Stackelberg evolutionary game theory: how to manage evolving systems

Stackelberg evolutionary game (SEG) theory combines classical and evolutionary game theory to frame interactions between a rational leader and evolving followers. In some of these interactions, the leader wants to preserve the evolving system (e.g. fisheries management), while in others, they try to drive the system to extinction (e.g. pest...

Game Theory for Managing Evolving Systems: Challenges and Opportunities of Including Vector-Valued Strategies and Life-History Traits

Nature exhibits rapid evolution in response to human activities. When using natural resources for their own profit, humans should account for such responses. Stackelberg evolutionary games (SEG) offer a method for modeling interactions between a rational leader (humans) and evolutionary followers (nature). The followers evolve according to...

Coordination games in cancer

We propose a model of cancer initiation and progression where tumor growth is modulated by an evolutionary coordination game. Evolutionary games of cancer are widely used to model frequency-dependent cell interactions with the most studied games being the Prisoner's Dilemma and public goods games. Coordination games, by their more obscure and...

Evolutionary Dynamics of Treatment-Induced Resistance in Cancer Informs Understanding of Rapid Evolution in Natural Systems

Rapid evolution is ubiquitous in nature. We briefly review some of this quite broadly, particularly in the context of response to anthropogenic disturbances. Nowhere is this more evident, replicated and accessible to study than in cancer. Curiously cancer has been late - relative to fisheries, antibiotic resistance, pest management and...

The Contribution of Evolutionary Game Theory to Understanding and Treating Cancer

Evolutionary game theory mathematically conceptualizes and analyzes biological interactions where one’s fitness not only depends on one’s own traits, but also on the traits of others. Typically, the individuals are not overtly rational and do not select, but rather inherit their traits. Cancer can be framed as such an evolutionary game, as it...

Fisheries management as a Stackelberg Evolutionary Game: Finding an evolutionarily enlightened strategy

Fish populations subject to heavy exploitation are expected to evolve over time smaller average body sizes. We introduce Stackelberg evolutionary game theory to show how fisheries management should be adjusted to mitigate the potential negative effects of such evolutionary changes. We present the game of a fisheries manager versus a fish...

Identifying key questions in the ecology and evolution of cancer

The application of evolutionary and ecological principles to cancer prevention and treatment, as well as recognizing cancer as a selection force in nature, has gained impetus over the last 50 years. Following the initial theoretical approaches that combined knowledge from interdisciplinary fields, it became clear that using the eco...

Optimal control to reach eco-evolutionary stability in metastatic castrate-resistant prostate cancer

In the absence of curative therapies, treatment of metastatic castrate-resistant prostate cancer (mCRPC) using currently available drugs can be improved by integrating evolutionary principles that govern proliferation of resistant subpopulations into current treatment protocols. Here we develop what is coined as an ‘evolutionary stable...

Including Blood Vasculature into a Game-Theoretic Model of Cancer Dynamics

For cancer, we develop a 2-D agent-based continuous-space game-theoretical model that considers cancer cells’ proximity to a blood vessel. Based on castrate resistant metastatic prostate cancer (mCRPC), the model considers the density and frequency (eco-evolutionary) dynamics of three cancer cell types: those that require exogenous...