Research Topics
 Martin NowakSummaryAffiliation: Harvard University Country: USA Publications
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Publications
 Theory is available lightMartin A Nowak
Program for Evolutionary Dynamics, Department of Organismic and Evolutionary Biology, Harvard University, Cambridge, Massachusetts 02138, USA
Curr Biol 14:R4067. 2004  Prevolutionary dynamics and the origin of evolutionMartin A Nowak
Program for Evolutionary Dynamics, Department of Organismic and Evolutionary Biology, Harvard University, Cambridge, MA 02138, USA
Proc Natl Acad Sci U S A 105:149247. 2008..Replication is not a prerequisite for selection, but instead, there can be selection for replication. Mutation leads to an error threshold between life and prelife...  Emergence of cooperation and evolutionary stability in finite populationsMartin A Nowak
Program for Evolutionary Dynamics, Harvard University, Cambridge, Massachusetts 02138, USA
Nature 428:64650. 2004..We specify the conditions required for natural selection to favour the emergence of cooperation and define evolutionary stability in finite populations...  Genetic instability and clonal expansionMartin A Nowak
Program for Evolutionary Dynamics, Department of Organismic and Evolutionary Biology, Harvard University, Cambridge, MA 02138, USA
J Theor Biol 241:2632. 2006....  Evolutionary dynamics in structured populationsMartin A Nowak
Department of Mathematics, Harvard University, Cambridge, MA 02138, USA
Philos Trans R Soc Lond B Biol Sci 365:1930. 2010..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...  Upstream reciprocity and the evolution of gratitudeMartin A Nowak
Program for Evolutionary Dynamics, Department of Organismic and Evolutionary Biology, Harvard University, Cambridge, MA 02138, USA
Proc Biol Sci 274:6059. 2007..Our analysis shows that gratitude and other positive emotions, which increase the willingness to help others, can evolve in the competitive world of natural selection...  Five rules for the evolution of cooperationMartin A Nowak
Program for Evolutionary Dynamics, Department of Organismic and Evolutionary Biology, and Department of Mathematics, Harvard University, Cambridge, MA 02138, USA
Science 314:15603. 2006..For each mechanism, a simple rule is derived that specifies whether natural selection can lead to cooperation...  The evolution of eusocialityMartin A Nowak
Program for Evolutionary Dynamics, Department of Mathematics, Harvard University, Cambridge, Massachusetts 02138, USA
Nature 466:105762. 2010....  Evolutionary dynamics of biological gamesMartin A Nowak
Program for Evolutionary Dynamics, Department of Mathematics, Department of Organismic and Evolutionary Biology, Harvard University, 1 Brattle Square, Cambridge, MA 02138, USA
Science 303:7939. 2004..Evolutionary game theory is an essential component of a mathematical and computational approach to biology...  Via freedom to coercion: the emergence of costly punishmentChristoph Hauert
Program for Evolutionary Dynamics, Department of Organismic and Evolutionary Biology, Department of Mathematics, Harvard University, Cambridge, MA 02138, USA
Science 316:19057. 2007..Paradoxically, the freedom to withdraw from the common enterprise leads to enforcement of social norms. Joint enterprises that are compulsory rather than voluntary are less likely to lead to cooperation...  Evolutionary graph theory: breaking the symmetry between interaction and replacementHisashi Ohtsuki
Program for Evolutionary Dynamics, Harvard University, Cambridge MA 02138, USA
J Theor Biol 246:68194. 2007....  Accumulation of driver and passenger mutations during tumor progressionIvana Bozic
Program for Evolutionary Dynamics, Harvard University, Cambridge, MA 02138, USA
Proc Natl Acad Sci U S A 107:1854550. 2010..This selective advantage is surprisingly small0.004 ± 0.0004and has major implications for experimental cancer research...  Winners don't punishAnna Dreber
Program for Evolutionary Dynamics, Harvard University, Cambridge, Massachusetts 02138, USA
