Martin Nowak

Summary

Affiliation: Harvard University
Country: USA

Publications

  1. ncbi request reprint Theory is available light
    Martin A Nowak
    Program for Evolutionary Dynamics, Department of Organismic and Evolutionary Biology, Harvard University, Cambridge, Massachusetts 02138, USA
    Curr Biol 14:R406-7. 2004
  2. pmc Evolutionary dynamics of cancer in response to targeted combination therapy
    Ivana Bozic
    Program for Evolutionary Dynamics, Harvard University, Cambridge, United States Department of Mathematics, Harvard University, Cambridge, United States
    elife 2:e00747. 2013
  3. pmc The effect of one additional driver mutation on tumor progression
    Johannes G Reiter
    IST Austria Institute of Science and Technology Austria Klosterneuburg, Austria
    Evol Appl 6:34-45. 2013
  4. pmc Forgiver triumphs in alternating Prisoner's Dilemma
    Benjamin M Zagorsky
    Program for Evolutionary Dynamics, Harvard University, Cambridge, Massachusetts, United States of America
    PLoS ONE 8:e80814. 2013
  5. pmc Five rules for the evolution of cooperation
    Martin A Nowak
    Program for Evolutionary Dynamics, Department of Organismic and Evolutionary Biology, and Department of Mathematics, Harvard University, Cambridge, MA 02138, USA
    Science 314:1560-3. 2006
  6. pmc Upstream reciprocity and the evolution of gratitude
    Martin A Nowak
    Program for Evolutionary Dynamics, Department of Organismic and Evolutionary Biology, Harvard University, Cambridge, MA 02138, USA
    Proc Biol Sci 274:605-9. 2007
  7. pmc Genetic instability and clonal expansion
    Martin A Nowak
    Program for Evolutionary Dynamics, Department of Organismic and Evolutionary Biology, Harvard University, Cambridge, MA 02138, USA
    J Theor Biol 241:26-32. 2006
  8. ncbi request reprint Emergence of cooperation and evolutionary stability in finite populations
    Martin A Nowak
    Program for Evolutionary Dynamics, Harvard University, Cambridge, Massachusetts 02138, USA
    Nature 428:646-50. 2004
  9. ncbi request reprint Evolutionary dynamics of biological games
    Martin 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 303:793-9. 2004
  10. pmc Evolutionary dynamics in structured populations
    Martin A Nowak
    Department of Mathematics, Harvard University, Cambridge, MA 02138, USA
    Philos Trans R Soc Lond B Biol Sci 365:19-30. 2010

Research Grants

  1. Evolutionary Graph Theory and Its Applications
    Martin Nowak; Fiscal Year: 2006
  2. Evolutionary Graph Theory and Its Applications
    Martin Nowak; Fiscal Year: 2007
  3. Evolutionary Graph Theory and Its Applications
    Martin Nowak; Fiscal Year: 2009

