Modelling molecular interactions with game networks' theory

We present a method to model biological systems, the theory of games networks. It extends game theory by multiplying the number of games, and by allowing agents to play several games simultaneously. Some important notions of biological systems, such as locality of interactions and modularity, can then be modelled.     

Modéliser les interactions moléculaires par la théorie des réseaux de jeux

We present a method to model biological systems, the theory of games networks. It extends game theory by multiplying the number of games, and by allowing agents to play several games simultaneously. Some important notions of biological systems, such as locality of interactions and modularity, can then be modelled. To cite this article: M. Manceny et al., C. R. Biologies 329 (2006).     

Asymmetric Evolutionary Games

Evolutionary game theory is a powerful framework for studying evolution in populations of interacting individuals. A common assumption in evolutionary game theory is that interactions are symmetric, which means that the players are distinguished by only their strategies. In nature, however, the microscopic interactions between players are nearly always asymmetric due to environmental effects, differing baseline characteristics, and other possible sources of heterogeneity. To model these phenomena, we introduce into evolutionary game theory two broad classes of asymmetric interactions: ecological and genotypic. Ecological asymmetry results from variation in the environments of the players, while genotypic asymmetry is a consequence of the players having differing baseline genotypes. We develop a theory of these forms of asymmetry for games in structured populations and use the classical social dilemmas, the Prisoner’s Dilemma and the Snowdrift Game, for illustrations. Interestingly, asymmetric games reveal essential differences between models of genetic evolution based on reproduction and models of cultural evolution based on imitation that are not apparent in symmetric games.     

Interaction rates,vital rates,background fitness and replicator dynamics: how to embed evolutionary game structure into realistic population dynamics

In this paper we are concerned with how aggregated outcomes of individual behaviours, during interactions with other individuals (games) or with environmental factors, determine the vital rates constituting the growth rate of the population. This approach needs additional elements, namely the rates of event occurrence (interaction rates). Interaction rates describe the distribution of the interaction events in time, which seriously affects the population dynamics, as is shown in this paper. This leads to the model of a population of individuals playing different games, where focal game affected by the considered trait can be extracted from the general model, and the impact on the dynamics of other events (which is not neutral) can be described by an average background fertility and mortality. This leads to a distinction between two types of background fitness, strategically neutral elements of the focal games (correlated with the focal game events) and the aggregated outcomes of other interactions (independent of the focal game). The new approach is useful for clarification of the biological meaning of concepts such as weak selection. Results are illustrated by a Hawk–Dove example.     

An analysis of network reciprocity in Prisoner's Dilemma games using Full Factorial Designs of Experiment

Despite hundreds of studies on the Prisoner's Dilemma (PD) game, understanding about network reciprocity remains a unsolved puzzle. Thus, we performed a series of Full Factorial Design of Experiments (FFDOE) to evaluate what dominates emerging cooperation in the PD game on various networks. The results qualitatively reveal the influence of each factor and show that some combinations of factors have complicated interactions. Remarkably, the choice of strategy update rule or update dynamics is much more important than the type of network imposed or, at least, the factorial effect of the average degree of the network reported by Nowak (Science 314, 5805, 1560-1563, 2006) and Ohtsuki et al. (Nature 441, 502-505, 2006). Furthermore, the decision of which PD game type to investigate (whether all PD games, PD-Chicken boundary games or Donor & Recipient games) is important for discussing network reciprocity.     

Access Point Selection Game with Mobile Users Using Correlated Equilibrium

One of the most important issues in wireless local area network (WLAN) systems with multiple access points (APs) is the AP selection problem. Game theory is a mathematical tool used to analyze the interactions in multiplayer systems and has been applied to various problems in wireless networks. Correlated equilibrium (CE) is one of the powerful game theory solution concepts, which is more general than the Nash equilibrium for analyzing the interactions in multiplayer mixed strategy games. A game-theoretic formulation of the AP selection problem with mobile users is presented using a novel scheme based on a regret-based learning procedure. Through convergence analysis, we show that the joint actions based on the proposed algorithm achieve CE. Simulation results illustrate that the proposed algorithm is effective in a realistic WLAN environment with user mobility and achieves maximum system throughput based on the game-theoretic formulation.     

