1
|
Lobinska G, Tretyachenko V, Dahan O, Nowak MA, Pilpel Y. The evolutionary safety of mutagenic drugs should be assessed before drug approval. PLoS Biol 2024; 22:e3002570. [PMID: 38489394 DOI: 10.1371/journal.pbio.3002570] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Revised: 03/27/2024] [Indexed: 03/17/2024] Open
Abstract
Some drugs increase the mutation rate of their target pathogen, a potentially concerning mechanism as the pathogen might evolve faster toward an undesired phenotype. We suggest a four-step assessment of evolutionary safety for the approval of such treatments.
Collapse
Affiliation(s)
- Gabriela Lobinska
- Department of Molecular Genetics, Weizmann Institute of Science, Rehovot, Israel
| | | | - Orna Dahan
- Department of Molecular Genetics, Weizmann Institute of Science, Rehovot, Israel
| | - Martin A Nowak
- Department of Mathematics & Department of Organismic and Evolutionary Biology, Harvard University, Cambridge, Massachusetts, United States of America
| | - Yitzhak Pilpel
- Department of Molecular Genetics, Weizmann Institute of Science, Rehovot, Israel
| |
Collapse
|
2
|
Olejarz JW, Nowak MA. Gene drives for the extinction of wild metapopulations. J Theor Biol 2024; 577:111654. [PMID: 37984587 DOI: 10.1016/j.jtbi.2023.111654] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/23/2023] [Revised: 09/15/2023] [Accepted: 10/31/2023] [Indexed: 11/22/2023]
Abstract
Population-suppressing gene drives may be capable of extinguishing wild populations, with proposed applications in conservation, agriculture, and public health. However, unintended and potentially disastrous consequences of release of drive-engineered individuals are extremely difficult to predict. We propose a model for the dynamics of a sex ratio-biasing drive, and using simulations, we show that failure of the suppression drive is often a natural outcome due to stochastic and spatial effects. We further demonstrate rock-paper-scissors dynamics among wild-type, drive-infected, and extinct populations that can persist for arbitrarily long times. Gene drive-mediated extinction of wild populations entails critical complications that lurk far beyond the reach of laboratory-based studies. Our findings help in addressing these challenges.
Collapse
Affiliation(s)
- Jason W Olejarz
- Department of Immunology and Infectious Diseases, Harvard T. H. Chan School of Public Health, Boston, MA, 02115, USA; Department of Mathematics, Harvard University, Cambridge, MA, 02138, USA.
| | - Martin A Nowak
- Department of Mathematics, Harvard University, Cambridge, MA, 02138, USA; Department of Organismic and Evolutionary Biology, Harvard University, Cambridge, MA, 02138, USA
| |
Collapse
|
3
|
Park HJ, Hilbe C, Nowak MA, Kim BJ, Jeong HC. Vacancies in growing habitats promote the evolution of cooperation. J Theor Biol 2023; 575:111629. [PMID: 37802182 DOI: 10.1016/j.jtbi.2023.111629] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/18/2023] [Revised: 09/23/2023] [Accepted: 09/28/2023] [Indexed: 10/08/2023]
Abstract
We study evolutionary game dynamics in a growing habitat with vacancies. Fitness is determined by the global effect of the environment and a local prisoner's dilemma among neighbors. We study population growth on a one-dimensional lattice and analyze how the environment affects evolutionary competition. As the environment becomes harsh, an absorbing phase transition from growing populations to extinction occurs. The transition point depends on which strategies are present in the population. In particular, we find a 'cooperative window' in parameter space, where only cooperators can survive. A mutant defector in a cooperative community might briefly proliferate, but over time naturally occurring vacancies separate cooperators from defectors, thereby driving defectors to extinction. Our model reveals that vacancies provide a strong boost for cooperation by spatial selection.
