scholarly journals Non-Equilibrial Dynamics in Under-Saturated Communities

2019 ◽  
Author(s):  
Abdel Halloway ◽  
Kateřina Staňková ◽  
Joel S. Brown
Keyword(s):  
Evolutionary Dynamics ◽  
Evolutionary Game ◽  
Evolutionary Games ◽  
Competition Model ◽  
Degree Of Saturation ◽  
Predator Prey ◽  
Evolutionary Response ◽  
Evolutionary Suicide ◽  
Predator Prey Models ◽  
Stability Concepts

A.AbstractThe concept of the evolutionary stable strategy (ESS) has been fundamental to the development of evolutionary game theory. It represents an equilibrial evolutionary state in which no rare invader can grow in population size. With additional work, the ESS concept has been formalized and united with other stability concepts such as convergent stability, neighborhood invasion stability, and mutual invisibility. Other work on evolutionary models, however, shows the possibility of unstable and/or non-equilibrial dynamics such as limit cycles and evolutionary suicide. Such “pathologies” remain outside of a well-defined context, especially the currently defined stability concepts of evolutionary games. Ripa et al. (2009) offer a possible reconciliation between work on non-equilibrial dynamics and the ESS concept. They noticed that the systems they analyzed show non-equilibrial dynamics when under-saturated and “far” from the ESS and that getting “closer” to the ESS through the addition of more species stabilized their systems. To that end, we analyzed three models of evolution, two predator-prey models and one competition model of evolutionary suicide, to see how the degree of saturation affects the stability of the system. In the predator-prey models, stability is linked to the degree of saturation. Specifically, a fully saturated community will only show stable dynamics, and unstable dynamics occur only when the community is under-saturated. With the competition model, we demonstrate it to be permanently under-saturated, likely showing such extreme dynamics for this reason. Though not a general proof, our analysis of the models provide evidence of the link between community saturation and evolutionary dynamics. Our results offer a possible placement of these evolutionary “pathologies” into a wider framework. In addition, the results concur with previous results showing greater evolutionary response to less biodiversity and clarifies the effect of extrinsic vs. intrinsic non-equilibrial evolutionary dynamics on a community.

scholarly journals How Should Cancer Models Be Constructed?

2020 ◽  
Vol 27 (1) ◽  
pp. 107327482096200
Author(s):  
Robert A. Beckman ◽  
Irina Kareva ◽  
Frederick R. Adler
Keyword(s):  
Complex Dynamics ◽  
Full Range ◽  
Evolutionary Game ◽  
Treatment Strategies ◽  
Predator Prey ◽  
Cancer Models ◽  
The Face ◽  
Predator Prey Models ◽  
The Right ◽  
Parameter Values

Choosing and optimizing treatment strategies for cancer requires capturing its complex dynamics sufficiently well for understanding but without being overwhelmed. Mathematical models are essential to achieve this understanding, and we discuss the challenge of choosing the right level of complexity to address the full range of tumor complexity from growth, the generation of tumor heterogeneity, and interactions within tumors and with treatments and the tumor microenvironment. We discuss the differences between conceptual and descriptive models, and compare the use of predator-prey models, evolutionary game theory, and dynamic precision medicine approaches in the face of uncertainty about mechanisms and parameter values. Although there is of course no one-size-fits-all approach, we conclude that broad and flexible thinking about cancer, based on combined modeling approaches, will play a key role in finding creative and improved treatments.

MORE SPATIAL GAMES

1994 ◽  
Vol 04 (01) ◽  
pp. 33-56 ◽  
Author(s):  
MARTIN A. NOWAK ◽  
SEBASTIAN BONHOEFFER ◽  
ROBERT M. MAY
Keyword(s):  
Prisoner's Dilemma ◽  
Evolutionary Dynamics ◽  
Evolutionary Game ◽  
Prisoner’S Dilemma ◽  
Evolutionary Games ◽  
Reproductive Rate ◽  
Spatial Effects ◽  
Random Drift ◽  
Low Frequencies ◽  
Spatial Games