Detail Information

Publications85

  1. ncbi request reprint Theory is available light
    Martin A Nowak
    Program for Evolutionary Dynamics, Department of Organismic and Evolutionary Biology, Harvard University, Cambridge, Massachusetts 02138, USA
    Curr Biol 14:R406-7. 2004
  2. pmc Evolutionary dynamics of cancer in response to targeted combination therapy
    Ivana Bozic
    Program for Evolutionary Dynamics, Harvard University, Cambridge, United States Department of Mathematics, Harvard University, Cambridge, United States
    elife 2:e00747. 2013
    ..Our results provide realistic expectations for the efficacy of new drug combinations and inform the design of trials for new cancer therapeutics. DOI:http://dx.doi.org/10.7554/eLife.00747.001. ..
  3. pmc The effect of one additional driver mutation on tumor progression
    Johannes G Reiter
    IST Austria Institute of Science and Technology Austria Klosterneuburg, Austria
    Evol Appl 6:34-45. 2013
    ..These results help to explain why additional driver mutations are typically not detected in fast-growing metastases...
  4. pmc Forgiver triumphs in alternating Prisoner's Dilemma
    Benjamin M Zagorsky
    Program for Evolutionary Dynamics, Harvard University, Cambridge, Massachusetts, United States of America
    PLoS ONE 8:e80814. 2013
    ..Our results show that although forgiving might incur a short-term loss it can lead to a long-term gain. Forgiveness facilitates stable cooperation in the presence of exploitation and noise. ..
  5. pmc Five rules for the evolution of cooperation
    Martin A Nowak
    Program for Evolutionary Dynamics, Department of Organismic and Evolutionary Biology, and Department of Mathematics, Harvard University, Cambridge, MA 02138, USA
    Science 314:1560-3. 2006
    ..For each mechanism, a simple rule is derived that specifies whether natural selection can lead to cooperation...
  6. pmc Upstream reciprocity and the evolution of gratitude
    Martin A Nowak
    Program for Evolutionary Dynamics, Department of Organismic and Evolutionary Biology, Harvard University, Cambridge, MA 02138, USA
    Proc Biol Sci 274:605-9. 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...
  7. pmc Genetic instability and clonal expansion
    Martin A Nowak
    Program for Evolutionary Dynamics, Department of Organismic and Evolutionary Biology, Harvard University, Cambridge, MA 02138, USA
    J Theor Biol 241:26-32. 2006
    ....
  8. ncbi request reprint Emergence of cooperation and evolutionary stability in finite populations
    Martin A Nowak
    Program for Evolutionary Dynamics, Harvard University, Cambridge, Massachusetts 02138, USA
    Nature 428:646-50. 2004
    ..We specify the conditions required for natural selection to favour the emergence of cooperation and define evolutionary stability in finite populations...
  9. ncbi request reprint Evolutionary dynamics of biological games
    Martin 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 303:793-9. 2004
    ..Evolutionary game theory is an essential component of a mathematical and computational approach to biology...
  10. pmc Evolutionary dynamics in structured populations
    Martin A Nowak
    Department of Mathematics, Harvard University, Cambridge, MA 02138, USA
    Philos Trans R Soc Lond B Biol Sci 365:19-30. 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...
  11. pmc The evolution of eusociality
    Martin A Nowak
    Program for Evolutionary Dynamics, Department of Mathematics, Harvard University, Cambridge, Massachusetts 02138, USA
    Nature 466:1057-62. 2010
    ....
  12. pmc Prevolutionary dynamics and the origin of evolution
    Martin 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 105:14924-7. 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...
  13. pmc Via freedom to coercion: the emergence of costly punishment
    Christoph Hauert
    Program for Evolutionary Dynamics, Department of Organismic and Evolutionary Biology, Department of Mathematics, Harvard University, Cambridge, MA 02138, USA
    Science 316:1905-7. 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...
  14. pmc Evolutionary graph theory: breaking the symmetry between interaction and replacement
    Hisashi Ohtsuki
    Program for Evolutionary Dynamics, Harvard University, Cambridge MA 02138, USA
    J Theor Biol 246:681-94. 2007
    ....
  15. pmc Accumulation of driver and passenger mutations during tumor progression
    Ivana Bozic
    Program for Evolutionary Dynamics, Harvard University, Cambridge, MA 02138, USA
    Proc Natl Acad Sci U S A 107:18545-50. 2010
    ..This selective advantage is surprisingly small--0.004 ± 0.0004--and has major implications for experimental cancer research...
  16. pmc Analytical results for individual and group selection of any intensity
    Arne Traulsen
    Program for Evolutionary Dynamics, Department of Organismic and Evolutionary Biology, Department of Mathematics, Harvard University, Cambridge, MA, 02138, USA
    Bull Math Biol 70:1410-24. 2008
    ..This approach also works for group selection (= multi-level selection). We discuss the difference between our approach and that of inclusive fitness theory...