Unpredictability induced by unfocused games in evolutionary game dynamics

Evolutionary game theory is a basis of replicator systems and has applications ranging from animal behavior and human language to ecosystems and other hierarchical network systems. Most studies in evolutionary game dynamics have focused on a single game, but, in many situations, we see that many games are played simultaneously. We construct a replicator equation with plural games by assuming that a reward of a player is a simple summation of the reward of each game. Even if the numbers of the strategies of the games are different, its dynamics can be described in one replicator equation. We here show that when players play several games at the same time, the fate of a single game cannot be determined without knowing the structures of the whole other games. The most absorbing fact is that even if a single game has a ESS (evolutionary stable strategy), the relative frequencies of strategies in the game does not always converge to the ESS point when other games are played simultaneously.     

Models of cooperation based on the Prisoner's Dilemma and the Snowdrift game

Understanding the mechanisms that can lead to the evolution of cooperation through natural selection is a core problem in biology. Among the various attempts at constructing a theory of cooperation, game theory has played a central role. Here, we review models of cooperation that are based on two simple games: the Prisoner's Dilemma, and the Snowdrift game. Both games are two‐person games with two strategies, to cooperate and to defect, and both games are social dilemmas. In social dilemmas, cooperation is prone to exploitation by defectors, and the average payoff in populations at evolutionary equilibrium is lower than it would be in populations consisting of only cooperators. The difference between the games is that cooperation is not maintained in the Prisoner's Dilemma, but persists in the Snowdrift game at an intermediate frequency. As a consequence, insights gained from studying extensions of the two games differ substantially. We review the most salient results obtained from extensions such as iteration, spatial structure, continuously variable cooperative investments, and multi‐person interactions. Bridging the gap between theoretical and empirical research is one of the main challenges for future studies of cooperation, and we conclude by pointing out a number of promising natural systems in which the theory can be tested experimentally.     

Tuning Cell Motility via Cell Tension with a Mechanochemical Cell Migration Model

Cell migration is orchestrated by a complicated mechanochemical system. However, few cell migration models take into account the coupling between the biochemical network and mechanical factors. Here, we construct a mechanochemical cell migration model to study the cell tension effect on cell migration. Our model incorporates the interactions between Rac-GTP, Rac-GDP, F-actin, myosin, and cell tension, and it is very convenient in capturing the change of cell shape by taking the phase field approach. This model captures the characteristic features of cell polarization, cell shape change, and cell migration modes. It shows that cell tension inhibits migration ability monotonically when cells are applied with persistent external stimuli. On the other hand, if random internal noise is significant, the regulation of cell tension exerts a nonmonotonic effect on cell migration. Because the increase of cell tension hinders the formation of multiple protrusions, migration ability could be maximized at intermediate cell tension under random internal noise. These model predictions are consistent with our single-cell experiments and other experimental results.     

On equilibrium properties of evolutionary multi-player games with random payoff matrices

The analysis of equilibrium points in biological dynamical systems has been of great interest in a variety of mathematical approaches to biology, such as population genetics, theoretical ecology or evolutionary game theory. The maximal number of equilibria and their classification based on stability have been the primary subjects of these studies, for example in the context of two-player games with multiple strategies. Herein, we address a different question using evolutionary game theory as a tool. If the payoff matrices are drawn randomly from an arbitrary distribution, what are the probabilities of observing a certain number of (stable) equilibria? We extend the domain of previous results for the two-player framework, which corresponds to a single diploid locus in population genetics, by addressing the full complexity of multi-player games with multiple strategies. In closing, we discuss an application and illustrate how previous results on the number of equilibria, such as the famous Feldman-Karlin conjecture on the maximal number of isolated fixed points in a viability selection model, can be obtained as special cases of our results based on multi-player evolutionary games. We also show how the probability of realizing a certain number of equilibria changes as we increase the number of players and number of strategies.     

Mechano-sensing and cell migration: a 3D model approach

Cell migration is essential for tissue development in different physiological and pathological conditions. It is a complex process orchestrated by chemistry, biological factors, microstructure and surrounding mechanical properties. Focusing on the mechanical interactions, cells do not only exert forces on the matrix that surrounds them, but they also sense and react to mechanical cues in a process called mechano-sensing. Here, we hypothesize the involvement of mechano-sensing in the regulation of directional cell migration through a three-dimensional (3D) matrix. For this purpose, we develop a 3D numerical model of individual cell migration, which incorporates the mechano-sensing process of the cell as the main mechanism regulating its movement. Consistent with this hypothesis, we found that factors, such as substrate stiffness, boundary conditions and external forces, regulate specific and distinct cell movements.     