Nature 452:34851. 2008..Those people who gain the highest total payoff tend not to use costly punishment: winners don't punish. This suggests that costly punishment behaviour is maladaptive in cooperation games and might have evolved for other reasons...  Analytical results for individual and group selection of any intensityArne Traulsen
Program for Evolutionary Dynamics, Department of Organismic and Evolutionary Biology, Department of Mathematics, Harvard University, Cambridge, MA, 02138, USA
Bull Math Biol 70:141024. 2008..This approach also works for group selection (= multilevel selection). We discuss the difference between our approach and that of inclusive fitness theory...  Stochastic dynamics of invasion and fixationArne Traulsen
Program for Evolutionary Dynamics, Harvard University, Cambridge, Massachusetts 02138, USA
Phys Rev E Stat Nonlin Soft Matter Phys 74:011909. 2006....  Evolutionary dynamics on graphsErez Lieberman
Program for Evolutionary Dynamics, Department of Organismic and Evolutionary Biology, Harvard University, Cambridge, Massachusetts 02138, USA
Nature 433:3126. 2005..Evolutionary graph theory has many fascinating applications ranging from ecology to multicellular organization and economics...  Reputationbased partner choice promotes cooperation in social networksFeng Fu
Program for Evolutionary Dynamics, Harvard University, One Brattle Square, Cambridge, Massachusetts 02138, USA
Phys Rev E Stat Nonlin Soft Matter Phys 78:026117. 2008..Our results highlight the importance of the consideration of reputation (indirect reciprocity) on the promotion of cooperation when individuals can adjust their partnerships...  Evolutionary dynamics on graphs: Efficient method for weak selectionFeng Fu
Program for Evolutionary Dynamics, Harvard University, Cambridge, Massachusetts 02138, USA
Phys Rev E Stat Nonlin Soft Matter Phys 79:046707. 2009..Computer simulations confirm the predictive power of our method and illustrate the improved accuracy as compared to previous studies...  Prisoners of the dilemmaMartin A Nowak
Program for Evolutionary Dynamics, One Brattle Square, Harvard University, Cambridge, Massachusetts 02138, USA
Nature 427:491. 2004  Evolutionary game dynamics in finite populations with strong selection and weak mutationDrew Fudenberg
Department of Economics, Harvard University, Cambridge, MA 02138, USA
Theor Popul Biol 70:35263. 2006..We determine which language will be spoken in finite large populations. The results have an intuitive interpretation but would not be expected from an analysis of the replicator dynamics...  The age incidence of chronic myeloid leukemia can be explained by a onemutation modelFranziska Michor
Program for Evolutionary Dynamics, Department of Mathematics, Harvard University, Cambridge, MA 02138, USA
Proc Natl Acad Sci U S A 103:149314. 2006..Therefore, the CML incidence data are consistent with the hypothesis that the Philadelphia translocation alone is sufficient to cause chronic phase CML...  Digital cows grazing on digital groundsThomas Pfeiffer
Program for Evolutionary Dynamics, Department of Organismic and Evolutionary Biology, Harvard University, Cambridge, Massachusetts 02138, USA
Curr Biol 16:R9469. 2006..Adding together the component partial utilities, the rational herdsman concludes that the only sensible course for him to pursue is to add another animal to the herd. And another; and another.....  Stochastic payoff evaluation increases the temperature of selectionArne Traulsen
Program for Evolutionary Dynamics, Harvard University, Cambridge, MA 02138, USA
J Theor Biol 244:34956. 2007..A simple meanfield approximation is derived that captures the average effect of the payoff stochasticity. Correction terms to the meanfield theory are computed and discussed...  Emotions as infectious diseases in a large social network: the SISa modelAlison L Hill
Program for Evolutionary Dynamics, Berkman Center for Internet and Society, Department of Mathematics, Harvard University, Cambridge, MA 02138, USA
Proc Biol Sci 277:382735. 2010..Our model provides a theoretical framework for studying the interpersonal spread of any state that may also arise spontaneously, such as emotions, behaviours, health states, ideas or diseases with reservoirs...  Pairwise comparison and selection temperature in evolutionary game dynamicsArne Traulsen
