulations, we find a prosperous dependence on initial conditions for species biodiversity. In particular, for fixed given equal densities of two relevant species, we find that only five basins for the existence of two independent species exist and they are spirally entangled for high mobility. A basin of coexistence is outbreaking when the mobility parameter is decreased through a critical value and surrounded by the other five basins. For fixed given equal densities of two independent species, however, we find that basin structures are not spirally entangled. Further, final states of two independent species are totally different. For all possible considerations, the extinction state is not witnessed which is verified by the survival probability. To provide the validity of basin structures from lattice simulations, we analyze the system in mean-field manners. Consequently, results on macroscopic levels are matched to direct lattice simulations for high mobility regimes. These findings provide a good insight into the fundamental issue of the biodiversity among many species than previous cases.

Flight Test Result for the Ground-Based Radio Navigation System Sensor with an Unmanned Air Vehicle.

The Ground-based Radio Navigation System (GRNS) is an alternative/backup navigation system based on time synchronized pseudolites. It has been studied for some years due to the potential vulnerability issue of satellite navigation systems (e.g., GPS or Galileo). In the framework of our study, a periodic pulsed sequence was used instead of the randomized pulse sequence recommended as the RTCM (radio technical commission for maritime services) SC (special committee)-104 pseudolite signal, as a randomized pulse sequence with a long dwell time is not suitable for applications requiring high dynamics. This paper introduces a mathematical model of the post-correlation output in a navigation sensor, showing that the aliasing caused by the additional frequency term of a periodic pulsed signal leads to a false lock (i.e., Doppler frequency bias) during the signal acquisition process or in the carrier tracking loop of the navigation sensor. We suggest algorithms to resolve the frequency false lock issue in this paper, relying on the use of a multi-correlator. A flight test with an unmanned helicopter was conducted to verify the implemented navigation sensor. The results of this analysis show that there were no false locks during the flight test and that outliers stem from bad dilution of precision (DOP) or fluctuations in the received signal quality.

Understanding the role of neutral species by means of high-order interaction in the rock-paper-scissors dynamics.

The existence of neutral species carries profound ecological implications that warrant further investigation. In this paper, we study the impact of neutral species on biodiversity in a spatial tritrophic system of cyclic competition, in which the neutral species are identified as the fourth species that may affect the competition process of the other three species under the rock-paper-scissors (RPS) rule. Extensive simulations showed that neutral species can promote coexistence in a high mobility regime within the system. When coexistence occurs, we found that the state can be maintained by two mechanisms: Species can either (i) adhere to traditional RPS rule or (ii) form patches to resist invasion. Our findings might aid in understanding the impact of neutral species on biodiversity in ecosystems.

Persistent coexistence of cyclically competing species in spatially extended ecosystems.

A fundamental result in the evolutionary-game paradigm of cyclic competition in spatially extended ecological systems, as represented by the classic Reichenbach-Mobilia-Frey (RMF) model, is that high mobility tends to hamper or even exclude species coexistence. This result was obtained under the hypothesis that individuals move randomly without taking into account the suitability of their local environment. We incorporate local habitat suitability into the RMF model and investigate its effect on coexistence. In particular, we hypothesize the use of "basic instinct" of an individual to determine its movement at any time step. That is, an individual is more likely to move when the local habitat becomes hostile and is no longer favorable for survival and growth. We show that, when such local habitat suitability is taken into account, robust coexistence can emerge even in the high-mobility regime where extinction is certain in the RMF model. A surprising finding is that coexistence is accompanied by the occurrence of substantial empty space in the system. Reexamination of the RMF model confirms the necessity and the important role of empty space in coexistence. Our study implies that adaptation/movements according to local habitat suitability are a fundamental factor to promote species coexistence and, consequently, biodiversity.

Treatment outcome in an SI model with evolutionary resistance: a Darwinian model for the evolution of resistance.

We consider a Darwinian (evolutionary game theoretic) version of a standard susceptible-infectious SI model in which the resistance of the disease causing pathogen to a treatment that prevents death to infected individuals is subject to evolutionary adaptation. We determine the existence and stability of all equilibria, both disease-free and endemic, and use the results to determine conditions under which the treatment will succeed or fail. Of particular interest are conditions under which a successful treatment in the absence of resistance adaptation (i.e. one that leads to a stable disease-free equilibrium) will succeed or fail when pathogen resistance is adaptive. These conditions are determined by the relative breadths of treatment effectiveness and infection transmission rate distributions as functions of pathogen resistance.

The role of recognition error in the stability of green-beard genes.

The empirical examples of the green-beard genes, once a conundrum of evolutionary biology, are accumulating, while theoretical analyses of this topic are occasional compared to those concerning (narrow-sense) kin selection. In particular, the recognition error of the green-beard effect that the cooperator fails to accurately recognize the other cooperators or defectors is readily found in numerous green-beard genes. To our knowledge, however, no model up to date has taken that effect into account. In this article, we investigated the effect of recognition error on the fitness of the green-beard gene. By employing theories of evolutionary games, our mathematical model predicts that the fitness of the green-beard gene is frequency dependent (frequency of the green-beard gene), which was corroborated by experiments performed with yeast FLO1. The experiment also shows that the cells with the green-beard gene (FLO1) are sturdier under severe stress. We conclude that the low recognition error among the cooperators, the higher reward of cooperation, and the higher cost of defection confer an advantage to the green-beard gene under certain conditions, confirmed by numerical simulation as well. Interestingly, we expect that the recognition error to the defectors may promote the cooperator fitness if the cooperator frequency is low and mutual defection is detrimental. Our ternary approach of mathematical analysis, experiments, and simulation lays the groundwork of the standard model for the green-beard gene that can be generalized to other species.

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.