Person: Nowak, Martin
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Nowak
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Nowak, Martin
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Publication Social Dilemmas Among Unequals(Springer Science and Business Media LLC, 2019-08) Hilbe, Christian; Hauser, Oliver; Chatterjee, Krishnendu; Nowak, MartinDirect reciprocity is a powerful mechanism for the evolution of cooperation on the basis of repeated interactions. It requires that interacting individuals are sufficiently equal, such that everyone faces similar consequences when they cooperate or defect. Yet inequality is ubiquitous among humans and is generally considered to undermine cooperation and welfare. Most previous models of reciprocity do not include inequality. These models assume that individuals are the same in all relevant aspects. Here we introduce a general framework to study direct reciprocity among unequal individuals. Our model allows for multiple sources of inequality. Subjects can differ in their endowments, their productivities and in how much they benefit from public goods. We find that extreme inequality prevents cooperation. But if subjects differ in productivity, some endowment inequality can be necessary for cooperation to prevail. Our mathematical predictions are supported by a behavioural experiment in which we vary the endowments and productivities of the subjects. We observe that overall welfare is maximized when the two sources of heterogeneity are aligned, such that more productive individuals receive higher endowments. By contrast, when endowments and productivities are misaligned, cooperation quickly breaks down. Our findings have implications for policy-makers concerned with equity, efficiency and the provisioning of public goods.Publication Evolution of resistance to COVID-19 vaccination with dynamic social distancing(Springer Science and Business Media LLC, 2022-02-24) Lobinska, Gabriela; Pauzner, Ady; Traulsen, Arne; Pilpel, Yitzhak; Nowak, MartinThe greatest hope for a return to normalcy following the COVID-19 pandemic is world-wide vaccination. Yet, a relaxation of social distancing that allows increased transmissibility, coupled with selection pressure due to vaccination, will likely lead to the emergence of vaccine resistance. We analyze the evolutionary dynamics of COVID-19 in the presence of dynamic contact reduction and in response to vaccination. We use infection and vaccination data of six different countries. We show that for slow vaccination, resistance is very likely to appear even if social distancing is maintained. For fast vaccination, the emergence of mutants can be prevented if social distancing is maintained during vaccination. We analyze multiple human factors that affect the evolutionary potential of the virus, including the extent of dynamic social distancing, vaccination campaigns, vaccine design, boosters and vaccine hesitancy. We provide guidelines for policies that aim to minimize the probability of emergence of vaccine resistant variants.Publication Evolution of Delayed Resistance to Immunotherapy in a Melanoma Responder(Springer Nature, 2021-05-03) Liu, David; Lin, Jia-Ren; Robitschek, Emily; Kasumova, Gyulnara; Heyde, Alexander; Shi, Alvin; Kraya, Adam; Zhang, Gao; Moll, Tabea; Frederick, Dennie; Chen, Yu-An; Schapiro, Denis; Ho, Li-Lun; Bi, Kevin; Sahu, Avinash; Mei, Shaolin; Miao, Benchun; Sharova, Tatyana; Alvarez-Breckenridge, Christopher; Stocking, Jackson; Kim, Tommy; Fadden, Riley; Lawrence, Donald; Hoang, Mai; Cahill, Daniel; Maleh Mir, Mohsen; Nowak, Martin; Brastianos, Priscilla; Lian, Christine; Ruppin, Eytan; Izar, Benjamin; Herlyn, Meenhard; Van Allen, Eliezer; Nathanson, Katherine; Flaherty, Keith; Sullivan, Ryan; Kellis, Manolis; Sorger, Peter; Boland, GenevieveDespite initial responses, most melanoma patients develop resistance to immune checkpoint blockade (ICB). To understand the evolution of resistance, we studied 37 tumor samples over 9 years from a metastatic melanoma patient with exceptional response followed by delayed recurrence and death. Phylogenetic analysis revealed co-evolution of 7 lineages with multiple convergent, but independent resistance-associated alterations (RAAs). All recurrent tumors emerged from a lineage characterized by loss of chromosome 15q, with post-treatment clones acquiring additional genomic driver events. Deconvolution of bulk RNAseq and highly-multiplexed immunofluorescence (t-CyCIF) revealed differences in immune composition amongst different lineages. Imaging revealed a vasculogenic mimicry phenotype in NGFR-High tumor cells with high PD-L1 expression in close proximity to immune cells. Rapid autopsy demonstrated 2 distinct NGFR spatial patterns with high polarity and proximity to immune cells in subcutaneous tumors versus a diffuse spatial pattern in lung tumors, suggesting different roles of this neural crest-like program in different tumor microenvironments. Broadly, this study establishes a high-resolution map of the evolutionary dynamics of resistance to ICB, characterizes a de-differentiated, neural crest tumor population in melanoma immunotherapy resistance, and describes site specific differences in tumor-immune interactions via longitudinal analysis of a melanoma patient with an unusual clinical