Mutation-selection equilibrium in games with multiple strategies (2009)
Antal, Tibor, Traulsen, Arne, Ohtsuki, Hisashi, Tarnita, Corina E., Nowak, Martin A.
In evolutionary games the fitness of individuals is not constant but depends on the relative abundance of the various strategies in the population. Here we study general games among n strategies in...
The pace of evolution across fitness valleys (2009)
Gokhale, Chaitanya S., Iwasa, Yoh, Nowak, Martin A., Traulsen, Arne
How fast does a population evolve from one fitness peak to another? We study the dynamics of evolving, asexually reproducing populations in which a certain number of mutations jointly confer a...
Mutation-selection equilibrium in games with multiple strategies (2008)
Antal, Tibor, Traulsen, Arne, Ohtsuki, Hisashi, Tarnita, Corina E., Nowak, Martin A.
In evolutionary games the fitness of individuals is not constant but depends on the relative abundance of the various strategies in the population. Here we study general games among n strategies in...
Strategy abundance in 2x2 games for arbitrary mutation rates (2008)
Antal, Tibor, Nowak, Martin A., Traulsen, Arne
We study evolutionary game dynamics in a well-mixed populations of finite size, N. A well-mixed population means that any two individuals are equally likely to interact. In particular we consider the...
Evolutionary game dynamics in phenotype space (2008)
Antal, Tibor, Ohtsuki, Hisashi, Wakeley, John, Taylor, Peter D., Nowak, Martin A.
Evolutionary dynamics can be studied in well-mixed or structured populations. Population structure typically arises from the heterogeneous distribution of individuals in physical space or on social...
Comparative lesion sequencing provides insights into tumor evolution (2008)
Jones, Siân, Chen, Wei-dong, Parmigiana, Giovanni, Diehl, Frank, Beerenwinkel, Niko, Antal, Tibor, ...
We show that the times separating the birth of benign, invasive, and metastatic tumor cells can be determined by analysis of the mutations they have in common. When combined with prior clinical...
Analytical results for individual and group selection of any intensity (2008)
Traulsen, Arne, Shoresh, Noam, Nowak, Martin A.
The idea of evolutionary game theory is to relate the payoff of a game to reproductive success (=fitness). An underlying assumption in most models is that fitness is a linear function of the payoff....
Public goods with punishment and abstaining in finite and infinite populations (2008)
Hauert, Christoph, Traulsen, Arne, Nowak, Martin A, Sigmund, Karl
The evolution and maintenance of cooperation in human and animal societies challenge various disciplines ranging from evolutionary biology to anthropology, social sciences, and economics. In social...
Strategy abundance in 2 x 2 games for arbitrary mutation rates (2008)
Antal, Tibor, Nowak, Martin A., Traulsen, Arne
We study evolutionary game dynamics in a well-mixed populations of finite size, N. A well-mixed population means that any two individuals are equally likely to interact. In particular we consider the...
Natalia L. Komarova, Martin A. Nowak
selection of the critical period for language acquisition
Genetic Progression and the Waiting Time to Cancer (2007)
Niko Beerenwinkel, Tibor Antal, David Dingli, Arne Traulsen, Kenneth W. Kinzler, Victor E. Velculescu, ...
Cancer results from genetic alterations that disturb the normal cooperative behavior of cells. Recent high-throughput genomic studies of cancer cells have shown that the mutational landscape of...
Phenotypic Mutation Rates and the Abundance of Abnormal Proteins in Yeast (2007)
Martin Willensdorfer, Reinhard Bürger, Martin A. Nowak
Phenotypic mutations are errors that occur during protein synthesis. These errors lead to amino acid substitutions that give rise to abnormal proteins. Experiments suggest that such errors are quite...
Genetic progression and the waiting time to cancer (2007)
Beerenwinkel, Niko, Antal, Tibor, Dingli, David, Traulsen, Arne, Kinzler, Kenneth W., Velculescu, Victor E., ...
Cancer results from genetic alterations that disturb the normal cooperative behavior of cells. Recent high-throughput genomic studies of cancer cells have shown that the mutational landscape of...
Co-evolution of strategy and structure in complex networks with dynamical linking (2007)
Pacheco, Jorge M., Traulsen, Arne, Nowak, Martin A.
Here we introduce a model in which individuals differ in the rate at which they seek new interactions with others, making rational decisions modeled as general symmetric two-player games. Once a link...
The fastest evolutionary trajectory (2007)
Traulsen, Arne, Iwasa, Yoh, Nowak, Martin A.
Given two mutants, A and B, separated by n mutational steps, what is the evolutionary trajectory which allows a homogeneous population of A to reach B in the shortest time? We show that the optimum...
