Martin A Nowak

Martin A Nowak
Harvard University | Harvard · Program for Evolutionary Dynamics

Ph.D

About

714
Publications
200,638
Reads
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103,610
Citations
Additional affiliations
July 2003 - present
Harvard University
Position
  • Professor (Full)
September 1998 - July 2003
Institute for Advanced Study
Position
  • Head of Theoretical Biology Group
July 1987 - August 1989
University of Vienna
Position
  • PhD Student

Publications

Publications (714)
Article
Full-text available
In repeated interactions, players can use strategies that respond to the outcome of previous rounds. Much of the existing literature on direct reciprocity assumes that all competing individuals use the same strategy space. Here, we study both learning and evolutionary dynamics of players that differ in the strategy space they explore. We focus on t...
Article
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In repeated social interactions, individuals often employ reciprocal strategies to maintain cooperation. To explore the emergence of reciprocity, many theoretical models assume synchronized decision making. In each round, individuals decide simultaneously whether to cooperate or not. Yet many manifestations of reciprocity in nature are asynchronous...
Article
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The greatest hope for a return to normalcy following the COVID-19 pandemic is worldwide vaccination. Yet, a relaxation of social distancing that allows increased transmissibility, coupled with selection pressure due to vaccination, will probably lead to the emergence of vaccine resistance. We analyse the evolutionary dynamics of COVID-19 in the pre...
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Motivated by COVID-19, we develop and analyze a simple stochastic model for the spread of disease in human population. We track how the number of infected and critically ill people develops over time in order to estimate the demand that is imposed on the hospital system. To keep this demand under control, we consider a class of simple policies for...
Preprint
Full-text available
Evolution occurs in populations of reproducing individuals. It is well known that population structure can affect evolutionary dynamics. Traditionally, natural selection is studied between mutants that differ in reproductive rate, but are subject to the same population structure. Here we study how natural selection acts on mutants that have the sam...
Preprint
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The process of vaccinating the world population against COVID-19 is expected to take well over a year to complete. As vaccination progresses and population immunity increases, a counteracting relaxation of social distancing measures is observed. The result will be a prolonged period of high disease prevalence combined with a fitness advantage for v...
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Direct and indirect reciprocity are key mechanisms for the evolution of cooperation. Direct reciprocity means that individuals use their own experience to decide whether to cooperate with another person. Indirect reciprocity means that they also consider the experiences of others. Although these two mechanisms are intertwined, they are typically st...
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Selection and random drift determine the probability that novel mutations fixate in a population. Population structure is known to affect the dynamics of the evolutionary process. Amplifiers of selection are population structures that increase the fixation probability of beneficial mutants compared to well-mixed populations. Over the past 15 years,...
Article
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The Great Oxygenation Event (GOE), ca. 2.4 billion years ago, transformed life and environments on Earth. Its causes, however, are debated. We mathematically analyze the GOE in terms of ecological dynamics coupled with a changing Earth. Anoxygenic photosynthetic bacteria initially dominate over cyanobacteria, but their success depends on the availa...
Preprint
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The COVID-19 pandemic has led to an unprecedented global response in terms of social lockdown in order to slow the spread of the virus 1,2. Currently the greatest hope is based on world-wide vaccination3,4. The expectation is that social and economic activities can gradually resume as more and more people become vaccinated. Yet, a relaxation of soc...
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Despite initial responses1–3, most melanoma patients develop resistance⁴ to immune checkpoint blockade (ICB). To understand the evolution of resistance, we studied 37 tumor samples over 9 years from a patient with metastatic melanoma with complete clinical response to ICB followed by delayed recurrence and death. Phylogenetic analysis revealed co-e...
Article
Clonal hematopoiesis, a condition in which individual hematopoietic stem cell clones generate a disproportionate fraction of blood leukocytes, correlates with higher risk for cardiovascular disease. The mechanisms behind this association are incompletely understood. Here, we show that hematopoietic stem cell division rates are increased in mice and...
Preprint
Full-text available
Motivated by COVID-19, we develop and analyze a simple stochastic model for a disease spread in human population. We track how the number of infected and critically ill people develops over time in order to estimate the demand that is imposed on the hospital system. To keep this demand under control, we consider a class of simple policies for slowi...