  17. ncbi request reprint Evolutionary dynamics on graphs
    Erez Lieberman
    Program for Evolutionary Dynamics, Department of Organismic and Evolutionary Biology, Harvard University, Cambridge, Massachusetts 02138, USA
    Nature 433:312-6. 2005
    ..Evolutionary graph theory has many fascinating applications ranging from ecology to multi-cellular organization and economics...
  18. pmc Winners don't punish
    Anna Dreber
    Program for Evolutionary Dynamics, Harvard University, Cambridge, Massachusetts 02138, USA
    Nature 452:348-51. 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...
  19. pmc Reputation-based partner choice promotes cooperation in social networks
    Feng 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...
  20. pmc Evolutionary dynamics on graphs: Efficient method for weak selection
    Feng 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...
  21. ncbi request reprint Prisoners of the dilemma
    Martin A Nowak
    Program for Evolutionary Dynamics, One Brattle Square, Harvard University, Cambridge, Massachusetts 02138, USA
    Nature 427:491. 2004
  22. pmc Stochastic dynamics of invasion and fixation
    Arne Traulsen
    Program for Evolutionary Dynamics, Harvard University, Cambridge, Massachusetts 02138, USA
    Phys Rev E Stat Nonlin Soft Matter Phys 74:011909. 2006
    ....
  23. pmc Chromodynamics of cooperation in finite populations
    Arne 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...
  24. pmc Pairwise comparison and selection temperature in evolutionary game dynamics
    Arne Traulsen
    Program for Evolutionary Dynamics, Harvard University, One Brattle Square, Cambridge, MA 02138, USA
    J Theor Biol 246:522-9. 2007
    ..For some payoff matrices the distribution of fixation times can become so broad that the average value is no longer very meaningful...
  25. pmc Infectious disease modeling of social contagion in networks
    Alison 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...
  26. pmc Digital cows grazing on digital grounds
    Thomas Pfeiffer
    Program for Evolutionary Dynamics, Department of Organismic and Evolutionary Biology, Harvard University, Cambridge, Massachusetts 02138, USA
    Curr Biol 16:R946-9. 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.....
  27. pmc Transforming the dilemma
    Christine Taylor
    Program for Evolutionary Dynamics, Department of Organismic and Evolutionary Biology, Harvard University, Cambridge, MA 02138, USA
    Evolution 61:2281-92. 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...
  28. pmc The one-third law of evolutionary dynamics
    Hisashi Ohtsuki
    Program for Evolutionary Dynamics, Harvard University, Cambridge, MA 02138, USA
    J Theor Biol 249:289-95. 2007
    ..We also show that the one-third law implies that the average Malthusian fitness of A is positive...
  29. pmc The fastest evolutionary trajectory
    Arne Traulsen
    Program for Evolutionary Dynamics, Harvard University, Cambridge, MA 02138, USA
    J Theor Biol 249:617-23. 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...
  30. pmc Phenotypic mutation rates and the abundance of abnormal proteins in yeast
    Martin 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)...
  31. pmc Invasion and expansion of cooperators in lattice populations: prisoner's dilemma vs. snowdrift games
    Feng Fu
    Program for Evolutionary Dynamics, Harvard University, Cambridge, MA 02138, USA
    J Theor Biol 266:358-66. 2010
    ....
  32. pmc Mutation-selection equilibrium in games with mixed strategies
    Corina E Tarnita
    Program for Evolutionary Dynamics, Department of Mathematics, Harvard University, Cambridge, MA 02138, USA
    J Theor Biol 261:50-7. 2009
    ..The result for any mutation rate is a linear combination of those two. As a specific example we study the Hawk-Dove game. We prove general statements about the relationship between games with pure and with mixed strategies...
  33. pmc Evolution of cooperation by phenotypic similarity
    Tibor Antal
    Program for Evolutionary Dynamics and Department of Mathematics, Harvard University, Cambridge, MA 02138, USA
    Proc Natl Acad Sci U S A 106:8597-600. 2009
    ..We also derive the fundamental condition for any two-strategy symmetric game and consider high-dimensional phenotype spaces...
  34. pmc Strategy selection in structured populations
    Corina E Tarnita
    Program for Evolutionary Dynamics, Department of Mathematics, Harvard University, Cambridge, MA 02138, USA
    J Theor Biol 259:570-81. 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...
  35. pmc Emotions as infectious diseases in a large social network: the SISa model
    Alison L Hill
    Program for Evolutionary Dynamics, Berkman Center for Internet and Society, Department of Mathematics, Harvard University, Cambridge, MA 02138, USA
    Proc Biol Sci 277:3827-35. 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...
  36. pmc Mutation-selection equilibrium in games with multiple strategies