Demographic and Social Predictors of Intimate Partner Violence in Colombia

Intimate partner violence (IPV) is a major health and human rights problem globally. However, empirical findings on the predictors of IPV cross-culturally are highly inconsistent, and the theory of IPV is underdeveloped. We propose a new analytical framework based on cooperative game theory in which IPV is a function of the power relations of the dyadic relationship, not simply the actors involved. Using data from the 2005 Colombian Demographic and Health Survey, we test the hypothesis that IPV is predicted by large asymmetries in dyadic power using a hierarchical generalized linear model. Results suggest that education, urban residence, age at sexual debut, whether the woman has other sexual partners, and the age difference between spouses have strong effects on the log-odds of a woman experiencing IPV. Cooperative game theory and social network analysis offer a general approach to the problem of intimate partner interactions which can be applied broadly cross-culturally.     

Exploring the effects of working for endowments on behaviour in standard economic games

In recent years, significant advances have been made in understanding the adaptive (ultimate) and mechanistic (proximate) explanations for the evolution and maintenance of cooperation. Studies of cooperative behaviour in humans invariably use economic games. These games have provided important insights into the mechanisms that maintain economic and social cooperation in our species. However, they usually rely on the division of monetary tokens which are given to participants by the investigator. The extent to which behaviour in such games may reflect behaviour in the real world of biological markets--where money must be earned and behavioural strategies incur real costs and benefits--is unclear. To provide new data on the potential scale of this problem, we investigated whether people behaved differently in two standard economic games (public goods game and dictator game) when they had to earn their monetary endowments through the completion of dull or physically demanding tasks, as compared with simply being given the endowment. The requirement for endowments to be 'earned' through labour did not affect behaviour in the dictator game. However, the requirement to complete a dull task reduced cooperation in the public goods game among the subset of participants who were not familiar with game theory. There has been some effort to test whether the conclusions drawn from standard, token-based cooperation games adequately reflect cooperative behaviour 'in the wild.' However, given the almost total reliance on such games to study cooperation, more exploration of this issue would be welcome. Our data are not unduly worrying, but they do suggest that further exploration is needed if we are to make general inferences about human behaviour from the results of structured economic games.     

Biodiversity gap analysis of the protected area system in poorly-documented Chad

Chad is amongst the richest countries in terms of biodiversity in Sahelo-Sudanian Africa with some of the last remaining populations of large mammals that once roamed West-Central Africa. Its protected area (PA) system, made up of three national parks (NP) and seven faunal reserves (FR) and introduced 40 years ago to focus on the protection of large game, has never been reviewed in terms of biodiversity coverage. This study (i) assesses whether the PA network captures Chad's current biodiversity (focusing on ecoregions and threatened mammal species), (ii) identifies gaps in the PA system and (iii) proposes recommendations to improve the representativeness of the PA system, in a country characterised by the lack of biological data. Of the seven ecoregions in Chad, three are not covered by PAs and two are represented only once and have less than 10% of their area included in the PA network. Of the 31 large mammal species used in the analysis, five occur only once in the network and five species are not represented. Analysis of the persistence of species shows that, of the nine historical PAs, all have lost at least one (and up to six) species of large mammals. The Ouadi Rimé-Ouadi Achim FR was found to have the highest irreplaceability index, with the Bahr Salamat FR and Zakouma NP second and third respectively. Zakouma NP has the highest number of large mammal populations of an internationally important size. Threatened large mammals, many depending on large-scale migration, and (migratory) waterbird populations highlight the lack of wetlands in the formal PA system. We recommend a more effective protection of these wetlands, an extension of the PA system into ecoregions not covered by current PAs and provide details on the realignment of several of the PAs that have been encroached upon and are no longer viable.     

Bipartite graphs as models of population structures in evolutionary multiplayer games

By combining evolutionary game theory and graph theory, "games on graphs" study the evolutionary dynamics of frequency-dependent selection in population structures modeled as geographical or social networks. Networks are usually represented by means of unipartite graphs, and social interactions by two-person games such as the famous prisoner's dilemma. Unipartite graphs have also been used for modeling interactions going beyond pairwise interactions. In this paper, we argue that bipartite graphs are a better alternative to unipartite graphs for describing population structures in evolutionary multiplayer games. To illustrate this point, we make use of bipartite graphs to investigate, by means of computer simulations, the evolution of cooperation under the conventional and the distributed N-person prisoner's dilemma. We show that several implicit assumptions arising from the standard approach based on unipartite graphs (such as the definition of replacement neighborhoods, the intertwining of individual and group diversity, and the large overlap of interaction neighborhoods) can have a large impact on the resulting evolutionary dynamics. Our work provides a clear example of the importance of construction procedures in games on graphs, of the suitability of bigraphs and hypergraphs for computational modeling, and of the importance of concepts from social network analysis such as centrality, centralization and bipartite clustering for the understanding of dynamical processes occurring on networked population structures.     