We extend our exploration of the dynamics of spatial evolutionary games [Nowak & May 1992, 1993] in three distinct but related ways. We analyse, first, deterministic versus stochastic rules; second, discrete versus continuous time (see Hubermann & Glance [1993]); and, third, different geometries of interaction in regular and random spatial arrays. We show that spatial effects can change some of the intuitive concepts in evolutionary game theory: (i) equilibria among strategies are no longer necessarily characterised by equal average payoffs; (ii) the strategy with the higher average payoff can steadily converge towards extinction; (iii) strategies can become extinct even though their basic reproductive rate (at very low frequencies) is larger than one. The equilibrium properties of spatial games are instead determined by “local relative payoffs.” We characterise the conditions for coexistence between cooperators and defectors in the spatial prisoner’s dilemma game. We find that cooperation can be maintained if the transition rules give more weight to the most successful neighbours, or if there is a certain probability that cells may remain unoccupied in the next generations when they are surrounded by players with low payoffs. In this second case the cooperators can survive despite a very large payoff advantage to defectors. We also compute average extinction times for random drift in neutral spatial models. Finally we briefly describe the spatial dynamics of an interaction among three species which dominate each other in a cyclic fashion. The emphasis of this paper is presenting a variety of ideas and possibilities for further research in the evolutionary dynamics of spatial games. The overall conclusion is that interactions with local neighbours in 2- or 3-dimensional spatial arrays can promote coexistence of different strategies (such as cooperators and defectors in the Prisoner’s Dilemma), in situations where one strategy would exclude all others if the interactions occurred randomly and homogeneously.

scholarly journals Evolutionary dynamics of group interactions on structured populations: a review

2013 ◽  
Vol 10 (80) ◽  
pp. 20120997 ◽  
Author(s):  
Matjaž Perc ◽  
Jesús Gómez-Gardeñes ◽  
Attila Szolnoki ◽  
Luis M. Floría ◽  
Yamir Moreno
Keyword(s):  
Statistical Physics ◽  
Evolutionary Dynamics ◽  
Evolutionary Game ◽  
Evolutionary Games ◽  
Structured Populations ◽  
Public Goods Game ◽  
Group Interactions ◽  
The Public ◽  
Living Organisms ◽  
Class Representative

Interactions among living organisms, from bacteria colonies to human societies, are inherently more complex than interactions among particles and non-living matter. Group interactions are a particularly important and widespread class, representative of which is the public goods game. In addition, methods of statistical physics have proved valuable for studying pattern formation, equilibrium selection and self-organization in evolutionary games. Here, we review recent advances in the study of evolutionary dynamics of group interactions on top of structured populations, including lattices, complex networks and coevolutionary models. We also compare these results with those obtained on well-mixed populations. The review particularly highlights that the study of the dynamics of group interactions, like several other important equilibrium and non-equilibrium dynamical processes in biological, economical and social sciences, benefits from the synergy between statistical physics, network science and evolutionary game theory.

scholarly journals Evolutionary Game Theory: Darwinian Dynamics and the G Function Approach

Games ◽  
2021 ◽  
Vol 12 (4) ◽  
pp. 72
Author(s):  
Anuraag Bukkuri ◽  
Joel S. Brown
Keyword(s):  
Game Theory ◽  
Drug Resistance ◽  
Population Dynamics ◽  
Evolutionary Game Theory ◽  
Evolutionary Dynamics ◽  
Evolutionary Game ◽  
Function Model ◽  
Predator Prey ◽  
Evolutionary Stable Strategies ◽  
Over Time

Classical evolutionary game theory allows one to analyze the population dynamics of interacting individuals playing different strategies (broadly defined) in a population. To expand the scope of this framework to allow us to examine the evolution of these individuals’ strategies over time, we present the idea of a fitness-generating (G) function. Under this model, we can simultaneously consider population (ecological) and strategy (evolutionary) dynamics. In this paper, we briefly outline the differences between game theory and classical evolutionary game theory. We then introduce the G function framework, deriving the model from fundamental biological principles. We introduce the concept of a G-function species, explain the process of modeling with G functions, and define the conditions for evolutionary stable strategies (ESS). We conclude by presenting expository examples of G function model construction and simulations in the context of predator–prey dynamics and the evolution of drug resistance in cancer.

scholarly journals Two-population Asymmetric Evolutionary Game Dynamics-based Decision-making Behavior Analysis for A Supply-side Electric Power Bidding Market