Collapse
Affiliation(s)
- Hye Jin Park
- Department of Physics, Inha University, Incheon, 22212, Republic of Korea.
| | - Christian Hilbe
- Max Planck Research Group 'Dynamics of Social Behavior', Max Planck Institute for Evolutionary Biology, Plön, 24306, Germany
| | - Martin A Nowak
- Department of Mathematics, Harvard University, Cambridge, MA, 02138, United States; Department of Organismic and Evolutionary Biology, Harvard University, Cambridge, MA, 02138, United States
| | - Beom Jun Kim
- Department of Physics, Sungkyunkwan University, Suwon, 16419, Republic of Korea
| | - Hyeong-Chai Jeong
- Department of Physics and Astronomy, Sejong University, Seoul, 05006, Republic of Korea.
| |
Collapse
|
4
|
LaPorte P, Nowak MA. A geometric process of evolutionary game dynamics. J R Soc Interface 2023; 20:20230460. [PMID: 38016638 PMCID: PMC10684345 DOI: 10.1098/rsif.2023.0460] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/06/2023] [Accepted: 11/02/2023] [Indexed: 11/30/2023] Open
Abstract
Many evolutionary processes occur in phenotype spaces which are continuous. It is therefore of interest to explore how selection operates in continuous spaces. One approach is adaptive dynamics, which assumes that mutants are local. Here we study a different process which also allows non-local mutants. We assume that a resident population is challenged by an invader who uses a strategy chosen from a random distribution on the space of all strategies. We study the repeated donation game of direct reciprocity. We consider reactive strategies given by two probabilities, denoting respectively the probability to cooperate after the co-player has cooperated or defected. The strategy space is the unit square. We derive analytic formulae for the stationary distribution of evolutionary dynamics and for the average cooperation rate as function of the cost-to-benefit ratio. For positive reactive strategies, we prove that cooperation is more abundant than defection if the area of the cooperative region is greater than 1/2 which is equivalent to benefit, b, divided by cost, c, exceeding [Formula: see text]. We introduce the concept of strategies that are stable with probability one. We also study an extended process and discuss other games.
Collapse
Affiliation(s)
- Philip LaPorte
- Department of Mathematics, University of California, Berkeley, CA 94720, USA
| | - Martin A. Nowak
- Department of Mathematics, Harvard University, Cambridge, MA 02138, USA
- Department of Organismic and Evolutionary Biology, Harvard University, Cambridge, MA 02138, USA
| |
Collapse
|
5
|
Tkadlec J, Kaveh K, Chatterjee K, Nowak MA. Evolutionary dynamics of mutants that modify population structure. J R Soc Interface 2023; 20:20230355. [PMID: 38016637 PMCID: PMC10684346 DOI: 10.1098/rsif.2023.0355] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/23/2023] [Accepted: 11/01/2023] [Indexed: 11/30/2023] Open
Abstract
Natural selection is usually studied between mutants that differ in reproductive rate, but are subject to the same population structure. Here we explore how natural selection acts on mutants that have the same reproductive rate, but different population structures. In our framework, population structure is given by a graph that specifies where offspring can disperse. The invading mutant disperses offspring on a different graph than the resident wild-type. We find that more densely connected dispersal graphs tend to increase the invader's fixation probability, but the exact relationship between structure and fixation probability is subtle. We present three main results. First, we prove that if both invader and resident are on complete dispersal graphs, then removing a single edge in the invader's dispersal graph reduces its fixation probability. Second, we show that for certain island models higher invader's connectivity increases its fixation probability, but the magnitude of the effect depends on the exact layout of the connections. Third, we show that for lattices the effect of different connectivity is comparable to that of different fitness: for large population size, the invader's fixation probability is either constant or exponentially small, depending on whether it is more or less connected than the resident.
Collapse
Affiliation(s)
- Josef Tkadlec
- Department of Mathematics, Harvard University, Cambridge, MA 02138, USA
- Computer Science Institute, Charles University, Prague, Czech Republic
| | - Kamran Kaveh
- Department of Applied Mathematics, University of Washington, Seattle, WA 98195, USA
| | - Krishnendu Chatterjee
- Institute of Science and Technology Austria, Am Campus 1, 3400 Klosterneuburg, Austria
| | - Martin A. Nowak
- Department of Mathematics, Harvard University, Cambridge, MA 02138, USA
- Department of Organismic and Evolutionary Biology, Harvard University, Cambridge, MA 02138, USA
| |
Collapse
|
6
|
Zhang X, Lobinska G, Feldman M, Dekel E, Nowak MA, Pilpel Y, Pauzner Y, Barzel B, Pauzner A. Correction: A spatial vaccination strategy to reduce the risk of vaccine-resistant variants. PLoS Comput Biol 2023; 19:e1011608. [PMID: 37903105 PMCID: PMC10615275 DOI: 10.1371/journal.pcbi.1011608] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/01/2023] Open
Abstract
[This corrects the article DOI: 10.1371/journal.pcbi.1010391.].