    Tibor Antal
    Program for Evolutionary Dynamics, Department of Mathematics, Harvard University, Cambridge, MA 02138, USA
    J Theor Biol 258:614-22. 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...
  37. pmc Strategy abundance in 2x2 games for arbitrary mutation rates
    Tibor Antal
    Harvard University, Cambridge, MA 02138, USA
    J Theor Biol 257:340-4. 2009
    ..Here we show that this result holds in fact for a wide class of stochastic birth-death processes for arbitrary mutation rate and for any intensity of selection...
  38. pmc Direct reciprocity with costly punishment: generous tit-for-tat prevails
    David G Rand
    Program for Evolutionary Dynamics, Harvard University, Cambridge MA 02138, USA
    J Theor Biol 256:45-57. 2009
    ..We find quantitative agreement between our simulation results and data from experimental observations...
  39. pmc Evolutionary stability on graphs
    Hisashi Ohtsuki
    Program for Evolutionary Dynamics, Harvard University, Cambridge, MA 02138, USA
    J Theor Biol 251:698-707. 2008
    ..Evolutionary stability on sparse graphs does not imply evolutionary stability in a well-mixed population, nor vice versa. We provide a geometrical interpretation of the ESS condition on graphs...
  40. pmc The logic of indirect speech
    Steven Pinker
    Department of Psychology, and Program for Evolutionary Dynamics, Harvard University, Cambridge, MA 02138, USA
    Proc Natl Acad Sci U S A 105:833-8. 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...
  41. pmc Spatial invasion of cooperation
    Philipp Langer
    Program for Evolutionary Dynamics, Department of Organismic and Evolutionary Biology, Harvard University, One Brattle Square, Cambridge, MA 02138, USA
    J Theor Biol 250:634-41. 2008
    ....
  42. pmc The age incidence of chronic myeloid leukemia can be explained by a one-mutation model
    Franziska Michor
    Program for Evolutionary Dynamics, Department of Mathematics, Harvard University, Cambridge, MA 02138, USA
    Proc Natl Acad Sci U S A 103:14931-4. 2006
    ..Therefore, the CML incidence data are consistent with the hypothesis that the Philadelphia translocation alone is sufficient to cause chronic phase CML...
  43. pmc Evolutionary game dynamics in finite populations with strong selection and weak mutation
    Drew Fudenberg
    Department of Economics, Harvard University, Cambridge, MA 02138, USA
    Theor Popul Biol 70:352-63. 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...
  44. pmc Stochastic payoff evaluation increases the temperature of selection
    Arne Traulsen
    Program for Evolutionary Dynamics, Harvard University, Cambridge, MA 02138, USA
    J Theor Biol 244:349-56. 2007
    ..A simple mean-field approximation is derived that captures the average effect of the payoff stochasticity. Correction terms to the mean-field theory are computed and discussed...
  45. ncbi request reprint Stochastic dynamics of metastasis formation
    Franziska Michor
    Program for Evolutionary Dynamics, Department of Organismic and Evolutionary Biology, Department of Mathematics, Harvard University, Cambridge, MA 02138, USA
    J Theor Biol 240:521-30. 2006
    ..Our theory shows how to calculate the expected number of metastases that are formed by a tumor...
  46. pmc Synergy and discounting of cooperation in social dilemmas
    Christoph Hauert
    Department of Zoology, University of British Columbia, 6270 University Boulevard, Vancouver BC, Canada V6T 1Z4
    J Theor Biol 239:195-202. 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...
  47. ncbi request reprint 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 15:43-9. 2005
    ..If two tumor suppressor genes have to be inactivated in rate-limiting steps, then CIN is likely to emerge before the inactivation of the first tumor suppressor gene...
  48. ncbi request reprint Dynamics of colorectal cancer
    Franziska Michor
    Program for Evolutionary Dynamics, Department of Organismic and Evolutionary Biology, Harvard University, Cambridge, MA 02138, USA
    Semin Cancer Biol 15:484-93. 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...
  49. ncbi request reprint Dynamics of chronic myeloid leukaemia
    Franziska Michor
    Program for Evolutionary Dynamics, Department of Organismic and Evolutionary Biology, Department of Mathematics, Harvard University, Cambridge, Massachusetts 02138, USA
    Nature 435:1267-70. 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...
  50. ncbi request reprint Local regulation of homeostasis favors chromosomal instability
    Franziska Michor
    Department of Organismic and Evolutionary Biology, Harvard University, Cambridge, MA 02138, USA
    Curr Biol 13:581-4. 2003
    ..Thus, small compartments protect against mutations in tumor suppressor genes or oncogenes but promote the emergence of genetic instability...
  51. ncbi request reprint Evolutionary game dynamics in finite populations
    Christine Taylor
    Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
    Bull Math Biol 66:1621-44. 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...
