scholarly journals Evolutionary games on isothermal graphs

2019 ◽  
Vol 10 (1) ◽  
Author(s):  
Benjamin Allen ◽  
Gabor Lippner ◽  
Martin A. Nowak
Keyword(s):  
Evolutionary Dynamics ◽  
Cooperative Behavior ◽  
Strong Support ◽  
Evolutionary Games ◽  
Edge Weight ◽  
Cost Ratio ◽  
Weak Selection ◽  
Update Rules ◽  
Effective Degree ◽  
Birth Death

Abstract Population structure affects the outcome of natural selection. These effects can be modeled using evolutionary games on graphs. Recently, conditions were derived for a trait to be favored under weak selection, on any weighted graph, in terms of coalescence times of random walks. Here we consider isothermal graphs, which have the same total edge weight at each node. The conditions for success on isothermal graphs take a simple form, in which the effects of graph structure are captured in the ‘effective degree’—a measure of the effective number of neighbors per individual. For two update rules (death-Birth and birth-Death), cooperative behavior is favored on a large isothermal graph if the benefit-to-cost ratio exceeds the effective degree. For two other update rules (Birth-death and Death-birth), cooperation is never favored. We relate the effective degree of a graph to its spectral gap, thereby linking evolutionary dynamics to the theory of expander graphs. Surprisingly, we find graphs of infinite average degree that nonetheless provide strong support for cooperation.

scholarly journals Aspiration dynamics of multi-player games in finite populations

2014 ◽  
Vol 11 (94) ◽  
pp. 20140077 ◽  
Author(s):  
Jinming Du ◽  
Bin Wu ◽  
Philipp M. Altrock ◽  
Long Wang
Keyword(s):  
Evolutionary Game ◽  
Pairwise Comparison ◽  
Evolutionary Games ◽  
Structured Populations ◽  
Weak Selection ◽  
Additional Information ◽  
Average Abundance ◽  
Imperfect Rationality ◽  
Update Rules ◽  
Limiting Case

On studying strategy update rules in the framework of evolutionary game theory, one can differentiate between imitation processes and aspiration-driven dynamics. In the former case, individuals imitate the strategy of a more successful peer. In the latter case, individuals adjust their strategies based on a comparison of their pay-offs from the evolutionary game to a value they aspire, called the level of aspiration. Unlike imitation processes of pairwise comparison, aspiration-driven updates do not require additional information about the strategic environment and can thus be interpreted as being more spontaneous. Recent work has mainly focused on understanding how aspiration dynamics alter the evolutionary outcome in structured populations. However, the baseline case for understanding strategy selection is the well-mixed population case, which is still lacking sufficient understanding. We explore how aspiration-driven strategy-update dynamics under imperfect rationality influence the average abundance of a strategy in multi-player evolutionary games with two strategies. We analytically derive a condition under which a strategy is more abundant than the other in the weak selection limiting case. This approach has a long-standing history in evolutionary games and is mostly applied for its mathematical approachability. Hence, we also explore strong selection numerically, which shows that our weak selection condition is a robust predictor of the average abundance of a strategy. The condition turns out to differ from that of a wide class of imitation dynamics, as long as the game is not dyadic. Therefore, a strategy favoured under imitation dynamics can be disfavoured under aspiration dynamics. This does not require any population structure, and thus highlights the intrinsic difference between imitation and aspiration dynamics.

scholarly journals Evolutionary games on cycles

2006 ◽  
Vol 273 (1598) ◽  
pp. 2249-2256 ◽  
Author(s):  
Hisashi Ohtsuki ◽  
Martin A Nowak
Keyword(s):  
Evolutionary Game Theory ◽  
Evolutionary Game ◽  
Evolutionary Games ◽  
Weak Selection ◽  
Stochastic Effects ◽  
Frequency Dependent Selection ◽  
Game Dynamics ◽  
Case Selection ◽  
Mixed Populations ◽  
Update Rules

Traditional evolutionary game theory explores frequency-dependent selection in well-mixed populations without spatial or stochastic effects. But recently there has been much interest in studying the evolutionary game dynamics in spatial settings, on lattices and other graphs. Here, we present an analytic approach for the stochastic evolutionary game dynamics on the simplest possible graph, the cycle. For three different update rules, called ‘birth–death’ (BD), ‘death–birth’ (DB) and ‘imitation’ (IM), we derive exact conditions for natural selection to favour one strategy over another. As specific examples, we consider a coordination game and Prisoner's Dilemma. In the latter case, selection can favour cooperators over defectors for DB and IM updating. We also study the case where the replacement graph of evolutionary updating remains a cycle, but the interaction graph for playing the game is a complete graph. In this setting, all three update rules lead to identical conditions in the limit of weak selection, where we find the ‘1/3-law’ of well-mixed populations.

scholarly journals Aspiration dynamics generate robust predictions in heterogeneous populations

