Intransitivity and coexistence in four species cyclic games

Intransitivity is a property of connected, oriented graphs representing species interactions that may drive their coexistence even in the presence of competition, the standard example being the three species Rock-Paper-Scissors game. We consider here a generalization with four species, the minimum number of species allowing other interactions beyond the single loop (one predator, one prey). We show that, contrary to the mean field prediction, on a square lattice the model presents a transition, as the parameter setting the rate at which one species invades another changes, from a coexistence to a state in which one species gets extinct. Such a dependence on the invasion rates shows that the interaction graph structure alone is not enough to predict the outcome of such models. In addition, different invasion rates permit to tune the level of transitiveness, indicating that for the coexistence of all species to persist, there must be a minimum amount of intransitivity.Comment: Final, published versio

Evolutionary games on graphs

Game theory is one of the key paradigms behind many scientific disciplines from biology to behavioral sciences to economics. In its evolutionary form and especially when the interacting agents are linked in a specific social network the underlying solution concepts and methods are very similar to those applied in non-equilibrium statistical physics. This review gives a tutorial-type overview of the field for physicists. The first three sections introduce the necessary background in classical and evolutionary game theory from the basic definitions to the most important results. The fourth section surveys the topological complications implied by non-mean-field-type social network structures in general. The last three sections discuss in detail the dynamic behavior of three prominent classes of models: the Prisoner's Dilemma, the Rock-Scissors-Paper game, and Competing Associations. The major theme of the review is in what sense and how the graph structure of interactions can modify and enrich the picture of long term behavioral patterns emerging in evolutionary games.Comment: Review, final version, 133 pages, 65 figure

Generalized Intransitive Dice: Mimicking an Arbitrary Tournament

A generalized $N$-sided die is a random variable $D$ on a sample space of $N$ equally likely outcomes taking values in the set of positive integers. We say of independent $N$ sided dice $D_i, D_j$ that $D_i$ beats $D_j$, written $D_i \to D_j$, if $Prob(D_i > D_j) > \frac{1}{2}$. Examples are known of intransitive $6$-sided dice, i.e. $D_1 \to D_2 \to D_3$ but $D_3 \to D_1$. A tournament of size $n$ is a choice of direction $i \to j$ for each edge of the complete graph on $n$ vertices. We show that if $R$ is tournament on the set $\{ 1, \dots, n \}$, then for sufficiently large $N$ there exist sets of independent $N$-sided dice $\{ D_1, \dots, D_n \}$ such that $D_i \to D_j$ if and only if $i \to j$ in $R$

Competition, Corporatization and Culture: A Contrast of Person-to-Person and Online Video Gaming Communities In America

My Senior Project is an exploration of contemporary competitive Video Gaming culture in the United States. Through a comparison of Person-to-Person gaming communities and Online gaming communities, I aim to elucidate the social nuances in these gaming communities and how they have created such vastly contrasting cultures

The BG News April 21, 2006

The BGSU campus student newspaper April 21, 2006. Volume 96 - Issue 141https://scholarworks.bgsu.edu/bg-news/8598/thumbnail.jp

Lattice-based versus lattice-free individual-based models : impact on coexistence in competitive communities

Individual-based modelling is an increasingly popular framework for modelling biological systems. Many of these models represent space as a lattice, thus imposing unrealistic limitations on the movement of the modelled individuals. We adapt an existing model of three competing species by using a lattice-free approach, thereby improving the realism of the spatial dynamics. We retrieve the same qualitative dynamics as the lattice-based approach. However, by facilitating a higher spatial heterogeneity and allowing for small spatial refuges to form and persist, the maintenance of coexistence is promoted, in correspondence with experimental results. We also implement a directed movement mechanism allowing individuals of different species to pursue or flee from each other. Simulations show that the effects on coexistence depend on the level of aggregation in the community: a high level of aggregation is advantageous for maintaining coexistence, whereas a low level of aggregation is disadvantageous. This agrees with experimental results, where pursuing and escaping behaviour has been observed to be advantageous only in certain circumstances

Moving forward in circles: challenges and opportunities in modelling population cycles

Population cycling is a widespread phenomenon, observed across a multitude of taxa in both laboratory and natural conditions. Historically, the theory associated with population cycles was tightly linked to pairwise consumer–resource interactions and studied via deterministic models, but current empirical and theoretical research reveals a much richer basis for ecological cycles. Stochasticity and seasonality can modulate or create cyclic behaviour in non-intuitive ways, the high-dimensionality in ecological systems can profoundly influence cycling, and so can demographic structure and eco-evolutionary dynamics. An inclusive theory for population cycles, ranging from ecosystem-level to demographic modelling, grounded in observational or experimental data, is therefore necessary to better understand observed cyclical patterns. In turn, by gaining better insight into the drivers of population cycles, we can begin to understand the causes of cycle gain and loss, how biodiversity interacts with population cycling, and how to effectively manage wildly fluctuating populations, all of which are growing domains of ecological research