Genetic progression and the waiting time to cancer (2007)
Beerenwinkel, Niko, Antal, Tibor, Dingli, David, Traulsen, Arne, Kinzler, Kenneth W., Velculescu, Victor E., ...
Cancer results from genetic alterations that disturb the normal cooperative behavior of cells. Recent high-throughput genomic studies of cancer cells have shown that the mutational landscape of...
Stochastic Dynamics of Invasion and Fixation (2006)
Traulsen, Arne, Nowak, Martin A., Pacheco, Jorge M.
We study evolutionary game dynamics in finite populations. We analyze an evolutionary process, which we call pairwise comparison, for which we adopt the ubiquitous Fermi distribution function from...
Stochastic Evolution as a Generalized Moran Process (2004)
Drew Fudenberg, Lorens Imhof, Martin A. Nowak, Christine Taylor
This paper proposes and analyzes a model of stochastic evolution in finite populations. The expected motion in our model resembles the standard replicator dynamic when the population is large, but is...
Competitive exclusion and coexistence of universal grammars (2003)
W. Garrett Mitchener, Martin A. Nowak
Universal grammar(UG) is a list of innate constraints that specify the set of grammars that can be learned by the child during primary language acquisition. UG of the human brain has been shaped by...
Major Transitions in Language Evolution (2001)
Joshua B. Plotkin, Martin A. Nowak
Abstract: Language is the most important evolutionary invention of the last few million years. How human language evolved from animal communication is a challenging question for evolutionary biology....
EVOLUTION OF VIRULENCE IN A HETEROGENEOUS HOST POPULATION (2000)
Roland R. Regoes, Martin A. Nowak, Sebastian Bonhoeffer
There is a large body of theoretical studies that investigate factors that affect the evolution of virulence, that is parasite-induced host mortality. In these studies the host population is assumed...
The role of antigen-independent persistence of memory cytotoxic T lymphocytes (2000)
Wodarz, Dominik, May, Robert M., Nowak, Martin A.
We use mathematical models to analyze the role of a memory cytotoxic T lymphocyte (CTL) response in viral infections. The model predicts that antigen-independent persistence of an elevated number of...
The Mathematical Biology of Human Infections (1999)
Nowak, Martin A; Institute For Advanced Study; Nowak@ias.edu
Humans are constant victims of infectious diseases. Biomedical research during this century has led to important insights into the molecular details of immune defense. Yet, many questions relating to...
The Mathematical Biology of Human Infections (1999)
"Humans are constant victims of infectious diseases. Biomedical research during this century has led to important insights into the molecular details of immune defense. Yet, many questions relating...
Article No. jt980775 The Dynamics of Indirect Reciprocity (1998)
Richard Alexander has argued that moral systems derive from indirect reciprocity. We analyse a simple case of a model of indirect reciprocity based on image scoring. Discriminators provide help to...
Evolution of Indirect Reciprocity by Image Scoring / The Dynamics of Indirect Reciprocity (1998)
The question of cooperation is crucial for understanding Darwinian evolution. Theories of cooperation have been based on kin selection 1,2 , group selection 3-5 , and reciprocal altruism 6-9 .Theidea...
Equal Pay for all Prisoners / The Logic of Contrition (1997)
Maarten C. Boerlijst, Martin A. Nowak, Karl Sigmund
This report deals with two questions concerning the emergence of cooperative strategies in repeated games. The first part is concerned with the Perfect Folk Theorem and presents a vast class of...
Dynamic multidrug therapies for HIV : a control theoretic approach (1995)
Wein, Lawrence M., Zenios, Stefanos, Nowak, Martin A.
Cover title.
A simple relationship between viral load and survival time in HIV-1 infection
Arnaout, Ramy A., Lloyd, Alun L., O’Brien, Thomas R., Goedert, James J., Leonard, John M., Nowak, Martin A.
Despite important recent insights into the short-term dynamics of HIV-1 infection, our understanding of the long-term pathogenesis of AIDS remains unclear. Using an approach that places rapid...
Virus dynamics and drug therapy
Bonhoeffer, Sebastian, May, Robert M., Shaw, George M., Nowak, Martin A.
The recent development of potent antiviral drugs not only has raised hopes for effective treatment of infections with HIV or the hepatitis B virus, but also has led to important quantitative insights...
Nowak, Martin A., Krakauer, David C.
The emergence of language was a defining moment in the evolution of modern humans. It was an innovation that changed radically the character of human society. Here, we provide an approach to language...
Jeffery, Katie J. M., Usuku, Koichiro, Hall, Sarah E., Matsumoto, Wataru, Taylor, Graham P., Procter, Jeanette, ...
The risk of disease associated with persistent virus infections such as HIV-I, hepatitis B and C, and human T-lymphotropic virus-I (HTLV-I) is strongly determined by the virus load. However, it is...