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Lei Zhou ◽  
Bin Wu ◽  
Jinming Du ◽  
Long Wang
Keyword(s):  
Evolutionary Dynamics ◽  
Weak Selection ◽  
Homogeneous Population ◽  
Weighted Networks ◽  
Self Evaluation ◽  
Aspiration Levels ◽  
Special Cases ◽  
Classical Condition ◽  
Population Structures ◽  
Update Rules

AbstractUpdate rules, which describe how individuals adjust their behavior over time, affect the outcome of social interactions. Theoretical studies have shown that evolutionary outcomes are sensitive to model details when update rules are imitation-based but are robust when update rules are self-evaluation based. However, studies of self-evaluation based rules have focused on homogeneous population structures where each individual has the same number of neighbors. Here, we consider heterogeneous population structures represented by weighted networks. Under weak selection, we analytically derive the condition for strategy success, which coincides with the classical condition of risk-dominance. This condition holds for all weighted networks and distributions of aspiration levels, and for individualized ways of self-evaluation. Our findings recover previous results as special cases and demonstrate the universality of the robustness property under self-evaluation based rules. Our work thus sheds light on the intrinsic difference between evolutionary dynamics under self-evaluation based and imitation-based update rules.

scholarly journals Dynamical analysis of the global elevational diversity gradient in passerine birds reveals a prominent role for highlands as species pumps

2020 ◽  
Author(s):  
Paul van Els ◽  
Leonel Herrera-Alsina ◽  
Alex L. Pigot ◽  
Rampal Etienne
Keyword(s):  
Evolutionary Dynamics ◽  
Strong Support ◽  
High Elevation ◽  
Dynamical Analysis ◽  
Reverse Direction ◽  
Passerine Birds ◽  
Diversification Rates ◽  
Diversity Gradient ◽  
As Species ◽  
Almost All

Abstract Low elevation regions harbor the majority of the world’s species diversity compared to high elevation areas. This global elevational diversity gradient, suggests that lowland species have had more time to diversify, or that net diversification rates have been higher in the lowlands (either due to higher ecological limits or intrinsically higher diversification rates). However, highlands seem to be cradles of diversity as they contain many young endemics, suggesting that their rates of speciation are exceptionally fast. Here, we use a phylogenetic diversification model that accounts for the dispersal of species between different elevations to examine the evolutionary dynamics of the elevational diversity gradient in passerine birds, a group that has radiated globally to occupy almost all elevations and latitudes. We find strong support for a model where passerines diversify at the same rate in the highlands and the lowlands but where the rate of dispersal from high to low elevations is more than twice as fast as in the reverse direction. This suggests that while there is no consistent trend in diversification across elevations, highland regions act as species pumps because the diversity they generate migrates into the lowlands, thus setting up the observed gradient in passerine diversity. This species pump is particularly strong in the tropics, where the inferred rate of speciation is 1.4 times faster than in the temperate zone. We conclude that despite their lower diversity, highland regions are disproportionally important for maintaining diversity in the adjacent lowlands. The extinction of species in the tropical highlands due to rapid climate change this century could thus have major and long-lasting impacts on global passerine diversity.

The role of biotic interactions in invasion ecology: theories and hypotheses.

2020 ◽  
pp. 26-44
Author(s):  
Cang Hui ◽  
◽  
Pietro Landi ◽  
Guillaume Latombe ◽  
◽  
...  
Keyword(s):  
Native Species ◽  
Evolutionary Dynamics ◽  
Biotic Interactions ◽  
Evolutionary Games ◽  
Invasion Ecology ◽  
Ecological Communities ◽  
Dynamic Interactions ◽  
Ecological Fitting ◽  
And Function

Changes in biotic interactions in the native and invaded range can enable a non-native species to establish and spread in novel environments. Invasive non-native species can in turn generate impacts in recipient systems partly through the changes they impose on biotic interactions; these interactions can lead to altered ecosystem processes in the recipient systems. This chapter reviews models, theories and hypotheses on how invasion performance and impact of introduced species in recipient ecosystems can be conjectured according to biotic interactions between native and non-native species. It starts by exploring the nature of biotic interactions as ensembles of ecological and evolutionary games between individuals of both the same and different groups. This allows us to categorize biotic interactions as direct and indirect (i.e. those involving more than two species) that emerge from both coevolution and ecological fitting during community assembly and invasion. We then introduce conceptual models that can reveal the ecological and evolutionary dynamics between interacting non-native and resident species in ecological networks and communities. Moving from such theoretical grounding, we review 20 hypotheses that have been proposed in invasion ecology to explain the invasion performance of a single non-native species, and seven hypotheses relating to the creation and function of assemblages of non-native species within recipient ecosystems. We argue that, although biotic interactions are ubiquitous and quintessential to the assessment of invasion performance, they are nonetheless difficult to detect and measure due to strength dependency on sampling scales and population densities, as well as the non-equilibrium transient dynamics of ecological communities and networks. We therefore call for coordinated efforts in invasion science and beyond, to devise and review approaches that can rapidly map out the entire web of dynamic interactions in a recipient ecosystem.