2020 ◽  
Vol 194 ◽  
pp. 03009
Author(s):  
Kaiwen Zeng ◽  
Lefeng Cheng ◽  
Jianing Liu ◽  
Haizhu Wang ◽  
Tao Yu
Keyword(s):  
Decision Making ◽  
Electric Power ◽  
Evolutionary Dynamics ◽  
Evolutionary Game ◽  
Evolutionary Games ◽  
Supply Side ◽  
Decision Making Processes ◽  
The Government ◽  
Behavior Characteristics ◽  
Decision Making Behavior

This paper systematically discusses two-population asymmetric evolutionary games (2PAEGs) from the perspective of decision-making behavior characteristics, and applies these game models to a two-population supply-side electric power bidding market. First, a 2PAEG model is established. Then, complete evolutionary equilibrium rules of this model are revealed during decision-making processes. Discussion shows that final evolutionary game equilibria achieved in the 2PAEG model are only determined by some payoff parameters, which are defined as relative net payoff (RNP) parameters in this paper. Finally, a case study of supply-side bidding simulation for two generator populations is conducted, which can effectively verify the universality and effectiveness of the evolutionary dynamics results obtained in the established general 2PAEG model. Moreover, it shows that reasonable policies made by the government can guide more appropriate power bidding for onto-grid electricity.

The predator-dependent replicator dynamics

2021 ◽  
Author(s):  
Ian Magalhaes Braga ◽  
Lucas Wardil
Keyword(s):  
Time Scales ◽  
Evolutionary Dynamics ◽  
Replicator Dynamics ◽  
Capture Rate ◽  
Evolutionary Game ◽  
Ecological Interactions ◽  
Evolutionary Time ◽  
Predator Prey ◽  
Environmental Interactions ◽  
Selection Of

Abstract Ecological interactions are central to understanding evolution. For example, Darwin noticed that the beautiful colours of the male peacock increase the chance of successful mating. However, the colours can be a threat because of the increased probability of being caught by predators. Eco-evolutionary dynamics takes into account environmental interactions to model the process of evolution. The selection of prey types in the presence of predators may be subjected to pressure on both reproduction and survival. Here, we analyze the evolutionary game dynamics of two types of prey in the presence of predators. We call this model \textit{the predator-dependent replicator dynamics}. If the evolutionary time scales are different, the number of predators can be assumed constant, and the traditional replicator dynamics is recovered. However, if the time scales are the same, we end up with sixteen possible dynamics: the combinations of four reproduction’s games with four predation’s games. We analyze the dynamics and calculate conditions for the coexistence of prey and predator. The main result is that predators can change the equilibrium of the traditional replicator dynamics. For example, the presence of predators can induce polymorphism in prey if one type of prey is more attractive than the other, with the prey ending with a lower capture rate in this new equilibrium. Lastly, we provide two illustrations of the dynamics, which can be seen as rapid feedback responses in a predator-prey evolutionary arm’s race.

The global dynamics of stochastic Holling type II predator-prey models with non constant mortality rate

Filomat ◽  
2017 ◽  
Vol 31 (18) ◽  
pp. 5811-5825
Author(s):  
Xinhong Zhang
Keyword(s):  
Mortality Rate ◽  
Stochastic Model ◽  
Sufficient Conditions ◽  
Positive Periodic Solution ◽  
Global Dynamics ◽  
Type Ii ◽  
Predator Prey ◽  
Persistence In The Mean ◽  
The Mean ◽  
Predator Prey Models

In this paper we study the global dynamics of stochastic predator-prey models with non constant mortality rate and Holling type II response. Concretely, we establish sufficient conditions for the extinction and persistence in the mean of autonomous stochastic model and obtain a critical value between them. Then by constructing appropriate Lyapunov functions, we prove that there is a nontrivial positive periodic solution to the non-autonomous stochastic model. Finally, numerical examples are introduced to illustrate the results developed.

Plugging Space into Predator-Prey Models: An Empirical Approach

2006 ◽  
Vol 167 (2) ◽  
pp. 246
Author(s):  
Bergström ◽  
Englund ◽  
Leonardsson
Keyword(s):  
Empirical Approach ◽  
Predator Prey ◽  
Predator Prey Models
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