scholarly journals Extinction rates in tumor public goods games

2017 ◽  
Author(s):  
Philip Gerlee ◽  
Philipp M. Altrock
Keyword(s):  
Population Growth ◽  
Evolutionary Dynamics ◽  
Replicator Dynamics ◽  
Evolutionary Game ◽  
Cell Types ◽  
Relative Fitness ◽  
Replicator Equation ◽  
Cellular Interactions ◽  
Cancer Evolution ◽  
Public Goods Games

AbstractCancer evolution and progression are shaped by cellular interactions and Darwinian selection. Evolutionary game theory incorporates both of these principles, and has been proposed as a framework to understand tumor cell population dynamics. A cornerstone of evolutionary dynamics is the replicator equation, which describes changes in the relative abundance of different cell types, and is able to predict evolutionary equilibria. Typically, the replicator equation focuses on differences in relative fitness. We here show that this framework might not be sufficient under all circumstances, as it neglects important aspects of population growth. Standard replicator dynamics might miss critical differences in the time it takes to reach an equilibrium, as this time also depends on cellular turnover in growing but bounded populations. As the system reaches a stable manifold, the time to reach equilibrium depends on cellular death and birth rates. These rates shape the timescales, in particular in co-evolutionary dynamics of growth factor producers and free-riders. Replicator dynamics might be an appropriate framework only when birth and death rates are of similar magnitude. Otherwise, population growth effects cannot be neglected when predicting the time to reach an equilibrium, and cell type specific rates have to be accounted for explicitly.

scholarly journals Extinction rates in tumour public goods games

2017 ◽  
Vol 14 (134) ◽  
pp. 20170342 ◽  
Author(s):  
Philip Gerlee ◽  
Philipp M. Altrock
Keyword(s):  
Population Growth ◽  
Evolutionary Dynamics ◽  
Replicator Dynamics ◽  
Evolutionary Game ◽  
Cell Types ◽  
Relative Fitness ◽  
Replicator Equation ◽  
Cellular Interactions ◽  
Cancer Evolution ◽  
Public Goods Games

Cancer evolution and progression are shaped by cellular interactions and Darwinian selection. Evolutionary game theory incorporates both of these principles, and has been proposed as a framework to understand tumour cell population dynamics. A cornerstone of evolutionary dynamics is the replicator equation, which describes changes in the relative abundance of different cell types, and is able to predict evolutionary equilibria. Typically, the replicator equation focuses on differences in relative fitness. We here show that this framework might not be sufficient under all circumstances, as it neglects important aspects of population growth. Standard replicator dynamics might miss critical differences in the time it takes to reach an equilibrium, as this time also depends on cellular turnover in growing but bounded populations. As the system reaches a stable manifold, the time to reach equilibrium depends on cellular death and birth rates. These rates shape the time scales, in particular, in coevolutionary dynamics of growth factor producers and free-riders. Replicator dynamics might be an appropriate framework only when birth and death rates are of similar magnitude. Otherwise, population growth effects cannot be neglected when predicting the time to reach an equilibrium, and cell-type-specific rates have to be accounted for explicitly.

scholarly journals Spatial Evolutionary Games of Interaction among Generic Cancer Cells

2003 ◽  
Vol 5 (1) ◽  
pp. 47-58 ◽  
Author(s):  
L. A. Bach ◽  
D. J. T. Sumpter ◽  
J. Alsner ◽  
V. Loeschcke
Keyword(s):  
Evolutionary Dynamics ◽  
Evolutionary Game ◽  
Mean Field ◽  
Cell Types ◽  
Growth Promoter ◽  
Cellular Interactions ◽  
Spatial Effects ◽  
Mean Field Models ◽  
Growth Promoting

Evolutionary game models of cellular interactions have shown that heterogeneity in the cellular genotypic composition is maintained through evolution to stable coexistence of growth-promoting and non-promoting cell types. We generalise these mean-field models and relax the assumption of perfect mixing of cells by instead implementing an individual-based model that includes the stochastic and spatial effects likely to occur in tumours. The scope for coexistence of genotypic strategies changed with the inclusion of explicit space and stochasticity. The spatial models show some interesting deviations from their mean-field counterparts, for example the possibility of altruistic (paracrine) cell strategies to thrive. Such effects can however, be highly sensitive to model implementation and the more realistic models with semi-synchronous and stochastic updating do not show evolution of altruism. We do find some important and consistent differences between the spatial and mean-field models, in particular that the parameter regime for coexistence of growth-promoting and nonpromoting cell types is narrowed. For certain parameters in the model a selective collapse of a generic growth promoter occurs, hence the evolutionary dynamics mimics observablein vivotumour phenomena such as (therapy induced) relapse behaviour. Our modelling approach differs from many of those previously applied in understanding growth of cancerous tumours in that it attempts to account for natural selection at a cellular level. This study thus points a new direction towards more plausible spatial tumour modelling and the understanding of cancerous growth.

