On Playing with Emotion: A Spatial Evolutionary Variation of the Ultimatum Game.

The Ultimatum Game is a simplistic representation of bargaining processes occurring in social networks. In the standard version of this game, the first player, called the proposer, makes an offer on how to split a certain amount of money. If the second player, called the responder, accepts the offer, the money is divided according to the proposal; if the responder declines the offer, both players receive no money. In this article, an agent-based model is employed to evaluate the performance of five distinct strategies of playing a modified version of this game. A strategy corresponds to instructions on how a player must act as the proposer and as the responder. Here, the strategies are inspired by the following basic emotions: anger, fear, joy, sadness, and surprise. Thus, in the game, each interacting agent is a player endowed with one of these five basic emotions. In the modified version explored in this article, the spatial dimension is taken into account and the survival of the players depends on successful negotiations. Numerical simulations are performed in order to determine which basic emotion dominates the population in terms of prevalence and accumulated money. Information entropy is also computed to assess the time evolution of population diversity and money distribution. From the obtained results, a conjecture on the emergence of the sense of fairness is formulated.

Containing misinformation: Modeling spatial games of fake news.

The spread of fake news on social media is a pressing issue. Here, we develop a mathematical model on social networks in which news sharing is modeled as a coordination game. We use this model to study the effect of adding designated individuals who sanction fake news sharers (representing, for example, correction of false claims or public shaming of those who share such claims). By simulating our model on synthetic square lattices and small-world networks, we demonstrate that social network structure allows fake news spreaders to form echo chambers and more than doubles fake news' resistance to distributed sanctioning efforts. We confirm our results are robust to a wide range of coordination and sanctioning payoff parameters as well as initial conditions. Using a Twitter network dataset, we show that sanctioners can help contain fake news when placed strategically. Furthermore, we analytically determine the conditions required for peer sanctioning to be effective, including prevalence and enforcement levels. Our findings have implications for developing mitigation strategies to control misinformation and preserve the integrity of public discourse.

How Lévy Flights Triggered by the Presence of Defectors Affect Evolution of Cooperation in Spatial Games.

Cooperation among individuals has been key to sustaining societies. However, natural selection favors defection over cooperation. Cooperation can be favored when the mobility of individuals allows cooperators to form a cluster (or group). Mobility patterns of animals sometimes follow a Lévy flight. A Lévy flight is a kind of random walk but it is composed of many small movements with a few big movements. The role of Lévy flights for cooperation has been studied by Antonioni and Tomassini, who showed that Lévy flights promoted cooperation combined with conditional movements triggered by neighboring defectors. However, the optimal condition for neighboring defectors and how the condition changes with the intensity of Lévy flights are still unclear. Here, we developed an agent-based model in a square lattice where agents perform Lévy flights depending on the fraction of neighboring defectors. We systematically studied the relationships among three factors for cooperation: sensitivity to defectors, the intensity of Lévy flights, and population density. Results of evolutionary simulations showed that moderate sensitivity most promoted cooperation. Then, we found that the shortest movements were best for cooperation when the sensitivity to defectors was high. In contrast, when the sensitivity was low, longer movements were best for cooperation. Thus, Lévy flights, the balance between short and long jumps, promoted cooperation in any sensitivity, which was confirmed by evolutionary simulations. Finally, as the population density became larger, higher sensitivity was more beneficial for cooperation to evolve. Our study highlights that Lévy flights are an optimal searching strategy not only for foraging but also for constructing cooperative relationships with others.

Spatial vs. non-spatial eco-evolutionary dynamics in a tumor growth model.

Metastatic prostate cancer is initially treated with androgen deprivation therapy (ADT). However, resistance typically develops in about 1 year - a clinical condition termed metastatic castrate-resistant prostate cancer (mCRPC). We develop and investigate a spatial game (agent based continuous space) of mCRPC that considers three distinct cancer cell types: (1) those dependent on exogenous testosterone (T+), (2) those with increased CYP17A expression that produce testosterone and provide it to the environment as a public good (TP), and (3) those independent of testosterone (T-). The interactions within and between cancer cell types can be represented by a 3 × 3 matrix. Based on the known biology of this cancer there are 22 potential matrices that give roughly three major outcomes depending upon the absence (good prognosis), near absence or high frequency (poor prognosis) of T- cells at the evolutionarily stable strategy (ESS). When just two cell types coexist the spatial game faithfully reproduces the ESS of the corresponding matrix game. With three cell types divergences occur, in some cases just two strategies coexist in the spatial game even as a non-spatial matrix game supports all three. Discrepancies between the spatial game and non-spatial ESS happen because different cell types become more or less clumped in the spatial game - leading to non-random assortative interactions between cell types. Three key spatial scales influence the distribution and abundance of cell types in the spatial game: i. Increasing the radius at which cells interact with each other can lead to higher clumping of each type, ii. Increasing the radius at which cells experience limits to population growth can cause densely packed tumor clusters in space, iii. Increasing the dispersal radius of daughter cells promotes increased mixing of cell types. To our knowledge the effects of these spatial scales on eco-evolutionary dynamics have not been explored in cancer models. The fact that cancer interactions are spatially explicit and that our spatial game of mCRPC provides in general different outcomes than the non-spatial game might suggest that non-spatial models are insufficient for capturing key elements of tumorigenesis.

Spatio-temporal dynamics in the response of woodland caribou and moose to the passage of grey wolf.

Predators impact prey populations not only by consuming individuals, but also by altering their behaviours. These nonlethal effects can influence food web properties as much as lethal effects. The mechanisms of nonlethal effects include chronic and temporary anti-predator behaviours, the nature of which depends on the spatial dynamics of predators and the range over which prey perceive risk. The relation between chronic and ephemeral responses to risk determines predator-prey interactions, with consequences that can ripple across the food web. Nonetheless, few studies have quantified the spatio-temporal scales over which prey respond to predation threat, and how this response varies with habitat features. We evaluated the reaction of radio-collared caribou and moose to the passage of radio-collared wolves, by considering changes in movement characteristics during winter and summer. We used an optimization algorithm to identify the rate at which the impact of prior passage of wolves decreases over time and with the predator's distance. The spatial and temporal scales of anti-predator responses varied with prey species and season. Caribou and moose displayed four types of behaviour following the passage of wolves: lack of response, increased selection of safe land cover types, decreased selection of risky cover types and increased selection of food-rich forest stands. For example, moose increased their avoidance of open conifer stands with lichen in summer, which are selected by wolves in this season. Also in winter, caribou increased their selection of conifer stands with lichen for nearly 10 days following a wolf's passage. This stronger selection for food-rich patches could indicate that the recent passage of wolves informs caribou on the current predator distribution and reveals the rate at which this information become less reliable over time. Caribou and moose used anti-predator responses that combine both long- and short-term behavioural adjustments. The spatial game between wolves and their prey involves complex and nonlinear mechanisms that vary between species and seasons. A comprehensive assessment of risk effects on ecosystem dynamics thus requires the characterization of chronic and temporary anti-predator behaviours.