M A Nowak

..We argue that grammar originated as a simplified rule system that evolved by natural selection to reduce mistakes in communication. Our theory provides a systematic approach for thinking about the origin and evolution of human language...

..We show that fairness will evolve if the proposer can obtain some information on what deals the responder has accepted in the past. Hence, the evolution of fairness, similarly to the evolution of cooperation, is linked to reputation...

..We calculate the condition under which natural selection favors the emergence of rule-based, generative grammars that underlie complex language...

..I will discuss how natural selection can lead to the emergence of arbitrary signs, the formation of words and syntactic communication...

..This result might explain why only humans evolved syntactic communication and hence complex language...

..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...

..Specifically, we calculate the conditions for CIN to initiate the process of colorectal tumorigenesis before the inactivation of tumor suppressor genes...

..Mistakes increase the overall efficacy of parental and role model learning: in a world with errors evolutionary adaptation is more efficient. Our model also provides a simple explanation why homonomy is common while synonymy is rare...

..Based on our models we suggest conceptual treatment regimes which ensure establishment of CTL memory. This would allow the immune response to control HIV in the long term in the absence of continued therapy...

..We calculate the maximum size of the search space that is compatible with coherent communication in a population. Thus, we specify the conditions for the evolution of universal grammar...

..This result is obtained analytically by means of a Nash equilibrium analysis of language acquisition devices. Interestingly, the evolutionarily stable learning period does not maximize the average fitness of the population...

..We show how mathematical models can help us devise therapy regimens that can restore CTL memory in HIV patients and result in long-term immunological control of the virus in the absence of life-long treatment...

..We propose a method to test this idea, and develop a framework that is readily applicable to treatment of other infections...

..Whether such treatment regimes would lead to long-term immunologic control deserves investigation under carefully controlled conditions...

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..Our analytic investigations are supplemented by numerical simulations that describe both incomplete and incorrect learning, and other extensions...

..These insights are important for understanding the disease process itself and for designing effective treatment regimes...

..We first show that in a non-spatial setting, natural selection chooses the unfair, rational solution. In a spatial setting, however, much fairer outcomes evolve...

..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...

..For a wide range of parameter values, we find support for the radical hypothesis that genetic instability initiates colonic tumorigenesis. We compare sporadic and hereditary forms of colorectal cancer...

..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...

..We find that the loss of DNA repair or the loss of apoptosis both hasten tumorigenesis, but in characteristically different ways...

..We develop a general model of word formation and demonstrate the connection between the error limit and Shannon's noisy coding theorem...

..We derive results specific to the treatment of human immunodeficiency virus infection, but emphasize that our method is applicable to a range of viral or other infections treated by chemotherapy...

..This approach can describe the long-term dynamics of the Ultimatum Game and also explain the evolution of fairness in a one-parameter Ultimatum Game...

..In all cases, some form of symmetry breaking is required to maintain functional redundancy indefinitely...

..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...

..Virus-mediated impairment of specific CTL production in HIV-1 infection can account for the negative correlation observed...

..From these equations, we obtain as special cases adaptive dynamics, evolutionary game dynamics, the Lotka-Volterra equation of ecology and the quasispecies equation of molecular evolution...

..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...

..The complexity of cancer progression can be understood as the result of multiple sequential mutations, each of which has a relatively small but positive effect on net cell growth...

..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...

..Moreover, for many graphs, it is sufficient to have an aspiration level demanding only two other individuals to use the same language...

..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...

..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...

..Our theory shows how to calculate the expected number of metastases that are formed by a tumor...

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..Hence a tumor subject to high rates of apoptosis will show a higher incidence of resistance than expected on its detection size only...

..This does not hold for Wright-Fisher models, nor when the mutants start from multiple copies...

..We also show that the one-third law implies that the average Malthusian fitness of A is positive...

..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...

..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...

..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...

..Although our theory is developed for cancer genetics, stochastic tunnels are general phenomena that could arise in many circumstances...

..Instead, the target of selection is an optimum distribution of mutation rates, a 'mutational quasispecies'...

..Here, we explore experimental and theoretical evidence for the initiation of chromosomal instability in very early colorectal cancers, and reflect on the role that chromosomal instability could have in colorectal tumorigenesis...

..If both deleterious and advantageous mutations participate in tumor initiation, then we find an intermediate optimum for the compartment size...

..This design can slow down the rate of somatic evolution dramatically and therefore delay the onset of cancer...

..Thus, small compartments protect against mutations in tumor suppressor genes or oncogenes but promote the emergence of genetic instability...

..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...

..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...

..This approach also works for group selection (= multi-level selection). We discuss the difference between our approach and that of inclusive fitness theory...

..For each mechanism, a simple rule is derived that specifies whether natural selection can lead to cooperation...

..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...

..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...

..For some payoff matrices the distribution of fixation times can become so broad that the average value is no longer very meaningful...

..TFT is never selected in this evolutionary process, but lowers the selection threshold for WSLS...

..Here we study the Ultimatum Game in an evolutionary context and show that empathy can lead to the evolution of fairness. Empathy means that individuals make offers which they themselves would be prepared to accept...

..We derive analytical conditions for evolutionary stability...

..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...

..Our study provides a quantitative analysis of the regularization process by which ancestral forms gradually yield to an emerging linguistic rule...

..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...

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..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...

..We study the consequences of mutations in different cell types and calculate the conditions for CIN to precede APC inactivation. We find that early emergence of CIN is very likely in colorectal tumorigenesis...

..Evolutionary graph theory has many fascinating applications ranging from ecology to multi-cellular organization and economics...

..We also study opposing selection on two or more levels by analysing the evolutionary dynamics of hierarchically embedded Moran processes...

..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...

..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...

..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...

..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...

..The parameters b and c denote the benefit and cost of the altruistic act, whereas n and m denote the maximum group size and the number of groups. The model can be extended to more than two levels of selection and to include migration...

..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...

..We specify the conditions required for natural selection to favour the emergence of cooperation and define evolutionary stability in finite populations...

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..Our results highlight the importance of the consideration of reputation (indirect reciprocity) on the promotion of cooperation when individuals can adjust their partnerships...