scholarly journals Steering eco-evolutionary game dynamics with manifold control

2020 ◽  
Vol 476 (2233) ◽  
pp. 20190643 ◽  
Author(s):  
Xin Wang ◽  
Zhiming Zheng ◽  
Feng Fu
Keyword(s):  
Evolutionary Dynamics ◽  
Replicator Dynamics ◽  
Evolutionary Game ◽  
Feedback Loops ◽  
Mathematical Framework ◽  
Stable Manifolds ◽  
Selection Gradient ◽  
Game Dynamics ◽  
Control Approach ◽  
Attraction Basin

Feedback loops between population dynamics of individuals and their ecological environment are ubiquitously found in nature and have shown profound effects on the resulting eco-evolutionary dynamics. By incorporating linear environmental feedback law into the replicator dynamics of two-player games, recent theoretical studies have shed light on understanding the oscillating dynamics of the social dilemma. However, the detailed effects of more general nonlinear feedback loops in multi-player games, which are more common especially in microbial systems, remain unclear. Here, we focus on ecological public goods games with environmental feedbacks driven by a nonlinear selection gradient. Unlike previous models, multiple segments of stable and unstable equilibrium manifolds can emerge from the population dynamical systems. We find that a larger relative asymmetrical feedback speed for group interactions centred on cooperators not only accelerates the convergence of stable manifolds but also increases the attraction basin of these stable manifolds. Furthermore, our work offers an innovative manifold control approach: by designing appropriate switching control laws, we are able to steer the eco-evolutionary dynamics to any desired population state. Our mathematical framework is an important generalization and complement to coevolutionary game dynamics, and also fills the theoretical gap in guiding the widespread problem of population state control in microbial experiments.

Alternate Models of Replicator Dynamics

2013 ◽  
Author(s):  
Elizabeth N. Wesson ◽  
Richard H. Rand
Keyword(s):  
Evolutionary Dynamics ◽  
Total Population ◽  
Replicator Dynamics ◽  
Standard Form ◽  
Exponential Model ◽  
Payoff Matrix ◽  
Replicator Equation ◽  
Game Theoretic ◽  
Average Fitness ◽  
Strategy I

Models of evolutionary dynamics are often approached via the replicator equation, which in its standard form is given by x.i=xifix-ϕ,i = 1,…, n, where xi is the frequency, or relative abundance, of strategy i, fi is its fitness, and ϕ=∑i=1nxifi is the average fitness. A game-theoretic aspect is introduced to the model via the payoff matrix A, where Ai,j is the expected payoff of i vs. j, by taking fi(x) = (A·x)i. This model is based on the exponential model of population growth, ẋi = xifi, with ϕ introduced in order both to hold the total population constant and to model competition between strategies. We analyze the dynamics of analogous models for the replicator equation of the form x.i=gxifi-ϕ, for selected growth functions g.

scholarly journals Group size effects in social evolution

2018 ◽  
Author(s):  
Jorge Peña ◽  
Georg Nöldeke
Keyword(s):  
Group Size ◽  
Size Effects ◽  
Evolutionary Biology ◽  
Social Evolution ◽  
Evolutionary Dynamics ◽  
Replicator Dynamics ◽  
Basin Of Attraction ◽  
Evolution Of Cooperation ◽  
Positive Effects ◽  
Public Goods Games

AbstractHow the size of social groups affects the evolution of cooperative behaviors is a classic question in evolutionary biology. Here we investigate group size effects in the evolutionary dynamics of games in which individuals choose whether to cooperate or defect and payoffs do not depend directly on the size of the group. We find that increasing the group size decreases the proportion of cooperators at both stable and unstable rest points of the replicator dynamics. This implies that larger group sizes can have negative effects (by reducing the amount of cooperation at stable polymorphisms) and positive effects (by enlarging the basin of attraction of more cooperative outcomes) on the evolution of cooperation. These two effects can be simultaneously present in games whose evolutionary dynamics feature both stable and unstable rest points, such as public goods games with participation thresholds. Our theory recovers and generalizes previous results and is applicable to a broad variety of social interactions that have been studied in the literature.