  52. pmc Evolutionary dynamics of tumor suppressor gene inactivation
    Martin A Nowak
    Program for Evolutionary Dynamics, Harvard University, Cambridge, MA 02138, USA
    Proc Natl Acad Sci U S A 101:10635-8. 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...
  53. ncbi request reprint Somatic selection for and against cancer
    Franziska 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 225:377-82. 2003
    ..If both deleterious and advantageous mutations participate in tumor initiation, then we find an intermediate optimum for the compartment size...
  54. pmc The linear process of somatic evolution
    Martin A Nowak
    Program for Evolutionary Dynamics, Harvard University, Cambridge, MA 02138, USA
    Proc Natl Acad Sci U S A 100:14966-9. 2003
    ..This design can slow down the rate of somatic evolution dramatically and therefore delay the onset of cancer...
  55. pmc Evolutionary game dynamics with non-uniform interaction rates
    Christine Taylor
    Program for Evolutionary Dynamics, Department of Mathematics, Department of Organismic and Evolutionary Biology, Harvard University, Cambridge, MA 02138, USA
    Theor Popul Biol 69:243-52. 2006
    ..For the Prisoner's Dilemma, non-uniform interaction rates allow the coexistence between cooperators and defectors. For the snowdrift game, non-uniform interaction rates change the equilibrium frequency of cooperators...
  56. ncbi request reprint Evolution of resistance to cancer therapy
    Franziska Michor
    Program for Evolutionary Dynamics, Department of Organismic and Evolutionary Biology, Department of Mathematics, Harvard University, Cambridge, MA 02138, USA
    Curr Pharm Des 12:261-71. 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...
  57. pmc A symmetry of fixation times in evoultionary dynamics
    Christine Taylor
    Program for Evolutionary Dynamics, Department of Mathematics, Harvard University, Cambridge, MA 02138, USA
    J Theor Biol 243:245-51. 2006
    ..This does not hold for Wright-Fisher models, nor when the mutants start from multiple copies...
  58. pmc Win-stay, lose-shift in language learning from peers
    Frederick 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 101:18053-7. 2004
    ..Moreover, for many graphs, it is sufficient to have an aspiration level demanding only two other individuals to use the same language...
  59. pmc Active linking in evolutionary games
    Jorge M Pacheco
    Program for Evolutionary Dynamics, Harvard University, Cambridge, MA 02138, USA
    J Theor Biol 243:437-43. 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...
  60. pmc Positive interactions promote public cooperation
    David G Rand
    Program for Evolutionary Dynamics, Harvard University, Cambridge, MA 02138, USA
    Science 325:1272-5. 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...
  61. pmc Calculating evolutionary dynamics in structured populations
    Charles 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...
  62. pmc Evolutionary dynamics in set structured populations
    Corina E Tarnita
    Program for Evolutionary Dynamics, Department of Mathematics, Harvard University, Cambridge, MA 02138, USA
    Proc Natl Acad Sci U S A 106:8601-4. 2009
    ..As a particular example, we study the evolution of cooperation and derive precise conditions for cooperators to be selected over defectors...
  63. pmc 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 172:197-206. 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...
  64. pmc Breaking the symmetry between interaction and replacement in evolutionary dynamics on graphs
    Hisashi 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...
  65. pmc Coevolution of strategy and structure in complex networks with dynamical linking
    Jorge 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...
  66. pmc Evolutionary dynamics of escape from biomedical intervention
    Yoh Iwasa
    Department of Biology, Kyushu University, Fukuoka 812 8581, Japan
    Proc Biol Sci 270:2573-8. 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...
  67. ncbi request reprint Cell biology: Developmental predisposition to cancer
    Steven A Frank
    Department of Ecology and Evolutionary Biology, University of California, Irvine, California 92697 2525, USA
    Nature 422:494. 2003
  68. ncbi request reprint Competitive exclusion and coexistence of universal grammars
    W Garrett Mitchener
    Program in Applied and Computational Mathematics, Fine Hall, Washington Road, Princeton, NJ 08544 1000, USA
    Bull Math Biol 65:67-93. 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...
  69. ncbi request reprint Evolution: the good, the bad and the lonely
    Franziska Michor
    Nature 419:677, 679. 2002
  70. ncbi request reprint Mutation-selection networks of cancer initiation: tumor suppressor genes and chromosomal instability
    Natalia L Komarova
    Institute for Advanced Study, Einstein Drive, Princeton, NJ 08540, USA
    J Theor Biol 223:433-50. 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 mutation-selection networks of the somatic evolution of cancer...