Program for Evolutionary Dynamics, Harvard University, One Brattle Square, Cambridge, MA 02138, USA
J Theor Biol 246:5229. 2007..For some payoff matrices the distribution of fixation times can become so broad that the average value is no longer very meaningful...  Chromodynamics of cooperation in finite populationsArne Traulsen
Program for Evolutionary Dynamics, Department of Organismic and Evolutionary Biology, Department of Mathematics, Harvard University, Cambridge, Massachusetts, United States of America
PLoS ONE 2:e270. 2007..Cooperators use a secret tag until they are discovered by defectors who then destroy cooperation based on this tag. Subsequently, a fraction of the population manages to establish cooperation based on a new tag...  Mutationselection equilibrium in games with mixed strategiesCorina E Tarnita
Program for Evolutionary Dynamics, Department of Mathematics, Harvard University, Cambridge, MA 02138, USA
J Theor Biol 261:507. 2009..The result for any mutation rate is a linear combination of those two. As a specific example we study the HawkDove game. We prove general statements about the relationship between games with pure and with mixed strategies...  Invasion and expansion of cooperators in lattice populations: prisoner's dilemma vs. snowdrift gamesFeng Fu
Program for Evolutionary Dynamics, Harvard University, Cambridge, MA 02138, USA
J Theor Biol 266:35866. 2010....  Evolution of cooperation by phenotypic similarityTibor Antal
Program for Evolutionary Dynamics and Department of Mathematics, Harvard University, Cambridge, MA 02138, USA
Proc Natl Acad Sci U S A 106:8597600. 2009..We also derive the fundamental condition for any twostrategy symmetric game and consider highdimensional phenotype spaces...  Transforming the dilemmaChristine Taylor
Program for Evolutionary Dynamics, Department of Organismic and Evolutionary Biology, Harvard University, Cambridge, MA 02138, USA
Evolution 61:228192. 2007..The transformed matrices can be used in standard frameworks of evolutionary dynamics such as the replicator equation or stochastic processes of game dynamics in finite populations...  Direct reciprocity with costly punishment: generous titfortat prevailsDavid G Rand
Program for Evolutionary Dynamics, Harvard University, Cambridge MA 02138, USA
J Theor Biol 256:4557. 2009..We find quantitative agreement between our simulation results and data from experimental observations...  Strategy abundance in 2x2 games for arbitrary mutation ratesTibor Antal
Harvard University, Cambridge, MA 02138, USA
J Theor Biol 257:3404. 2009..Here we show that this result holds in fact for a wide class of stochastic birthdeath processes for arbitrary mutation rate and for any intensity of selection...  Mutationselection equilibrium in games with multiple strategiesTibor Antal
Program for Evolutionary Dynamics, Department of Mathematics, Harvard University, Cambridge, MA 02138, USA
J Theor Biol 258:61422. 2009..A linear combination of these two conditions holds for any mutation rate. Our results allow a complete characterization of nxn games in the limit of weak selection...  The logic of indirect speechSteven Pinker
Department of Psychology, and Program for Evolutionary Dynamics, Harvard University, Cambridge, MA 02138, USA
Proc Natl Acad Sci U S A 105:8338. 2008..This feature makes an indirect request qualitatively different from a direct one even when the speaker and listener can infer each other's intentions with high confidence...  Spatial invasion of cooperationPhilipp Langer
Program for Evolutionary Dynamics, Department of Organismic and Evolutionary Biology, Harvard University, One Brattle Square, Cambridge, MA 02138, USA
J Theor Biol 250:63441. 2008....  Strategy selection in structured populationsCorina E Tarnita
Program for Evolutionary Dynamics, Department of Mathematics, Harvard University, Cambridge, MA 02138, USA
J Theor Biol 259:57081. 2009..The single parameter, sigma, allows us to quantify the ability of a population structure to promote the evolution of cooperation or to choose efficient equilibria in coordination games...  Phenotypic mutation rates and the abundance of abnormal proteins in yeastMartin Willensdorfer
