Predator-Prey Coevolution as an Evolutionary Game

How Should Cancer Models Be Constructed?

Cancer Control ◽

10.1177/1073274820962008 ◽

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.

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Organization of Predator-Prey Communities as an Evolutionary Game

Evolution ◽

10.2307/2409936 ◽

1992 ◽

Vol 46 (5) ◽

pp. 1269 ◽

Cited By ~ 53

Author(s):

Joel S. Brown ◽

Thomas L. Vincent

Keyword(s):

Evolutionary Game ◽

Predator Prey

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ORGANIZATION OF PREDATOR-PREY COMMUNITIES AS AN EVOLUTIONARY GAME

Evolution ◽

10.1111/j.1558-5646.1992.tb01123.x ◽

1992 ◽

Vol 46 (5) ◽

pp. 1269-1283 ◽

Cited By ~ 78

Author(s):

Joel S. Brown ◽

Thomas L. Vincent

Keyword(s):

Evolutionary Game ◽

Predator Prey

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Evolutionary Game Theory: Darwinian Dynamics and the G Function Approach

Games ◽

10.3390/g12040072 ◽

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.

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The predator-dependent replicator dynamics

Journal of Physics A Mathematical and Theoretical ◽

10.1088/1751-8121/ac40e4 ◽

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.

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Non-Equilibrial Dynamics in Under-Saturated Communities

10.1101/834838 ◽

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.

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