Presence of an inducible HIV-1 latent reservoir during highly active antiretroviral therapy
Chun, Tae-Wook, Stuyver, Lieven, Mizell, Stephanie B., Ehler, Linda A., Mican, Jo Ann M., Baseler, Michael, ...
Although highly active antiretroviral therapy (HAART) in the form of triple combinations of drugs including protease inhibitors can reduce the plasma viral load of some HIV-1-infected individuals to...
Specific therapy regimes could lead to long-term immunological control of HIV
Wodarz, Dominik, Nowak, Martin A.
We use mathematical models to study the relationship between HIV and the immune system during the natural course of infection and in the context of different antiviral treatment regimes. The models...
Predicting species diversity in tropical forests
Plotkin, Joshua B., Potts, Matthew D., Yu, Douglas W., Bunyavejchewin, Sarayudh, Condit, Richard, Foster, Robin, ...
A fundamental question in ecology is how many species occur within a given area. Despite the complexity and diversity of different ecosystems, there exists a surprisingly simple, approximate answer:...
Sigmund, Karl, Hauert, Christoph, Nowak, Martin A.
Minigames capturing the essence of Public Goods experiments show that even in the absence of rationality assumptions, both punishment and reward will fail to bring about prosocial behavior. This...
Lifson, Jeffrey D., Rossio, Jeffrey L., Arnaout, Ramy, Li, Li, Parks, Thomas L., Schneider, Douglas K., ...
To better understand the viral and host factors involved in the establishment of persistent productive infection by primate lentiviruses, we varied the time of initiation and duration of...
Lifson, Jeffrey D., Rossio, Jeffrey L., Piatak, Michael, Parks, Thomas, Li, Li, Kiser, Rebecca, ...
Transient antiretroviral treatment with tenofovir, (R)-9-(2-phosphonylmethoxypropyl)adenine, begun shortly after inoculation of rhesus macaques with the highly pathogenic simian immunodeficiency...
Compromised Influenza Virus-Specific CD8+-T-Cell Memory in CD4+-T-Cell-Deficient Mice
Belz, Gabrielle T., Wodarz, Dominik, Diaz, Gabriela, Nowak, Martin A., Doherty, Peter C.
The primary influenza A virus-specific CD8+-T-cell responses measured by tetramer staining of spleen, lymph node, and bronchoalveolar lavage (BAL) lymphocyte populations were similar in magnitude for...
The role of chromosomal instability in tumor initiation
Nowak, Martin A., Komarova, Natalia L., Sengupta, Anirvan, Jallepalli, Prasad V., Shih, Ie-Ming, Vogelstein, Bert, ...
Chromosomal instability (CIN) is a defining characteristic of most human cancers. Mutation of CIN genes increases the probability that whole chromosomes or large fractions of chromosomes are gained...
The linear process of somatic evolution
Nowak, Martin A., Michor, Franziska, Iwasa, Yoh
Cancer is the consequence of an unwanted evolutionary process. Cells receive mutations that alter their phenotype. Especially dangerous are those mutations that increase the net reproductive rate of...
Evolutionary dynamics of tumor suppressor gene inactivation
Nowak, Martin A., Michor, Franziska, Komarova, Natalia L., Iwasa, Yoh
Tumor suppressor genes (TSGs) are important gatekeepers that protect against somatic evolution of cancer. Losing both alleles of a TSG in a single cell represents a step toward cancer. We study how...
Win–stay, lose–shift in language learning from peers
Matsen, Frederick A., Nowak, Martin A.
Traditional language learning theory explores an idealized interaction between a teacher and a learner. The teacher provides sentences from a language, while the learner has to infer the underlying...
Evolutionary cycles of cooperation and defection
Imhof, Lorens A., Fudenberg, Drew, Nowak, Martin A.
The main obstacle for the evolution of cooperation is that natural selection favors defection in most settings. In the repeated prisoner's dilemma, two individuals interact several times, and, in...
Why Are Phenotypic Mutation Rates Much Higher Than Genotypic Mutation Rates?
Bürger, Reinhard, Willensdorfer, Martin, Nowak, Martin A.
The evolution of genotypic mutation rates has been investigated in numerous theoretical and experimental studies. Mutations, however, occur not only when copying DNA, but also when building the...
Evolution of Resistance During Clonal Expansion
Iwasa, Yoh, Nowak, Martin A., Michor, Franziska
Acquired drug resistance is a major limitation for cancer therapy. Often, one genetic alteration suffices to confer resistance to an otherwise successful therapy. However, little is known about the...
Patterns of cell division and the risk of cancer.
Frank, Steven A, Iwasa, Yoh, Nowak, Martin A
Epidermal and intestinal tissues divide throughout life to replace lost surface cells. These renewing tissues have long-lived basal stem cell lineages that divide many times, each division producing...