Program for Evolutionary Dynamics, Harvard University, Cambridge, Massachusetts, United States of America
PLoS Comput Biol 3:e203. 2007..Our work allows us to estimate the phenotypic mutation rate based on data on the fraction of abnormal proteins. For S. cerevisiae, we predict that the value for the phenotypic mutation rate is between 2 x 10(4) and 6 x 10(4)...  The fastest evolutionary trajectoryArne Traulsen
Program for Evolutionary Dynamics, Harvard University, Cambridge, MA 02138, USA
J Theor Biol 249:61723. 2007..We discuss deviations for large mutation rates and including back mutations. For very large mutation rates, the optimum fitness landscape is flat and has a single peak at type B...  The onethird law of evolutionary dynamicsHisashi Ohtsuki
Program for Evolutionary Dynamics, Harvard University, Cambridge, MA 02138, USA
J Theor Biol 249:28995. 2007..We also show that the onethird law implies that the average Malthusian fitness of A is positive...  Evolutionary stability on graphsHisashi Ohtsuki
Program for Evolutionary Dynamics, Harvard University, Cambridge, MA 02138, USA
J Theor Biol 251:698707. 2008..Evolutionary stability on sparse graphs does not imply evolutionary stability in a wellmixed population, nor vice versa. We provide a geometrical interpretation of the ESS condition on graphs...  Stochastic dynamics of metastasis formationFranziska Michor
Program for Evolutionary Dynamics, Department of Organismic and Evolutionary Biology, Department of Mathematics, Harvard University, Cambridge, MA 02138, USA
J Theor Biol 240:52130. 2006..Our theory shows how to calculate the expected number of metastases that are formed by a tumor...  Dynamics of colorectal cancerFranziska Michor
Program for Evolutionary Dynamics, Department of Organismic and Evolutionary Biology, Harvard University, Cambridge, MA 02138, USA
Semin Cancer Biol 15:48493. 2005..An early emergence of genetic instability could drive most of the somatic evolution of cancer. Here, we review mathematical models of colorectal tumorigenesis and discuss the role of genetic instability...  Dynamics of chronic myeloid leukaemiaFranziska Michor
Program for Evolutionary Dynamics, Department of Organismic and Evolutionary Biology, Department of Mathematics, Harvard University, Cambridge, Massachusetts 02138, USA
Nature 435:126770. 2005..We calculate the probability of developing imatinib resistance mutations and estimate the time until detection of resistance. Our model provides the first quantitative insights into the in vivo kinetics of a human cancer...  Can chromosomal instability initiate tumorigenesis?Franziska Michor
Program for Evolutionary Dynamics, Department of Organismic and Evolutionary Biology, Department of Mathematics, Harvard University, Cambridge, MA 02138, USA
Semin Cancer Biol 15:439. 2005..If two tumor suppressor genes have to be inactivated in ratelimiting steps, then CIN is likely to emerge before the inactivation of the first tumor suppressor gene...  Local regulation of homeostasis favors chromosomal instabilityFranziska Michor
Department of Organismic and Evolutionary Biology, Harvard University, Cambridge, MA 02138, USA
Curr Biol 13:5814. 2003..Thus, small compartments protect against mutations in tumor suppressor genes or oncogenes but promote the emergence of genetic instability...  Evolutionary game dynamics in finite populationsChristine Taylor
Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
Bull Math Biol 66:162144. 2004..For finite populations, there are eight selection scenarios. For a fixed payoff matrix a number of these scenarios can occur for different population sizes. We discuss several examples with unexpected behavior...  Evolutionary dynamics of tumor suppressor gene inactivationMartin A Nowak
Program for Evolutionary Dynamics, Harvard University, Cambridge, MA 02138, USA
Proc Natl Acad Sci U S A 101:106358. 2004..Small lesions without genetic instability can take a very long time to inactivate the next TSG, whereas the same lesions with genetic instability pose a much greater risk for cancer progression...  Infectious disease modeling of social contagion in networksAlison L Hill
Program for Evolutionary Dynamics, Harvard University, Cambridge, Massachusetts, United States of America