Article
Full-text available
We donate billions to charities each year, yet much of our giving is ineffective. Why are we motivated to give but not to give effectively? Building on evolutionary game theory, we argue that donors evolved (genetically or culturally) to be insensitive to efficacy because people tend not to reward efficacy, as social rewards tend to depend on well-...
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Resources are rarely distributed uniformly within a population. Heterogeneity in the concentration of a drug, the quality of breeding sites, or wealth can all affect evolutionary dynamics. In this study, we represent a collection of properties affecting the fitness at a given location using a color. A green node is rich in resources while a red nod...
Article
The genomic proportion that two relatives share identically by descent-their genetic relatedness-can vary depending on the history of recombination and segregation in their pedigree. Previous calculations of the variance of genetic relatedness have defined genetic relatedness as the proportion of total genetic map length (cM) shared by relatives, a...
Preprint
Full-text available
Resources are rarely distributed uniformly within a population. Heterogeneity in the concentration of a drug, the quality of breeding sites, or wealth can all affect evolutionary dynamics. In this study, we represent a collection of properties affecting the fitness at a given location using a color. A green node is rich in resources while a red nod...
Article
Full-text available
Humans routinely engage in many distinct interactions in parallel. Team members collaborate on several concurrent projects, and even whole nations interact with each other across a variety of issues, including trade, climate change and security. Yet the existing theory of direct reciprocity studies isolated repeated games. Such models cannot accoun...
Article
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Prosocial behaviours are encountered in the donation game, the prisoner’s dilemma, relaxed social dilemmas and public goods games. Many studies assume that the population structure is homogeneous, meaning that all individuals have the same number of interaction partners or that the social good is of one particular type. Here, we explore general evo...
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Antibiotic-resistant infections are a growing threat to human health, but basic features of the eco-evolutionary dynamics remain unexplained. Most prominently, there is no clear mechanism for the long-term coexistence of both drug-sensitive and resistant strains at intermediate levels, a ubiquitous pattern seen in surveillance data. Here we show th...
Preprint
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The genomic proportion that two relatives share identically by descent—their genetic relatedness—can vary depending on the history of recombination and segregation in their pedigree. This variation is important in many applications of genetics, including pedigree-based estimation of the genetic variance and heritability of traits, and estimation of...
Article
Full-text available
Major evolutionary transitions, including the emergence of life, likely occurred in aqueous environments. While the role of water’s chemistry in early life is well studied, the effects of water’s ability to manipulate population structure are less clear. Population structure is known to be critical, as effective replicators must be insulated from p...
Article
Surgery is the only curative option for Stage I/II pancreatic cancer, nonetheless most patients will recur after surgery and die of their disease. To identify novel opportunities for management of recurrent pancreatic cancer we performed whole exome or targeted sequencing of 10 resected primary cancers and matched intrapancreatic recurrences or dis...
Article
Full-text available
The fixation probability of a single mutant invading a population of residents is among the most widely-studied quantities in evolutionary dynamics. Amplifiers of natural selection are population structures that increase the fixation probability of advantageous mutants, compared to well-mixed populations. Extensive studies have shown that many ampl...
Article
We present the spectral and timing evolution of the persistent black hole X-ray binary GRS 1758−258 based on almost 12 years of observations using the Rossi X-ray Timing Explorer Proportional Counter Array. While the source was predominantly found in the hard state during this time, it entered the thermally dominated soft state seven times. In the...
Article
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The environment has a strong influence on a population’s evolutionary dynamics. Driven by both intrinsic and external factors, the environment is subject to continual change in nature. To capture an ever-changing environment, we consider a model of evolutionary dynamics with game transitions, where individuals’ behaviors together with the games tha...
Preprint
Full-text available
DNA introgressed from one species into another is typically deleterious at many genomic loci in the recipient species. It is therefore purged by selection over time. Here, we use mathematical modeling and whole-genome simulations to study the influence of recombination on the purging of introgressed DNA. We find that aggregate recombination control...
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Population structure affects the outcome of natural selection. These effects can be modeled using evolutionary games on graphs. Recently, conditions were derived for a trait to be favored under weak selection, on any weighted graph, in terms of coalescence times of random walks. Here we consider isothermal graphs, which have the same total edge wei...
Preprint
Full-text available
Surgery is the only curative option for Stage I/II pancreatic cancer, nonetheless most patients will recur after surgery and die of their disease. To identify novel opportunities for management of recurrent pancreatic cancer we performed whole exome or targeted sequencing of 10 resected primary cancers and matched intrapancreatic recurrences or dis...
