16,861 research outputs found
Evolutionary dynamics on any population structure
Evolution occurs in populations of reproducing individuals. The structure of
a biological population affects which traits evolve. Understanding evolutionary
game dynamics in structured populations is difficult. Precise results have been
absent for a long time, but have recently emerged for special structures where
all individuals have the same number of neighbors. But the problem of
determining which trait is favored by selection in the natural case where the
number of neighbors can vary, has remained open. For arbitrary selection
intensity, the problem is in a computational complexity class which suggests
there is no efficient algorithm. Whether there exists a simple solution for
weak selection was unanswered. Here we provide, surprisingly, a general formula
for weak selection that applies to any graph or social network. Our method uses
coalescent theory and relies on calculating the meeting times of random walks.
We can now evaluate large numbers of diverse and heterogeneous population
structures for their propensity to favor cooperation. We can also study how
small changes in population structure---graph surgery---affect evolutionary
outcomes. We find that cooperation flourishes most in societies that are based
on strong pairwise ties.Comment: 68 pages, 10 figure
Evolutionary multiplayer games on graphs with edge diversity
Evolutionary game dynamics in structured populations has been extensively
explored in past decades. However, most previous studies assume that payoffs of
individuals are fully determined by the strategic behaviors of interacting
parties and social ties between them only serve as the indicator of the
existence of interactions. This assumption neglects important information
carried by inter-personal social ties such as genetic similarity, geographic
proximity, and social closeness, which may crucially affect the outcome of
interactions. To model these situations, we present a framework of evolutionary
multiplayer games on graphs with edge diversity, where different types of edges
describe diverse social ties. Strategic behaviors together with social ties
determine the resulting payoffs of interactants. Under weak selection, we
provide a general formula to predict the success of one behavior over the
other. We apply this formula to various examples which cannot be dealt with
using previous models, including the division of labor and relationship- or
edge-dependent games. We find that labor division facilitates collective
cooperation by decomposing a many-player game into several games of smaller
sizes. The evolutionary process based on relationship-dependent games can be
approximated by interactions under a transformed and unified game. Our work
stresses the importance of social ties and provides effective methods to reduce
the calculating complexity in analyzing the evolution of realistic systems.Comment: 50 pages, 7 figure
Evolutionary game theory: Temporal and spatial effects beyond replicator dynamics
Evolutionary game dynamics is one of the most fruitful frameworks for
studying evolution in different disciplines, from Biology to Economics. Within
this context, the approach of choice for many researchers is the so-called
replicator equation, that describes mathematically the idea that those
individuals performing better have more offspring and thus their frequency in
the population grows. While very many interesting results have been obtained
with this equation in the three decades elapsed since it was first proposed, it
is important to realize the limits of its applicability. One particularly
relevant issue in this respect is that of non-mean-field effects, that may
arise from temporal fluctuations or from spatial correlations, both neglected
in the replicator equation. This review discusses these temporal and spatial
effects focusing on the non-trivial modifications they induce when compared to
the outcome of replicator dynamics. Alongside this question, the hypothesis of
linearity and its relation to the choice of the rule for strategy update is
also analyzed. The discussion is presented in terms of the emergence of
cooperation, as one of the current key problems in Biology and in other
disciplines.Comment: Review, 48 pages, 26 figure
Strategy evolution on dynamic networks
Models of strategy evolution on static networks help us understand how
population structure can promote the spread of traits like cooperation. One key
mechanism is the formation of altruistic spatial clusters, where neighbors of a
cooperative individual are likely to reciprocate, which protects prosocial
traits from exploitation. But most real-world interactions are ephemeral and
subject to exogenous restructuring, so that social networks change over time.
Strategic behavior on dynamic networks is difficult to study, and much less is
known about the resulting evolutionary dynamics. Here, we provide an analytical
treatment of cooperation on dynamic networks, allowing for arbitrary spatial
and temporal heterogeneity. We show that transitions among a large class of
network structures can favor the spread of cooperation, even if each individual
social network would inhibit cooperation when static. Furthermore, we show that
spatial heterogeneity tends to inhibit cooperation, whereas temporal
heterogeneity tends to promote it. Dynamic networks can have profound effects
on the evolution of prosocial traits, even when individuals have no agency over
network structures.Comment: 45 pages; final versio
Evolutionary dynamics in structured populations
Evolutionary dynamics shape the living world around us. At the centre of every evolutionary process is a population of reproducing individuals. The structure of that population affects evolutionary dynamics. The individuals can be molecules, cells, viruses, multicellular organisms or humans. Whenever the fitness of individuals depends on the relative abundance of phenotypes in the population, we are in the realm of evolutionary game theory. Evolutionary game theory is a general approach that can describe the competition of species in an ecosystem, the interaction between hosts and parasites, between viruses and cells, and also the spread of ideas and behaviours in the human population. In this perspective, we review the recent advances in evolutionary game dynamics with a particular emphasis on stochastic approaches in finite sized and structured populations. We give simple, fundamental laws that determine how natural selection chooses between competing strategies. We study the well-mixed population, evolutionary graph theory, games in phenotype space and evolutionary set theory. We apply these results to the evolution of cooperation. The mechanism that leads to the evolution of cooperation in these settings could be called ‘spatial selection’: cooperators prevail against defectors by clustering in physical or other spaces
Evolution of cooperation in multilayer networks
Dissertation presented as the partial requirement for obtaining a Master's degree in Information Management, specialization in Information Systems and Technologies ManagementIndividuals take part in multiple layers of networks of interactions simultaneously. These interdependent networks account for the different sort of social ties individuals maintain per layer. In each layer individuals participate in N-Player Public Goods Games where benefits collected increase with amounts invested. It is, however, tempting to be a free-rider, i.e., to take advantage of the common pool without contributing to it, a situation from which a social dilemma results. This thesis offers new insights on how cooperation dynamics is shaped by multiple layers of social interactions and diversity of contributions invested per game. To this end, we resort to Evolutionary Game Theory and Network Science to provide a convenient framework to address the most important prototypical social conflicts and/or dilemmas in large networked populations. In particular, we propose a novel mean-field approach capable of tracking the self-organization of Cooperators when co-evolving with Defectors in a multilayer environment. We show that the emerging collective dynamics, which depends (i) on the underlying layer networks of interactions and (ii) on the criteria to share a finite investment across all games, often does not bear any resemblance with the local processes supporting them. Our findings suggest that, whenever individual investments are distributed among games or layers, resilience of cooperation against free-riders increases with the number of layers, and that cooperation emerges from a non-trivial organization of cooperation across the layers. In opposition, under constant, non-distributed investments, the level of cooperation shows little sensibility to variations in the number of layers. These findings put in evidence the importance of asymmetric contributions across games and social contexts in the emergence of human cooperation
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