PLoS Comput Biol 6:e1000968. 2010..It provides a theoretical framework for studying the interpersonal spread of any state that may also arise spontaneously, such as emotions, behaviors, health states, ideas or diseases with reservoirs...  The linear process of somatic evolutionMartin A Nowak
Program for Evolutionary Dynamics, Harvard University, Cambridge, MA 02138, USA
Proc Natl Acad Sci U S A 100:149669. 2003..This design can slow down the rate of somatic evolution dramatically and therefore delay the onset of cancer...  Synergy and discounting of cooperation in social dilemmasChristoph Hauert
Department of Zoology, University of British Columbia, 6270 University Boulevard, Vancouver BC, Canada V6T 1Z4
J Theor Biol 239:195202. 2006..Generically, for groups of three or more interacting individuals further, more complex, dynamics can occur. Our framework provides the first unifying approach to model cooperation in different kinds of social dilemmas...  Somatic selection for and against cancerFranziska Michor
Program in Theoretical Biology and Evolutionary Dynamics, Department of Organismic and Evolutionary Biology, Department of Mathematics, Harvard University, Cambridge, MA 02138, USA
J Theor Biol 225:37782. 2003..If both deleterious and advantageous mutations participate in tumor initiation, then we find an intermediate optimum for the compartment size...  Winstay, loseshift in language learning from peersFrederick A Matsen
Program for Evolutionary Dynamics, Department of Mathematics, Harvard University, One Brattle Square, Cambridge, MA 02138, USA
Proc Natl Acad Sci U S A 101:180537. 2004..Moreover, for many graphs, it is sufficient to have an aspiration level demanding only two other individuals to use the same language...  A symmetry of fixation times in evoultionary dynamicsChristine Taylor
Program for Evolutionary Dynamics, Department of Mathematics, Harvard University, Cambridge, MA 02138, USA
J Theor Biol 243:24551. 2006..This does not hold for WrightFisher models, nor when the mutants start from multiple copies...  Evolution of resistance to cancer therapyFranziska Michor
Program for Evolutionary Dynamics, Department of Organismic and Evolutionary Biology, Department of Mathematics, Harvard University, Cambridge, MA 02138, USA
Curr Pharm Des 12:26171. 2006..We apply the general model to evolution of resistance of cancer cells and discuss examples for diverse mechanisms of resistance. Our theory shows how to estimate the probability of success for any treatment regimen...  Evolutionary game dynamics with nonuniform interaction ratesChristine Taylor
Program for Evolutionary Dynamics, Department of Mathematics, Department of Organismic and Evolutionary Biology, Harvard University, Cambridge, MA 02138, USA
Theor Popul Biol 69:24352. 2006..For the Prisoner's Dilemma, nonuniform interaction rates allow the coexistence between cooperators and defectors. For the snowdrift game, nonuniform interaction rates change the equilibrium frequency of cooperators...  Why are phenotypic mutation rates much higher than genotypic mutation rates?Reinhard Burger
Program for Evolutionary Dynamics, Department of Mathematics and Department of Organismic and Evolutionary Biology, Harvard University, Cambridge, Massachusetts 02138, USA
Genetics 172:197206. 2006..Despite its simplicity, our model can explain part of the huge difference between genotypic and phenotypic mutation rates that is observed in nature. The relevant data are summarized...  Breaking the symmetry between interaction and replacement in evolutionary dynamics on graphsHisashi Ohtsuki
Program for Evolutionary Dynamics, Harvard University, Cambridge, Massachusetts 02138, USA
Phys Rev Lett 98:108106. 2007..Analytical results are obtained in the pair approximation and for weak selection. Their validity is confirmed by computer simulations...  Calculating evolutionary dynamics in structured populationsCharles G Nathanson
Department of Economics, Harvard University, Cambridge, Massachusetts, USA
PLoS Comput Biol 5:e1000615. 2009..We derive an intuitive formula for the structure coefficient, sigma, and provide a method for efficient numerical calculation...  Evolutionary dynamics in set structured populationsCorina E Tarnita