Preprint
Prosocial behavior, which means paying a cost for others to receive a benefit, is encountered in the donation game, the prisoner's dilemma, relaxed social dilemmas, and public goods games. Many studies of prosociality assume that the population structure is either homogeneous, meaning all individuals have the same number of interaction partners, or...
Article
Genetic intratumoural heterogeneity is a natural consequence of imperfect DNA replication. Any two randomly selected cells, whether normal or cancerous, are therefore genetically different. Here, we review the different forms of genetic heterogeneity in cancer and re-analyse the extent of genetic heterogeneity within seven types of untreated epithe...
Article
Full-text available
Understanding intrinsic and acquired resistance is crucial to overcoming cancer chemotherapy failure. While it is well-established that intratumor, subclonal genetic and phenotypic heterogeneity significantly contribute to resistance, it is not fully understood how tumor sub-clones interact with each other to withstand therapy pressure. Here, we re...
Preprint
A great number of biological organisms live in aqueous environments. Major evolutionary transitions, including the emergence of life itself, likely occurred in such environments. While the chemical aspects of the role of water in biology are well-studied, the effects of water's physical characteristics on evolutionary events, such as the control of...
Article
Full-text available
Direct reciprocity is a powerful mechanism for the evolution of cooperation on the basis of repeated interactions1–4. It requires that interacting individuals are sufficiently equal, such that everyone faces similar consequences when they cooperate or defect. Yet inequality is ubiquitous among humans5,6 and is generally considered to undermine coop...
Article
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During metastasis, only a fraction of genetic diversity in a primary tumor is passed on to metastases. We calculate this fraction of transferred diversity as a function of the seeding rate between tumors. At one extreme, if a metastasis is seeded by a single cell, then it inherits only the somatic mutations present in the founding cell, so that non...
Preprint
The fixation probability of a single mutant invading a population of residents is among the most widely-studied quantities in evolutionary dynamics. Amplifiers of natural selection are population structures that increase the fixation probability of advantageous mutants, compared to well-mixed populations. Extensive studies have shown that many ampl...
Article
Full-text available
How the genomic features of a patient’s cancer relate to individual disease kinetics remains poorly understood. Here we used the indolent growth dynamics of chronic lymphocytic leukaemia (CLL) to analyse the growth rates and corresponding genomic patterns of leukaemia cells from 107 patients with CLL, spanning decades-long disease courses. We found...
Preprint
Full-text available
The environment has a strong influence on a population's evolutionary dynamics. Driven by both intrinsic and external factors, the environment is subject to continuous change in nature. To model an ever-changing environment, we develop a framework of evolutionary dynamics with stochastic game transitions, where individuals' behaviors together with...
Article
We present an analysis of three Chandra High Energy Transmission Gratings observations of the black hole binary Cyg X-1/HDE 226868 at different orbital phases. The stellar wind that is powering the accretion in this system is characterized by temperature and density inhomogeneities including structures, or “clumps”, of colder, more dense material e...
Article
Full-text available
The rate of biological evolution depends on the fixation probability and on the fixation time of new mutants. Intensive research has focused on identifying population structures that augment the fixation probability of advantageous mutants. But these amplifiers of natural selection typically increase fixation time. Here we study population structur...
Article
Full-text available
If they are able to spread in wild populations, CRISPR-based gene-drive elements would provide new ways to address ecological problems by altering the traits of wild organisms, but the potential for uncontrolled spread tremendously complicates ethical development and use. Here, we detail a self-exhausting form of CRISPR-based drive system comprisin...
Article
Cooperation is a major factor in the evolution of human societies. The structure of social networks, which affects the dynamics of cooperation and other interpersonal phenomena, have common structural signatures. One of these signatures is the tendency to organize as groups. This tendency gives rise to networks with community structure, which are c...
Preprint
Population structure affects the outcome of natural selection. Static population structures can be described by graphs, where individuals occupy the nodes, and interactions occur along the edges. General conditions for evolutionary success on any weighted graph were recently derived, for weak selection, in terms of coalescence times of random walks...
Preprint
In an iterated game between two players, there is much interest in characterizing the set of feasible payoffs for both players when one player uses a fixed strategy and the other player is free to switch. Such characterizations have led to extortionists, equalizers, partners, and rivals. Most of those studies use memory-one strategies, which specif...