Collapse
|
7
|
Lobinska G, Pilpel Y, Nowak MA. Evolutionary safety of lethal mutagenesis driven by antiviral treatment. PLoS Biol 2023; 21:e3002214. [PMID: 37552682 PMCID: PMC10409280 DOI: 10.1371/journal.pbio.3002214] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/07/2022] [Accepted: 06/23/2023] [Indexed: 08/10/2023] Open
Abstract
Nucleoside analogs are a major class of antiviral drugs. Some act by increasing the viral mutation rate causing lethal mutagenesis of the virus. Their mutagenic capacity, however, may lead to an evolutionary safety concern. We define evolutionary safety as a probabilistic assurance that the treatment will not generate an increased number of mutants. We develop a mathematical framework to estimate the total mutant load produced with and without mutagenic treatment. We predict rates of appearance of such virus mutants as a function of the timing of treatment and the immune competence of patients, employing realistic assumptions about the vulnerability of the viral genome and its potential to generate viable mutants. We focus on the case study of Molnupiravir, which is an FDA-approved treatment against Coronavirus Disease-2019 (COVID-19). We estimate that Molnupiravir is narrowly evolutionarily safe, subject to the current estimate of parameters. Evolutionary safety can be improved by restricting treatment with this drug to individuals with a low immunological clearance rate and, in future, by designing treatments that lead to a greater increase in mutation rate. We report a simple mathematical rule to determine the fold increase in mutation rate required to obtain evolutionary safety that is also applicable to other pathogen-treatment combinations.
Collapse
Affiliation(s)
- Gabriela Lobinska
- Department of Molecular Genetics, Weizmann Institute of Science, Rehovot, Israel
| | - Yitzhak Pilpel
- Department of Molecular Genetics, Weizmann Institute of Science, Rehovot, Israel
| | - Martin A. Nowak
- Department of Mathematics, Department of Organismic and Evolutionary Biology, Harvard University, Cambridge, Massachusetts, United States of America
| |
Collapse
|
8
|
Kleshnina M, Hilbe C, Šimsa Š, Chatterjee K, Nowak MA. The effect of environmental information on evolution of cooperation in stochastic games. Nat Commun 2023; 14:4153. [PMID: 37438341 DOI: 10.1038/s41467-023-39625-9] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/04/2022] [Accepted: 06/22/2023] [Indexed: 07/14/2023] Open
Abstract
Many human interactions feature the characteristics of social dilemmas where individual actions have consequences for the group and the environment. The feedback between behavior and environment can be studied with the framework of stochastic games. In stochastic games, the state of the environment can change, depending on the choices made by group members. Past work suggests that such feedback can reinforce cooperative behaviors. In particular, cooperation can evolve in stochastic games even if it is infeasible in each separate repeated game. In stochastic games, participants have an interest in conditioning their strategies on the state of the environment. Yet in many applications, precise information about the state could be scarce. Here, we study how the availability of information (or lack thereof) shapes evolution of cooperation. Already for simple examples of two state games we find surprising effects. In some cases, cooperation is only possible if there is precise information about the state of the environment. In other cases, cooperation is most abundant when there is no information about the state of the environment. We systematically analyze all stochastic games of a given complexity class, to determine when receiving information about the environment is better, neutral, or worse for evolution of cooperation.
Collapse
Affiliation(s)
| | - Christian Hilbe
- Max Planck Research Group Dynamics of Social Behavior, Max Planck Institute for Evolutionary Biology, Plön, Germany
| | - Štěpán Šimsa
- IST Austria, Klosterneuburg, Austria
- Faculty of Mathematics and Physics, Charles University, Prague, Czech Republic
| | | | - Martin A Nowak
- Department of Mathematics, Harvard University, Cambridge, MA, USA
- Department of Organismic and Evolutionary Biology, Harvard University, Cambridge, MA, USA
| |
Collapse
|
9
|
LaPorte P, Hilbe C, Nowak MA. Adaptive dynamics of memory-one strategies in the repeated donation game. PLoS Comput Biol 2023; 19:e1010987. [PMID: 37384811 DOI: 10.1371/journal.pcbi.1010987] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/02/2023] [Accepted: 06/13/2023] [Indexed: 07/01/2023] Open
Abstract
Human interactions can take the form of social dilemmas: collectively, people fare best if all cooperate but each individual is tempted to free ride. Social dilemmas can be resolved when individuals interact repeatedly. Repetition allows them to adopt reciprocal strategies which incentivize cooperation. The most basic model for direct reciprocity is the repeated donation game, a variant of the prisoner's dilemma. Two players interact over many rounds; in each round they decide whether to cooperate or to defect. Strategies take into account the history of the play. Memory-one strategies depend only on the previous round. Even though they are among the most elementary strategies of direct reciprocity, their evolutionary dynamics has been difficult to study analytically. As a result, much previous work has relied on simulations. Here, we derive and analyze their adaptive dynamics. We show that the four-dimensional space of memory-one strategies has an invariant three-dimensional subspace, generated by the memory-one counting strategies. Counting strategies record how many players cooperated in the previous round, without considering who cooperated. We give a partial characterization of adaptive dynamics for memory-one strategies and a full characterization for memory-one counting strategies.