scholarly journals Evolutionary games and population dynamics: maintenance of cooperation in public goods games

2006 ◽  
Vol 273 (1600) ◽  
pp. 2565-2571 ◽  
Author(s):  
Christoph Hauert ◽  
Miranda Holmes ◽  
Michael Doebeli
Keyword(s):  
Public Goods ◽  
Prisoner's Dilemma ◽  
Replicator Dynamics ◽  
Evolutionary Game ◽  
Natural Extension ◽  
Prisoner’S Dilemma ◽  
Evolutionary Games ◽  
Darwinian Evolution ◽  
Ecological Dynamics ◽  
Public Goods Games

The emergence and abundance of cooperation in nature poses a tenacious and challenging puzzle to evolutionary biology. Cooperative behaviour seems to contradict Darwinian evolution because altruistic individuals increase the fitness of other members of the population at a cost to themselves. Thus, in the absence of supporting mechanisms, cooperation should decrease and vanish, as predicted by classical models for cooperation in evolutionary game theory, such as the Prisoner's Dilemma and public goods games. Traditional approaches to studying the problem of cooperation assume constant population sizes and thus neglect the ecology of the interacting individuals. Here, we incorporate ecological dynamics into evolutionary games and reveal a new mechanism for maintaining cooperation. In public goods games, cooperation can gain a foothold if the population density depends on the average population payoff. Decreasing population densities, due to defection leading to small payoffs, results in smaller interaction group sizes in which cooperation can be favoured. This feedback between ecological dynamics and game dynamics can generate stable coexistence of cooperators and defectors in public goods games. However, this mechanism fails for pairwise Prisoner's Dilemma interactions and the population is driven to extinction. Our model represents natural extension of replicator dynamics to populations of varying densities.

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.

scholarly journals Evolutionary dynamics of multiple games

2018 ◽  
Author(s):  
Vandana R. Venkateswaran ◽  
Chaitanya S. Gokhale
Keyword(s):  
Game Theory ◽  
Population Dynamics ◽  
Social Behavior ◽  
Evolutionary Game Theory ◽  
Bacterial Population ◽  
Evolutionary Dynamics ◽  
Evolutionary Game ◽  
Fixation Probability ◽  
Replicator Equation ◽  
Multiple Games

AbstractEvolutionary game theory has been successful in describing phenomena from bacterial population dynamics to the evolution of social behavior. Interactions between individuals are usually captured by a single game. In reality, however, individuals take part in many interactions. Here, we include multiple games and analyze their individual and combined evolutionary dynamics. A typical assumption is that the evolutionary dynamics of individual behavior can be understood by constructing one big comprehensive interactions structure, a single big game. But if any one of the multiple games has more than two strategies, then the combined dynamics cannot be understood by looking only at individual games. Devising a method to study multiple games – where each game could have an arbitrary number of players and strategies – we provide a concise replicator equation, and analyze its resulting dynamics. Moreover, in the case of finite populations, we formulate and calculate a basic and useful property of stochasticity, fixation probability. Our results reveal that even when interactions become incredibly complex, their properties can be captured by relatively simple concepts of evolutionary game(s) theory.

scholarly journals Cell-cell interactions and evolution using evolutionary game theory

2015 ◽  
Author(s):  
David Basanta
Keyword(s):  
Game Theory ◽  
Evolutionary Game Theory ◽  
Tumor Heterogeneity ◽  
Evolutionary Dynamics ◽  
Evolutionary Game ◽  
Cell Interactions ◽  
Cancer Evolution ◽  
Ideal Tool ◽  
Darwinian Dynamics ◽  
Cell Cell

Cancers arise from genetic abberations but also consistently display high levels of intra-tumor heterogeneity and evolve according to Darwinian dynamics. This makes evolutionary game theory an ideal tool in which to mathematically capture these cell-cell interactions and in which to investigate how they impact evolutionary dynamics. In this chapter we present some examples of how evolutionary game theory can elucidate cancer evolution.

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