Article
Full-text available
Cancer evolution is predominantly studied by focusing on differences in the genetic characteristics of malignant cells within tumors. However, the spatiotemporal dynamics of clonal outgrowth that underlie evolutionary trajectories remain largely unresolved. Here, we sought to unravel the clonal dynamics of colorectal cancer (CRC) expansion in space...
Article
Full-text available
Four experiments examine how lack of awareness of inequality affect behaviour towards the rich and poor. In Experiment 1, participants who became aware that wealthy individuals donated a smaller percentage of their income switched from rewarding the wealthy to rewarding the poor. In Experiments 2 and 3, participants who played a public goods game –...
Article
Full-text available
Many mathematical models of evolution assume that all individuals experience the same environment. Here, we study the Moran process in heterogeneous environments. The population is of finite size with two competing types, which are exposed to a fixed number of environmental conditions. Reproductive rate is determined by both the type and the enviro...
Article
Comparative studies in evolutionary genetics rely critically on evaluation of the total amount of genetic shuffling that occurs during gamete production. Such studies have been hampered by the absence of a direct measure of this quantity. Existing measures consider crossing-over by simply counting the average number of crossovers per meiosis. This...
Preprint
Full-text available
Hematopoiesis is a dynamic process involving the up- and down-regulation of genes, as well as feed-back loops that stimulate or suppress circulating cytokine concentrations. More complete pictures of the gene regulatory networks that control the production of the blood system have emerged with the advent of single-cell sequencing techniques and ref...
Article
We study evolution of cooperation by indirect reciprocity with optional interactions. There are repeated interactions between two types of players, cooperators and defectors, in a population of finite size. Previously, we considered the scenario where an encounter between a cooperator and a defector results in the defector's identity being revealed...
Article
Full-text available
Indirect reciprocity is a mechanism for cooperation based on shared moral systems and individual reputations. It assumes that members of a community routinely observe and assess each other and that they use this information to decide who is good or bad, and who deserves cooperation. When information is transmitted publicly, such that all community...
Preprint
Comparative studies in evolutionary genetics rely critically on evaluation of the total amount of genetic shuffling that occurs during gamete production. However, such studies have been ham-pered by the fact that there has been no direct measure of this quantity. Existing measures consider crossing over by simply counting the average number of cros...
Article
We study a general setting of neutral evolution in which the population is of finite, constant size and can have spatial structure. Mutation leads to different genetic types (traits), which can be discrete or continuous. Under minimal assumptions, we show that the marginal trait distributions of the evolutionary process, which specify the probabili...
Preprint
The rate of biological evolution depends on the fixation probability and on the fixation time of new mutants. Intensive research has focused on identifying population structures that augment the fixation probability of advantageous mutants. But these `amplifiers of natural selection' typically increase fixation time. Here we study population struct...
Preprint
We study a general setting of neutral evolution in which the population is of finite, constant size and can have spatial structure. Mutation leads to different genetic types ("traits"), which can be discrete or continuous. Under minimal assumptions, we show that the marginal trait distributions of the evolutionary process, which specify the probabi...
Article
Metastases are responsible for the majority of cancer-related deaths. Although genomic heterogeneity within primary tumors is associated with relapse, heterogeneity among treatment-naïve metastases has not been comprehensively assessed. We analyzed sequencing data for 76 untreated metastases from 20 patients and inferred cancer phylogenies for brea...
Article
Full-text available
The odds of living a long and healthy life with HIV infection have dramatically improved with the advent of combination antiretroviral therapy. Along with the early development and clinical trials of these drugs, and new field of research emerged called viral dynamics, which uses mathematical models to interpret and predict the time‐course of viral...
Article
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Most adult carcinomas develop from noninvasive precursor lesions, a progression that is supported by genetic analysis. However, the evolutionary and genetic relationships among co-existing lesions are unclear. Here we analysed the somatic variants of pancreatic cancers and precursor lesions sampled from distinct regions of the same pancreas. After...
Preprint
Full-text available
Cooperation is a major factor in the evolution of human societies. The structure of human social networks, which affects the dynamics of cooperation and other interpersonal phenomena, have common structural signatures. One of these signatures is the tendency to organize as groups. Among the generative models that network theorists use to emulate th...
Article
Full-text available
In the version of this Review Article originally published, in Fig. 4 an arrow pointing from ALLC to ALLD was mistakenly omitted. This has now been corrected in all versions of the Review Article.