Collapse
Affiliation(s)
- Philip LaPorte
- Department of Mathematics, University of California, Berkeley, Berkeley, California, United States of America
| | - Christian Hilbe
- Max Planck Research Group 'Dynamics of Social Behavior', Max Planck Institute for Evolutionary Biology, Plön, Germany
| | - Martin A Nowak
- Department of Mathematics, Harvard University, Cambridge, Massachussetts, United States of America
- Department of Organismic and Evolutionary Biology, Harvard University, Cambridge, Massachussetts, United States of America
| |
Collapse
|
10
|
Abstract
Direct reciprocity is a powerful mechanism for the evolution of cooperation based on repeated interactions between the same individuals. But high levels of cooperation evolve only if the benefit-to-cost ratio exceeds a certain threshold that depends on memory length. For the best-explored case of one-round memory, that threshold is two. Here, we report that intermediate mutation rates lead to high levels of cooperation, even if the benefit-to-cost ratio is only marginally above one, and even if individuals only use a minimum of past information. This surprising observation is caused by two effects. First, mutation generates diversity which undermines the evolutionary stability of defectors. Second, mutation leads to diverse communities of cooperators that are more resilient than homogeneous ones. This finding is relevant because many real-world opportunities for cooperation have small benefit-to-cost ratios, which are between one and two, and we describe how direct reciprocity can attain cooperation in such settings. Our result can be interpreted as showing that diversity, rather than uniformity, promotes evolution of cooperation.
Collapse
Affiliation(s)
- Josef Tkadlec
- Department of Mathematics, Harvard University, Cambridge, MA02138
| | - Christian Hilbe
- Max Planck Research Group ‘Dynamics of Social Behavior’, Max Planck Institute for Evolutionary Biology, 24306, Plön, Germany
| | - Martin A. Nowak
- Department of Mathematics, Harvard University, Cambridge, MA02138
- Department of Organismic and Evolutionary Biology, Harvard University, Cambridge, MA02138
| |
Collapse
|
11
|
Veller C, Edelman NB, Muralidhar P, Nowak MA. Recombination and Selection Against Introgressed DNA. Evolution 2023; 77:1131-1144. [PMID: 36775972 DOI: 10.1093/evolut/qpad021] [Citation(s) in RCA: 6] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/25/2022] [Revised: 01/19/2023] [Accepted: 02/06/2023] [Indexed: 02/14/2023]
Abstract
Introgressed DNA is often deleterious at many loci in the recipient species' genome, and is therefore purged by selection. Here, we use mathematical modeling and whole-genome simulations to study the influence of recombination on this process. We find that aggregate recombination controls the genome-wide rate of purging in the early generations after admixture, when purging is most rapid. Aggregate recombination is influenced by the number of chromosomes and heterogeneity in their size, and by the number of crossovers and their locations along chromosomes. A comparative prediction is that species with fewer chromosomes should purge introgressed ancestry more profoundly, and should therefore exhibit weaker genomic signals of historical introgression. Turning to within-genome patterns, we show that, in species with autosomal recombination in both sexes, more purging is expected on sex chromosomes than autosomes, all else equal. The opposite prediction holds for species without autosomal recombination in the heterogametic sex. Finally, positive correlations between recombination rate and introgressed ancestry have recently been observed within the genomes of several species. We show that these correlations are likely driven not by recombination's effect in unlinking neutral from deleterious introgressed alleles, but by recombination's effect on the rate of purging of deleterious introgressed alleles themselves.