Program for Evolutionary Dynamics, Department of Mathematics, Harvard University, Cambridge, MA 02138, USA
Proc Natl Acad Sci U S A 106:86014. 2009..As a particular example, we study the evolution of cooperation and derive precise conditions for cooperators to be selected over defectors...  Positive interactions promote public cooperationDavid G Rand
Program for Evolutionary Dynamics, Harvard University, Cambridge, MA 02138, USA
Science 325:12725. 2009..We conclude that reward outperforms punishment in repeated public goods games and that human cooperation in such repeated settings is best supported by positive interactions with others...  Active linking in evolutionary gamesJorge M Pacheco
Program for Evolutionary Dynamics, Harvard University, Cambridge, MA 02138, USA
J Theor Biol 243:43743. 2006..As a specific example, we study the interaction between cooperators and defectors. We find a simple relationship that characterizes those linking dynamics which allow natural selection to favour cooperation over defection...  Coevolution of strategy and structure in complex networks with dynamical linkingJorge M Pacheco
Program for Evolutionary Dynamics, Harvard University, Cambridge, Massachusetts 02138, USA
Phys Rev Lett 97:258103. 2006..For intermediate ranges, we investigate numerically the detailed interplay determined by these two time scales and show that the scope of validity of the analytical results extends to a much wider ratio of time scales than expected...  Mutationselection networks of cancer initiation: tumor suppressor genes and chromosomal instabilityNatalia L Komarova
Institute for Advanced Study, Einstein Drive, Princeton, NJ 08540, USA
J Theor Biol 223:43350. 2003..In this case, CIN is an early event and a driving force of cancer progression. The techniques developed in this paper can be used to study arbitrarily complex mutationselection networks of the somatic evolution of cancer...  Patterns of cell division and the risk of cancerSteven A Frank
Department of Ecology and Evolutionary Biology, University of California, Irvine, California 92697 2525, USA
Genetics 163:152732. 2003....  Evolutionary dynamics of escape from biomedical interventionYoh Iwasa
Department of Biology, Kyushu University, Fukuoka 812 8581, Japan
Proc Biol Sci 270:25738. 2003..Our theory shows how to estimate the probability of success or failure of biomedical intervention, such as drug treatment and vaccination, against rapidly evolving organisms...  Evolution: the good, the bad and the lonelyFranziska Michor
Nature 419:677, 679. 2002  Cell biology: Developmental predisposition to cancerSteven A Frank
Department of Ecology and Evolutionary Biology, University of California, Irvine, California 92697 2525, USA
Nature 422:494. 2003  Evolution of resistance during clonal expansionYoh Iwasa
Department of Biology, Faculty of Sciences, Kyushu University, Fukuoka, Japan
Genetics 172:255766. 2006..Hence a tumor subject to high rates of apoptosis will show a higher incidence of resistance than expected on its detection size only...  Competitive exclusion and coexistence of universal grammarsW Garrett Mitchener
Program in Applied and Computational Mathematics, Fine Hall, Washington Road, Princeton, NJ 08544 1000, USA
Bull Math Biol 65:6793. 2003..An interesting finding is that less specific UGs can resist invasion by more specific UGs if learning is more accurate. In other words, accurate learning stabilizes UGs that admit large numbers of candidate grammars...  The role of chromosomal instability in tumor initiationMartin A Nowak
Institute for Advanced Study, Princeton, NJ 08540, USA
Proc Natl Acad Sci U S A 99:1622631. 2002..Specifically, we calculate the conditions for CIN to initiate the process of colorectal tumorigenesis before the inactivation of tumor suppressor genes...  Problems of somatic mutation and cancerSteven A Frank
Department of Ecology and Evolutionary Biology, University of California, Irvine CA 92717, USA