  71. pmc The role of chromosomal instability in tumor initiation
    Martin A Nowak
    Institute for Advanced Study, Princeton, NJ 08540, USA
    Proc Natl Acad Sci U S A 99:16226-31. 2002
    ..Specifically, we calculate the conditions for CIN to initiate the process of colorectal tumorigenesis before the inactivation of tumor suppressor genes...
  72. pmc Patterns of cell division and the risk of cancer
    Steven A Frank
    Department of Ecology and Evolutionary Biology, University of California, Irvine, California 92697 2525, USA
    Genetics 163:1527-32. 2003
    ....
  73. ncbi request reprint Problems of somatic mutation and cancer
    Steven A Frank
    Department of Ecology and Evolutionary Biology, University of California, Irvine CA 92717, USA
    Bioessays 26:291-9. 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...
  74. pmc The replicator equation on graphs
    Hisashi Ohtsuki
    Department of Biology, Faculty of Sciences, Kyushu University, Fukuoka 812 8581, Japan
    J Theor Biol 243:86-97. 2006
    ..We discuss the application of our theory to four particular examples, the Prisoner's Dilemma, the Snow-Drift game, a coordination game and the Rock-Scissors-Paper game...
  75. pmc A simple rule for the evolution of cooperation on graphs and social networks
    Hisashi Ohtsuki
    Department of Biology, Kyushu University, Fukuoka 812 8581, Japan
    Nature 441:502-5. 2006
    ..In this case, cooperation can evolve as a consequence of 'social viscosity' even in the absence of reputation effects or strategic complexity...
  76. pmc Evolution of resistance during clonal expansion
    Yoh Iwasa
    Department of Biology, Faculty of Sciences, Kyushu University, Fukuoka, Japan
    Genetics 172:2557-66. 2006
    ..Hence a tumor subject to high rates of apoptosis will show a higher incidence of resistance than expected on its detection size only...
  77. pmc Tit-for-tat or win-stay, lose-shift?
    Lorens A Imhof
    Statistische Abteilung, Universitat Bonn, D 53113 Bonn, Germany
    J Theor Biol 247:574-80. 2007
    ..TFT is never selected in this evolutionary process, but lowers the selection threshold for WSLS...
  78. pmc Evolutionary game dynamics in a Wright-Fisher process
    Lorens A Imhof
    Statistische Abteilung, Universitat Bonn, Germany
    J Math Biol 52:667-81. 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...
  79. ncbi request reprint Stochastic evolutionary dynamics on two levels
    Arne Traulsen
    Institut für Theoretische Physik und Astrophysik, Christian Albrechts Universitat, Olshausenstr 40, D 24098 Kiel, Germany
    J Theor Biol 235:393-401. 2005
    ..We also study opposing selection on two or more levels by analysing the evolutionary dynamics of hierarchically embedded Moran processes...
  80. ncbi request reprint Population genetics of tumor suppressor genes
    Yoh Iwasa
    Department of Biology, Faculty of Sciences, Kyushu University, Hakozoki 6 10 1, Higashi ku, Fukuoka 812 8581, Japan
    J Theor Biol 233:15-23. 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...
  81. pmc Repeated games and direct reciprocity under active linking
    Jorge M Pacheco
    ATP Group and CFTC, Departamento de Física da Faculdade de Ciências, P 1649 003 Lisboa Codex, Portugal
    J Theor Biol 250:723-31. 2008
    ..We derive analytical conditions for evolutionary stability...
  82. ncbi request reprint Computational and evolutionary aspects of language
    Martin A Nowak
    Institute for Advanced Study, Einstein Drive, Princeton, New Jersey 08540, USA
    Nature 417:611-7. 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...
  83. pmc Chaos and language
    W Garrett Mitchener
    Institute for Advanced Study, Princeton University, New Jersey, USA
    Proc Biol Sci 271:701-4. 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...
  84. pmc Stochastic tunnels in evolutionary dynamics
    Yoh Iwasa
    Department of Biology, Kyushu University, Fukuoka 812 8581, Japan
    Genetics 166:1571-9. 2004
    ..Although our theory is developed for cancer genetics, stochastic tunnels are general phenomena that could arise in many circumstances...
  85. pmc Evolutionary games on cycles
    Hisashi Ohtsuki
    Department of Biology, Faculty of Sciences, Kyushu University, Fukuoka 812 8581, Japan
    Proc Biol Sci 273:2249-56. 2006
    ..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...

Research Grants4

  1. Evolutionary Graph Theory and Its Applications
    Martin Nowak; Fiscal Year: 2006
    ..The results promise a new structuralevolutionary framework for understanding processes that are of vital importance to medicine. ..
  2. Evolutionary Graph Theory and Its Applications
    Martin Nowak; Fiscal Year: 2007
    ..The results promise a new structuralevolutionary framework for understanding processes that are of vital importance to medicine. ..
  3. Evolutionary Graph Theory and Its Applications
    Martin Nowak; Fiscal Year: 2009
    ..The results promise a new structuralevolutionary framework for understanding processes that are of vital importance to medicine. ..