course.Publication A Unified Framework of Direct and Indirect Reciprocity(Springer Science and Business Media LLC, 2021-05-13) Schmid, Laura; Chatterjee, Krishnendu; Hilbe, Christian; Nowak, MartinDirect and indirect reciprocity are key mechanisms for evolution of cooperation. Direct reciprocity means individuals use their own experience to decide whether to cooperate with another person. Indirect reciprocity means they also consider the experiences of others. Although the two mechanisms are intertwined, they are typically studied in isolation. Here, we introduce a mathematical framework that allows us to explore both kinds of reciprocity simultaneously. We show that the well-known strategy ‘Generous Tit-for-Tat’ of direct reciprocity has a natural analogue in indirect reciprocity, which we call ‘Generous Scoring’. With an equilibrium analysis, we characterize under which conditions either of the two strategies can maintain cooperation. With simulations, we additionally explore which kind of reciprocity evolves when members of a population engage in social learning to adapt to their environment. We find that indirect reciprocity evolves if any two individuals meet only occasionally, when information about others is reliable, and when strategy mutations are rare. Our results draw unexpected connections between direct and indirect reciprocity, while highlighting important differences regarding their evolvability.Publication An experimental investigation of evolutionary dynamics in the Rock-Paper-Scissors game(Nature Publishing Group, 2015) Hoffman, Moshe; Suetens, Sigrid; Gneezy, Uri; Nowak, MartinGame theory describes social behaviors in humans and other biological organisms. By far, the most powerful tool available to game theorists is the concept of a Nash Equilibrium (NE), which is motivated by perfect rationality. NE specifies a strategy for everyone, such that no one would benefit by deviating unilaterally from his/her strategy. Another powerful tool available to game theorists are evolutionary dynamics (ED). Motivated by evolutionary and learning processes, ED specify changes in strategies over time in a population, such that more successful strategies typically become more frequent. A simple game that illustrates interesting ED is the generalized Rock-Paper-Scissors (RPS) game. The RPS game extends the children's game to situations where winning or losing can matter more or less relative to tying. Here we investigate experimentally three RPS games, where the NE is always to randomize with equal probability, but the evolutionary stability of this strategy changes. Consistent with the prediction of ED we find that aggregate behavior is far away from NE when it is evolutionarily unstable. Our findings add to the growing literature that demonstrates the predictive validity of ED in large-scale incentivized laboratory experiments with human subjects.Publication Evolution and emergence of infectious diseases in theoretical and real-world networks(Nature Pub. Group, 2015) Leventhal, Gabriel E.; Hill, Alison L.; Nowak, Martin; Bonhoeffer, SebastianOne of the most important advancements in theoretical epidemiology has been the development of methods that account for realistic host population structure. The central finding is that heterogeneity in contact networks, such as the presence of ‘superspreaders’, accelerates infectious disease spread in real epidemics. Disease control is also complicated by the continuous evolution of pathogens in response to changing environments and medical interventions. It remains unclear, however, how population structure influences these adaptive processes. Here we examine the evolution of infectious disease in empirical and theoretical networks. We show that the heterogeneity in contact structure, which facilitates the spread of a single disease, surprisingly renders a resident strain more resilient to invasion by new variants. Our results suggest that many host contact structures suppress invasion of new strains and may slow disease adaptation. These findings are important to the natural history of disease evolution and the spread of drug-resistant strains.Publication Spatial Heterogeneity in Drug Concentrations Can Facilitate the Emergence of Resistance to Cancer Therapy(Public Library of Science, 2015) Fu, Feng; Nowak, Martin; Bonhoeffer, SebastianAcquired resistance is one of the major barriers to successful cancer therapy. The development of resistance is commonly attributed to genetic heterogeneity. However, heterogeneity of drug penetration of the tumor microenvironment both on the microscopic level within solid tumors as well as on the macroscopic level across metastases may also contribute to acquired drug resistance. Here we use mathematical models to investigate the effect of drug heterogeneity on the probability of escape from treatment and the time to resistance. Specifically we address scenarios with sufficiently potent therapies that suppress growth of all preexisting genetic variants in the compartment with the highest possible drug concentration. To study the joint effect of drug heterogeneity, growth rate, and evolution of resistance, we analyze a multi-type stochastic branching process describing growth of cancer cells in multiple compartments with different drug concentrations and limited