Stochastic tunnels in evolutionary dynamics.
Iwasa, Yoh, Michor, Franziska, Nowak, Martin A
We study a situation that arises in the somatic evolution of cancer. Consider a finite population of replicating cells and a sequence of mutations: type 0 can mutate to type 1, which can mutate to...
Evolution of cooperation by multilevel selection
Traulsen, Arne, Nowak, Martin A.
We propose a minimalist stochastic model of multilevel (or group) selection. A population is subdivided into groups. Individuals interact with other members of the group in an evolutionary game that...
Stochastic elimination of cancer cells.
Michor, Franziska, Nowak, Martin A, Frank, Steven A, Iwasa, Yoh
Tissues of multicellular organisms consist of stem cells and differentiated cells. Stem cells divide to produce new stem cells or differentiated cells. Differentiated cells divide to produce new...
Evolutionary dynamics of escape from biomedical intervention.
Iwasa, Yoh, Michor, Franziska, Nowak, Martin A
Viruses, bacteria, eukaryotic parasites, cancer cells, agricultural pests and other inconvenient animates have an unfortunate tendency to escape from selection pressures that are meant to control...
Mitchener, W Garrett, Nowak, Martin A
Human language is a complex communication system with unlimited expressibility. Children spontaneously develop a native language by exposure to linguistic data from their speech community. Over...
The age incidence of chronic myeloid leukemia can be explained by a one-mutation model
Michor, Franziska, Iwasa, Yoh, Nowak, Martin A.
Chronic myeloid leukemia (CML) is associated with the Philadelphia chromosome, which arises by a reciprocal translocation between chromosomes 9 and 22 and harbors the BCR-ABL fusion oncogene. It is...
Ohtsuki, Hisashi, Nowak, Martin A
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...
Genetic Progression and the Waiting Time to Cancer
Beerenwinkel, Niko, Antal, Tibor, Dingli, David, Traulsen, Arne, Kinzler, Kenneth W, Velculescu, Victor E, ...
Cancer results from genetic alterations that disturb the normal cooperative behavior of cells. Recent high-throughput genomic studies of cancer cells have shown that the mutational landscape of...
Phenotypic Mutation Rates and the Abundance of Abnormal Proteins in Yeast
Willensdorfer, Martin, Bürger, Reinhard, Nowak, Martin A
Phenotypic mutations are errors that occur during protein synthesis. These errors lead to amino acid substitutions that give rise to abnormal proteins. Experiments suggest that such errors are quite...
Upstream reciprocity and the evolution of gratitude
Nowak, Martin A, Roch, Sébastien
If someone is nice to you, you feel good and may be inclined to be nice to somebody else. This every day experience is borne out by experimental games: the recipients of an act of kindness are more...
Jones, Nicola A., Wei, Xiping, Flower, Darren R., Wong, MaiLee, Michor, Franziska, Saag, Michael S., ...
CD8+ cytotoxic T lymphocytes (CTLs) play an important role in containment of virus replication in primary human immunodeficiency virus (HIV) infection. HIV's ability to mutate to escape from CTL...
Hockett, Richard D., Michael Kilby, J., Derdeyn, Cynthia A., Saag, Michael S., Sillers, Michael, Squires, Kathleen, ...
Quantitative analysis of the relationship between virus expression and disease outcome has been critical for understanding HIV-1 pathogenesis. Yet the amount of viral RNA contained within an...
Pinker, Steven, Nowak, Martin A., Lee, James J.
When people speak, they often insinuate their intent indirectly rather than stating it as a bald proposition. Examples include sexual come-ons, veiled threats, polite requests, and concealed bribes....
Comparative lesion sequencing provides insights into tumor evolution
Jones, Siân, Chen, Wei-dong, Parmigiani, Giovanni, Diehl, Frank, Beerenwinkel, Niko, Antal, Tibor, ...
We show that the times separating the birth of benign, invasive, and metastatic tumor cells can be determined by analysis of the mutations they have in common. When combined with prior clinical...
Prevolutionary dynamics and the origin of evolution
Nowak, Martin A., Ohtsuki, Hisashi
Life is that which replicates and evolves. The origin of life is also the origin of evolution. A fundamental question is when do chemical kinetics become evolutionary dynamics? Here, we formulate a...
Exploration dynamics in evolutionary games
Traulsen, Arne, Hauert, Christoph, De Silva, Hannelore, Nowak, Martin A., Sigmund, Karl
Evolutionary game theory describes systems where individual success is based on the interaction with others. We consider a system in which players unconditionally imitate more successful strategies...
Spatial dynamics of ecological public goods
Wakano, Joe Yuichiro, Nowak, Martin A., Hauert, Christoph
The production, consumption, and exploitation of common resources ranging from extracellular products in microorganisms to global issues of climate change refer to public goods interactions....