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183
Evolutionarily Singular Strategies and the Adaptive Growth and Branching of the Evolutionary Tree
 EVOL. ECOL
, 1996
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On the Origin of Species by Sympatric Speciation
 Interim Report IR99013. International Institute for Applied Systems Analysis, Laxenburg, Austria. Available on the Internet: http://www.iiasa.ac.at
, 1999
"... Interim Reports on work of the International Institute for Applied Systems Analysis receive only limited review. Views or opinions expressed herein do not necessarily represent those of the Institute, its National Member Organizations, or other organizations supporting the work. IIASA STUDIES IN ADA ..."
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Cited by 148 (7 self)
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Interim Reports on work of the International Institute for Applied Systems Analysis receive only limited review. Views or opinions expressed herein do not necessarily represent those of the Institute, its National Member Organizations, or other organizations supporting the work. IIASA STUDIES IN ADAPTIVE DYNAMICS NO. 35 The Adaptive Dynamics Network at IIASA fosters the development of new mathematical and conceptual techniques for understanding the evolution of complex adaptive systems. Focusing on these longterm implications of adaptive processes in systems of limited growth, the Adaptive Dynamics Network brings together scientists and institutions from around the world with IIASA acting as the central node.
Evolutionary games on graphs
, 2007
"... Game theory is one of the key paradigms behind many scientific disciplines from biology to behavioral sciences to economics. In its evolutionary form and especially when the interacting agents are linked in a specific social network the underlying solution concepts and methods are very similar to ..."
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Cited by 143 (0 self)
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Game theory is one of the key paradigms behind many scientific disciplines from biology to behavioral sciences to economics. In its evolutionary form and especially when the interacting agents are linked in a specific social network the underlying solution concepts and methods are very similar to those applied in nonequilibrium statistical physics. This review gives a tutorialtype overview of the field for physicists. The first four sections introduce the necessary background in classical and evolutionary game theory from the basic definitions to the most important results. The fifth section surveys the topological complications implied by nonmeanfieldtype social network structures in general. The next three sections discuss in detail the dynamic behavior of three prominent classes of models: the Prisoner’s Dilemma, the Rock–Scissors–Paper game, and Competing Associations. The major theme of the review is in what sense and how the graph structure of interactions can modify and enrich the picture of long term behavioral patterns emerging in evolutionary games.
Unifying evolutionary dynamics: From individual stochastic processes to macroscopic evolution
 Theor. Pop. Biol
"... Running head: From individual processes to evolutionary dynamics ..."
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Cited by 83 (13 self)
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Running head: From individual processes to evolutionary dynamics
Models of cooperation based on the Prisoner’s Dilemma and the Snowdrift game
, 2005
"... Understanding the mechanisms that can lead to the evolution of cooperation through natural selection is a core problem in biology. Among the various attempts at constructing a theory of cooperation, game theory has played a central role. Here, we review models of cooperation that are based on two si ..."
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Cited by 77 (3 self)
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Understanding the mechanisms that can lead to the evolution of cooperation through natural selection is a core problem in biology. Among the various attempts at constructing a theory of cooperation, game theory has played a central role. Here, we review models of cooperation that are based on two simple games: the Prisoner’s Dilemma, and the Snowdrift game. Both games are twoperson games with two strategies, to cooperate and to defect, and both games are social dilemmas. In social dilemmas, cooperation is prone to exploitation by defectors, and the average payoff in populations at evolutionary equilibrium is lower than it would be in populations consisting of only cooperators. The difference between the games is that cooperation is not maintained in the Prisoner’s Dilemma, but persists in the Snowdrift game at an intermediate frequency. As a consequence, insights gained from studying extensions of the two games differ substantially. We review the most salient results obtained from extensions such as iteration, spatial structure, continuously variable cooperative investments, and multiperson interactions. Bridging the gap between theoretical and empirical research is one of the main challenges for future studies of cooperation, and we conclude by pointing out a number of promising natural systems in which the theory can be tested experimentally.
A microscopic interpretation for adaptive dynamics trait substitution sequence models
 Stoch. Proc. Appl
"... We consider an interacting particle Markov process for Darwinian evolution in an asexual population with nonconstant population size, involving a linear birth rate, a densitydependent logistic death rate, and a probability µ of mutation at each birth event. We introduce a renormalization parameter ..."
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Cited by 62 (12 self)
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We consider an interacting particle Markov process for Darwinian evolution in an asexual population with nonconstant population size, involving a linear birth rate, a densitydependent logistic death rate, and a probability µ of mutation at each birth event. We introduce a renormalization parameter K scaling the size of the population, which leads, when K → +∞, to a deterministic dynamics for the density of individuals holding a given trait. By combining in a nonstandard way the limits of large population (K → +∞) and of small mutations (µ → 0), we prove that a time scales separation between the birth and death events and the mutation events occurs and that the interacting particle microscopic process converges for finite dimensional distributions to the biological model of evolution known as the “monomorphic trait substitution sequence ” model of adaptive dynamics, which describes the Darwinian evolution in an asexual population as a Markov jump process in the trait space.