Can mixed strategies be stable in asymmetric games?

Selten (1980, J. theor. Biol. 84, 93(N)/01) has shown that mixed strategies cannot be evolutionarily stable in asymmetric games. Because every interaction features some asymmetry, this result apparently precludes mixed strategies in an evolutionary setting. In Maynard Smith's Hawk-Dove game (1982, Evolution and the theory of games (UP-Cambridge), for example, Selten's result restricts attention to pure-strategy evolutionarily stable outcomes in which the animals use the ability to condition their actions on asymmetries to coordinate, with one playing Hawk and one playing Dove, and with conflicts in which both animals play Hawk never arising. This result contrasts with the intuition that the mixed equilibrium of the Hawk-Dove game captures important aspects of many animal interactions, including the possibility of conflict. In this paper, we follow Eshel and Sansone (1995, J. theor. Biol. 177, 341-356) in enriching Selten's model to incorporate an important aspect of animal interactions, namely that payoffs and asymmetries may both be imperfectly observed. In the richer model, we find conditions under which effectively mixed strategies are stable in asymmetric games, as well as conditions under which they are not stable. Behavior will be conditioned on asymmetries, leading to pure-strategy equilibria in which conflict is avoided, when there are relatively large, observable asymmetries and small observable variations in payoffs. Under opposite conditions, evolutionarily stable equilibria will appear that are effectively mixed, including the potential for conflict.     

On the mechanochemical theory of biological pattern formation with application to vasculogenesis

We first describe the Murray-Oster mechanical theory of pattern formation, the biological basis of which is experimentally well documented. The model quantifies the interaction of cells and the extracellular matrix via the cell-generated forces. The model framework is described in quantitative detail. Vascular endothelial cells, when cultured on gelled basement membrane matrix, rapidly aggregate into clusters while deforming the matrix into a network of cord-like structures tessellating the planar culture. We apply the mechanical theory of pattern formation to this culture system and show that neither strain-biased anisotropic cell traction nor cell migration are necessary for pattern formation: isotropic, strain-stimulated cell traction is sufficient to form the observed patterns. Predictions from the model were confirmed experimentally.     

Peptide YY and neuropeptide Y induce villin expression, reduce adhesion, and enhance migration in small intestinal cells through the regulation of CD63, matrix metalloproteinase-3, and Cdc42 activity

Peptide YY (PYY) and neuropeptide Y (NPY) are regulatory peptides synthesized in the intestine and brain, respectively, that modify physiological functions affecting nutrient assimilation and feeding behavior. Because PYY and NPY also alter the expression of intestine-specific differentiation marker proteins and the tetraspanin CD63, which is involved in cell adhesion, we investigated whether intestinal cell differentiation could be linked to mucosal cell adhesion and migration through these peptides. PYY and NPY significantly decreased cell adhesion and increased cell migration in a dose-dependent manner prior to cell confluency in our model system, non-tumorigenic small intestinal hBRIE 380i cells. Both peptides reduced CD63 expression and CD63-dependent cell adhesion. CD63 overexpression increased and antisense CD63 cDNA decreased intestinal cell adhesion. In parallel, both PYY and NPY increased expression of matrix metalloproteinase-3 (MMP-3) to a level sufficient to induce cell migration by activating the Rho GTPase Cdc42. The effects of both peptides on cell migration were blocked in cells constitutively overexpressing dominant-negative Cdc42. PYY and NPY also significantly induced the expression of the differentiation marker villin, which could be eliminated by an MMP inhibitor at a concentration that inhibits cell migration. Increased MMP-3 activity, which enhanced cell migration, also induced villin mRNA levels. Therefore, these data indicate that the alteration of adhesion and migration by PYY and NPY occurs in part by synchronous modulation of three proteins that are involved in extracellular matrix-basolateral membrane interactions, CD63, MMP-3 and Cdc42, and that PYY/NPY regulation of expression of mucosal proteins such as villin is linked to the process of cell migration and adhesion.