migration between compartments. We show that resistance is likely to arise first in the sanctuary compartment with poor drug penetrations and from there populate non-sanctuary compartments with high drug concentrations. Moreover, we show that only below a threshold rate of cell migration does spatial heterogeneity accelerate resistance evolution, otherwise deterring drug resistance with excessively high migration rates. Our results provide new insights into understanding why cancers tend to quickly become resistant, and that cell migration and the presence of sanctuary sites with little drug exposure are essential to this end.Publication The Molecular Clock of Neutral Evolution Can Be Accelerated or Slowed by Asymmetric Spatial Structure(Public Library of Science, 2015) Allen, Benjamin; Sample, Christine; Dementieva, Yulia; Medeiros, Ruben C.; Paoletti, Christopher; Nowak, MartinOver time, a population acquires neutral genetic substitutions as a consequence of random drift. A famous result in population genetics asserts that the rate, K, at which these substitutions accumulate in the population coincides with the mutation rate, u, at which they arise in individuals: K = u. This identity enables genetic sequence data to be used as a “molecular clock” to estimate the timing of evolutionary events. While the molecular clock is known to be perturbed by selection, it is thought that K = u holds very generally for neutral evolution. Here we show that asymmetric spatial population structure can alter the molecular clock rate for neutral mutations, leading to either Ku. Our results apply to a general class of haploid, asexually reproducing, spatially structured populations. Deviations from K = u occur because mutations arise unequally at different sites and have different probabilities of fixation depending on where they arise. If birth rates are uniform across sites, then K ≤ u. In general, K can take any value between 0 and Nu. Our model can be applied to a variety of population structures. In one example, we investigate the accumulation of genetic mutations in the small intestine. In another application, we analyze over 900 Twitter networks to study the effect of network topology on the fixation of neutral innovations in social evolution.Publication Vertical suppression of the EGFR pathway prevents onset of resistance in colorectal cancers(Nature Pub. Group, 2015) Misale, Sandra; Bozic, Ivana; Tong, Jingshan; Peraza-Penton, Ashley; Lallo, Alice; Baldi, Federica; Lin, Kevin H.; Truini, Mauro; Trusolino, Livio; Bertotti, Andrea; Di Nicolantonio, Federica; Nowak, Martin; Zhang, Lin; Wood, Kris C.; Bardelli, AlbertoMolecular targeted drugs are clinically effective anti-cancer therapies. However, tumours treated with single agents usually develop resistance. Here we use colorectal cancer (CRC) as a model to study how the acquisition of resistance to EGFR-targeted therapies can be restrained. Pathway-oriented genetic screens reveal that CRC cells escape from EGFR blockade by downstream activation of RAS-MEK signalling. Following treatment of CRC cells with anti-EGFR, anti-MEK or the combination of the two drugs, we find that EGFR blockade alone triggers acquired resistance in weeks, while combinatorial treatment does not induce resistance. In patient-derived xenografts, EGFR-MEK combination prevents the development of resistance. We employ mathematical modelling to provide a quantitative understanding of the dynamics of response and resistance to these single and combination therapies. Mechanistically, we find that the EGFR-MEK Combo blockade triggers Bcl-2 and Mcl-1 downregulation and initiates apoptosis. These results provide the rationale for clinical trials aimed at preventing rather than intercepting resistance.Publication Multiple Strategies in Structured Populations(National Academy of Sciences, 2011) Tarnita, Corina; Wage, Nicholas; Nowak, MartinMany specific models have been proposed to study evolutionary game dynamics in structured populations, but most analytical results so far describe the competition of only two strategies. Here we derive a general result that holds for any number of strategies, for a large class of population structures under weak selection. We show that for the purpose of strategy selection any evolutionary process can be characterized by two key parameters that are coefficients in a linear inequality containing the payoff values. These structural coefficients, \(\sigma1\) and \(\sigma2\), depend on the particular process that is being studied, but not on the number of strategies, \(n\), or the payoff matrix. For calculating these structural coefficients one has to investigate games with three strategies, but more are not needed. Therefore, \(n=3\) is the general case. Our main result has a geometric interpretation: Strategy selection is determined by the sum of two terms, the first one describing competition on the edges of the simplex and the second one in the center. Our formula includes all known weak selection criteria of evolutionary games as special cases. As a specific example we calculate games on sets and explore the synergistic interaction between direct reciprocity and spatial selection. We show that for certain parameter values both repetition and space are needed to promote evolution of cooperation.