scholarly journals PHASE TRANSITION IN EVOLUTIONARY GAMES

1999 ◽  
Vol 14 (10) ◽  
pp. 1551-1559 ◽  
Author(s):  
ZHEN CAO ◽  
RUDOLPH C. HWA
Keyword(s):  
Phase Transition ◽  
Critical Region ◽  
Nuclear Physics ◽  
Cooperative Behavior ◽  
Evolutionary Games ◽  
Scaling Exponent ◽  
Factorial Moments ◽  
Physical Systems ◽  
Prisoners Dilemma ◽  
Evolution Dynamics

The evolution of cooperative behavior is studied in the deterministic version of the Prisoners' Dilemma on a two-dimensional lattice. The payoff parameter is set at the critical region 1.8<b<2.0, where clusters of cooperators are formed in all spatial sizes. Using the factorial moments developed in particle and nuclear physics for the study of phase transition, the distribution of cooperators is studied as a function of the bin size covering varying numbers of lattice cells. From the scaling behavior of the moments a scaling exponent is determined and is found to lie in the range where phase transitions are known to take place in physical systems. It is therefore inferred that when the payoff parameter is increased through the critical region the biological system of cooperators undergoes a phase transition to defectors. The universality of the critical behavior is thus extended to include also this particular model of evolution dynamics.

EFFECTS OF SPACE IN 2 × 2 GAMES

2002 ◽  
Vol 12 (07) ◽  
pp. 1531-1548 ◽  
Author(s):  
CH. HAUERT
Keyword(s):  
Cooperative Behavior ◽  
Mean Field ◽  
Systematic Analysis ◽  
Von Neumann ◽  
Spatial Extension ◽  
Moore Neighborhood ◽  
The Mean ◽  
Mixed Populations ◽  
Update Rules ◽  
Rectangular Lattices

A systematic analysis of the effects of spatial extension on the equilibrium frequency of cooperators and defectors in 2 × 2 games is presented and compared to well mixed populations where spatial extension can be neglected. We demonstrate that often spatial extension is indeed capable of promoting cooperative behavior. This holds in particular for the prisoner's dilemma for a small but important parameter range. For the hawk–dove game, spatial extension may lead to both, increases of the hawk- as well as the dove-strategy. The outcome subtly depends on the parameters as well as on the degree of stochasticity in the different update rules. For rectangular lattices, the general conclusions are rather robust and hold for different neighborhood types i.e. for the von Neumann as well as the Moore neighborhood and, in addition, they appear to be almost independent of the update rule of the lattice. However, increasing stochasticity for the update rules of the players results in equilibrium frequencies more closely related to the mean field description.

scholarly journals Extrapolating Weak Selection in Evolutionary Games

2013 ◽  
Vol 9 (12) ◽  
pp. e1003381 ◽  
Author(s):  
Bin Wu ◽  
Julián García ◽  
Christoph Hauert ◽  
Arne Traulsen
Keyword(s):  
Evolutionary Games ◽  
Weak Selection

scholarly journals Oscillatory dynamics in a bacterial cross-protection mutualism

2016 ◽  
Vol 113 (22) ◽  
pp. 6236-6241 ◽  
Author(s):  
Eugene Anatoly Yurtsev ◽  
Arolyn Conwill ◽  
Jeff Gore
Keyword(s):  
Evolutionary Dynamics ◽  
Cooperative Behavior ◽  
Cross Protection ◽  
Common Mechanism ◽  
Natural Environments ◽  
Term Survival ◽  
Bacterial Populations ◽  
Oscillatory Dynamics ◽  
Protection Mutualism

Cooperation between microbes can enable microbial communities to survive in harsh environments. Enzymatic deactivation of antibiotics, a common mechanism of antibiotic resistance in bacteria, is a cooperative behavior that can allow resistant cells to protect sensitive cells from antibiotics. Understanding how bacterial populations survive antibiotic exposure is important both clinically and ecologically, yet the implications of cooperative antibiotic deactivation on the population and evolutionary dynamics remain poorly understood, particularly in the presence of more than one antibiotic. Here, we show that two Escherichia coli strains can form an effective cross-protection mutualism, protecting each other in the presence of two antibiotics (ampicillin and chloramphenicol) so that the coculture can survive in antibiotic concentrations that inhibit growth of either strain alone. Moreover, we find that daily dilutions of the coculture lead to large oscillations in the relative abundance of the two strains, with the ratio of abundances varying by nearly four orders of magnitude over the course of the 3-day period of the oscillation. At modest antibiotic concentrations, the mutualistic behavior enables long-term survival of the oscillating populations; however, at higher antibiotic concentrations, the oscillations destabilize the population, eventually leading to collapse. The two strains form a successful cross-protection mutualism without a period of coevolution, suggesting that similar mutualisms may arise during antibiotic treatment and in natural environments such as the soil.

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