Bioessays 26:2919. 2004..We consider how various aspects of tissue architecture and cellular competition affect the pace of mutation accumulation. We also discuss the rise and fall of somatic mutation rates during cancer progression...  A simple rule for the evolution of cooperation on graphs and social networksHisashi Ohtsuki
Department of Biology, Kyushu University, Fukuoka 812 8581, Japan
Nature 441:5025. 2006..In this case, cooperation can evolve as a consequence of 'social viscosity' even in the absence of reputation effects or strategic complexity...  Evolutionary game dynamics in a WrightFisher processLorens A Imhof
Statistische Abteilung, Universitat Bonn, Germany
J Math Biol 52:66781. 2006..In the limit of weak selection, we obtain the 1/3 law: if A and B are strict Nash equilibria then selection favors replacement of B by A, if the unstable equilibrium occurs at a frequency of A which is less than 1/3...  Evolutionary games on cyclesHisashi Ohtsuki
Department of Biology, Faculty of Sciences, Kyushu University, Fukuoka 812 8581, Japan
Proc Biol Sci 273:224956. 2006..In this setting, all three update rules lead to identical conditions in the limit of weak selection, where we find the '1/3law' of wellmixed populations...  Titfortat or winstay, loseshift?Lorens A Imhof
Statistische Abteilung, Universitat Bonn, D 53113 Bonn, Germany
J Theor Biol 247:57480. 2007..TFT is never selected in this evolutionary process, but lowers the selection threshold for WSLS...  Stochastic evolutionary dynamics on two levelsArne Traulsen
Institut für Theoretische Physik und Astrophysik, Christian Albrechts Universitat, Olshausenstr 40, D 24098 Kiel, Germany
J Theor Biol 235:393401. 2005..We also study opposing selection on two or more levels by analysing the evolutionary dynamics of hierarchically embedded Moran processes...  Population genetics of tumor suppressor genesYoh Iwasa
Department of Biology, Faculty of Sciences, Kyushu University, Hakozoki 6 10 1, Higashi ku, Fukuoka 812 8581, Japan
J Theor Biol 233:1523. 2005..The inactivation of the first and of the second allele can occur at equal or different rates. Our calculations provide insights into basic aspects of population genetics determining cancer initiation and progression...  Repeated games and direct reciprocity under active linkingJorge M Pacheco
ATP Group and CFTC, Departamento de Física da Faculdade de Ciências, P 1649 003 Lisboa Codex, Portugal
J Theor Biol 250:72331. 2008..We derive analytical conditions for evolutionary stability...  Computational and evolutionary aspects of languageMartin A Nowak
Institute for Advanced Study, Einstein Drive, Princeton, New Jersey 08540, USA
Nature 417:6117. 2002..Universal grammar specifies the restricted set of languages learnable by the human brain. Evolutionary dynamics can be formulated to describe the cultural evolution of language and the biological evolution of universal grammar...  Chaos and languageW Garrett Mitchener
Institute for Advanced Study, Princeton University, New Jersey, USA
Proc Biol Sci 271:7014. 2004..Hence, language dynamical equations mimic complicated and unpredictable changes of languages over time. In terms of evolutionary game theory, we note that imperfect learning can induce chaotic switching among strict Nash equilibria...  Stochastic tunnels in evolutionary dynamicsYoh Iwasa
Department of Biology, Kyushu University, Fukuoka 812 8581, Japan
Genetics 166:15719. 2004..Although our theory is developed for cancer genetics, stochastic tunnels are general phenomena that could arise in many circumstances...  The replicator equation on graphsHisashi Ohtsuki
Department of Biology, Faculty of Sciences, Kyushu University, Fukuoka 812 8581, Japan
J Theor Biol 243:8697. 2006..We discuss the application of our theory to four particular examples, the Prisoner's Dilemma, the SnowDrift game, a coordination game and the RockScissorsPaper game...
Research Grants
 Evolutionary Graph Theory and Its ApplicationsMartin Nowak; Fiscal Year: 2007..The results promise a new structuralevolutionary framework for understanding processes that are of vital importance to medicine. ..
 Evolutionary Graph Theory and Its ApplicationsMartin Nowak; Fiscal Year: 2009..The results promise a new structuralevolutionary framework for understanding processes that are of vital importance to medicine. ..