Adaptive dynamics in Allele space: Evolution of Genetic Polymorphism by. . .
, 1998
"... We investigate how a genetic polymorphism of distinctly different alleles can evolve in an initially monomorphic population under frequencydependent selection if mutations have only a small phenotypic effect. We consider the case of a single additive locus with a continuum of potential allele types ..."
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Cited by 45 (5 self)
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We investigate how a genetic polymorphism of distinctly different alleles can evolve in an initially monomorphic population under frequencydependent selection if mutations have only a small phenotypic effect. We consider the case of a single additive locus with a continuum of potential allele types in a diploid outbreeding population. As a specific example, we use a version of Levene's (1953) soft selection model, where stabilizing selection acts on a continuous trait within each of two habitats. If the optimal phenotypes within the habitats are sufficiantly different, then two distinctly different alleles evolve gradually from a single ancestral allele. In a wide range of parameter values, the two locally optimal phenotypes will be realized by one of the homozygotes and the heterozygote, rather than the two homozygotes. Unlike in the haploid analogue of the model, there can be multiple polymorphic evolutionary attractors with different probabilities of convergence. Keywords: adaptive...
Concentrations and constrained HamiltonJacobi equations arising in adaptive dynamics
 In Recent Developments in Nonlinear Partial Differential Equations
"... We consider an integral equation that exhibits a concentration phenomena. It describes a general birth and death process for a population structured by a quantitative trait and subject to small and frequent mutations. The population interacts through an environmental variable that is shared by the f ..."
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Cited by 44 (8 self)
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We consider an integral equation that exhibits a concentration phenomena. It describes a general birth and death process for a population structured by a quantitative trait and subject to small and frequent mutations. The population interacts through an environmental variable that is shared by the full population. This leads to the exponential growth of the population with the best adapted trait and to the exponential decay of the rest of the population. A small parameter that measure the mutations is introduced and after time rescaling, the population density typically converges to a Dirac mass in the trait space with weight and position evolving according to the new time scale. Following a formalism introduced in [12], these parameters are described by a HamiltonJacobi equation with a constraint and a Lagrange multiplier. The aim of the paper is to prove uniqueness for a class of such constrained H.J. equations, naturally posed in the viscosity solution sense. Our method combines changes of variables and unknowns with a contraction principle. 1
An error limit for the evolution of language
 PROC. R. SOC
, 1999
"... On the evolutionary trajectory that led to human language there must have been a transition from a fairly limited to an essentially unlimited communication system. The structure of modern human languages reveals at least two steps that are required for such a transition: in all languages (i) a small ..."
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Cited by 41 (6 self)
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On the evolutionary trajectory that led to human language there must have been a transition from a fairly limited to an essentially unlimited communication system. The structure of modern human languages reveals at least two steps that are required for such a transition: in all languages (i) a small number of phonemes are used to generate a large number of words; and (ii) a large number of words are used to a produce an unlimited number of sentences. The first (and simpler) step is the topic of the current paper. We study the evolution of communication in the presence of errors and show that this limits the number of objects (or concepts) that can be described by a simple communication system. The evolutionary optimum is achieved by using only a small number of signals to describe a few valuable concepts. Adding more signals does not increase the fitness of a language. This represents an error limit for the evolution of communication. We show that this error limit can be overcome by combining signals (phonemes) into words. The transition from an analogue to a digital system was a necessary step toward the evolution of human language.
Beginner’s guide to adaptive dynamics
 Banach Center Publications
, 2004
"... Abstract. The aim of these notes is to illustrate, largely by way of examples, how standard ecological models can be put into an evolutionary perspective in order to gain insight in the role of natural selection in shaping life history characteristics. We limit ourselves to phenotypic evolution unde ..."
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Cited by 41 (0 self)
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Abstract. The aim of these notes is to illustrate, largely by way of examples, how standard ecological models can be put into an evolutionary perspective in order to gain insight in the role of natural selection in shaping life history characteristics. We limit ourselves to phenotypic evolution under clonal reproduction (that is, we simply ignore the importance of genes and sex). Another basic assumption is that mutation occurs on a time scale which is long relative to the time scale of convergence to an ecological attractor. We begin by illustrating the idea of interaction via environmental variables through the example of competition for substrate in the chemostat. In this context we explain the trait/strategy substitution sequence, capturing how successful invaders/mutants outcompete the resident and then become the new resident. We also introduce the PIP, the pairwise invasibility plot, as a convenient graphical tool to study the adaptive dynamics of a onedimensional trait. We highlight the pessimization principle: if the environmental condition is onedimensional, mutation and natural selection inevitably lead to deterioration/Verelendung. We illuminate the Tragedy of the Commons as well as evolutionary suicide and, while we're about it, adaptive dynamics as an added feature to a bifurcation diagram (with, possibly, ADinduced branch