Collapse
Affiliation(s)
- Carl Veller
- Center for Population Biology, University of California Davis, Davis, California, USA.,Department of Evolution and Ecology, University of California Davis, Davis, California, USA
| | - Nathaniel B Edelman
- Yale Institute for Biospheric Studies, Yale University, New Haven, Connecticut, USA.,Yale School for the Environment, Yale University, New Haven, Connecticut, USA
| | - Pavitra Muralidhar
- Center for Population Biology, University of California Davis, Davis, California, USA.,Department of Evolution and Ecology, University of California Davis, Davis, California, USA
| | - Martin A Nowak
- Department of Mathematics, Harvard University, Cambridge, Massachusetts, USA.,Department of Organismic and Evolutionary Biology, Harvard University, Cambridge, Massachusetts, USA
| |
Collapse
|
12
|
Zhang X, Lobinska G, Feldman M, Dekel E, Nowak MA, Pilpel Y, Pauzner Y, Barzel B, Pauzner A. A spatial vaccination strategy to reduce the risk of vaccine-resistant variants. PLoS Comput Biol 2022; 18:e1010391. [PMID: 35947602 PMCID: PMC9394842 DOI: 10.1371/journal.pcbi.1010391] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/16/2021] [Revised: 08/22/2022] [Accepted: 07/14/2022] [Indexed: 11/18/2022] Open
Abstract
The COVID-19 pandemic demonstrated that the process of global vaccination against a novel virus can be a prolonged one. Social distancing measures, that are initially adopted to control the pandemic, are gradually relaxed as vaccination progresses and population immunity increases. The result is a prolonged period of high disease prevalence combined with a fitness advantage for vaccine-resistant variants, which together lead to a considerably increased probability for vaccine escape. A spatial vaccination strategy is proposed that has the potential to dramatically reduce this risk. Rather than dispersing the vaccination effort evenly throughout a country, distinct geographic regions of the country are sequentially vaccinated, quickly bringing each to effective herd immunity. Regions with high vaccination rates will then have low infection rates and vice versa. Since people primarily interact within their own region, spatial vaccination reduces the number of encounters between infected individuals (the source of mutations) and vaccinated individuals (who facilitate the spread of vaccine-resistant strains). Thus, spatial vaccination may help mitigate the global risk of vaccine-resistant variants.
Collapse
Affiliation(s)
- Xiyun Zhang
- Department of Physics, Jinan University, Guangzhou, China
| | - Gabriela Lobinska
- Department of Molecular Genetics, Weizmann Institute of Science, Israel
| | - Michal Feldman
- School of Computer Science and Center for Combating Pandemics, Tel Aviv University, Israel
| | - Eddie Dekel
- Department of Economics, Northwestern University, Illinois, United States of America, and School of Economics, Tel Aviv University, Israel
| | - Martin A. Nowak
- Department of Mathematics and Department of Organismic and Evolutionary Biology, Harvard University, Massachusetts, United States of America
| | - Yitzhak Pilpel
- Department of Molecular Genetics, Weizmann Institute of Science, Israel
| | | | - Baruch Barzel
- Department of Mathematics and Gonda Multidisciplinary Brain Research Center Bar-Ilan University, Israel, and Network Science Institute, Northeastern University, Boston, Massachusetts, United States of America
| | - Ady Pauzner
- School of Economics and Center for Combating Pandemics, Tel Aviv University, Israel
| |
Collapse
|
13
|
Schmid L, Hilbe C, Chatterjee K, Nowak MA. Direct reciprocity between individuals that use different strategy spaces. PLoS Comput Biol 2022; 18:e1010149. [PMID: 35700167 PMCID: PMC9197081 DOI: 10.1371/journal.pcbi.1010149] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/26/2021] [Accepted: 04/28/2022] [Indexed: 12/04/2022] Open
Abstract
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 the infinitely repeated donation game and compare three natural strategy spaces: memory-1 strategies, which consider the last moves of both players, reactive strategies, which respond to the last move of the co-player, and unconditional strategies. These three strategy spaces differ in the memory capacity that is needed. We compute the long term average payoff that is achieved in a pairwise learning process. We find that smaller strategy spaces can dominate larger ones. For weak selection, unconditional players dominate both reactive and memory-1 players. For intermediate selection, reactive players dominate memory-1 players. Only for strong selection and low cost-to-benefit ratio, memory-1 players dominate the others. We observe that the supergame between strategy spaces can be a social dilemma: maximum payoff is achieved if both players explore a larger strategy space, but smaller strategy spaces dominate. Direct reciprocity can lead to cooperation between individuals who meet in repeated encounters. The shadow of the future casts an incentive to cooperate. If I cooperate today, you may cooperate tomorrow. But if I defect today, you may defect tomorrow. In most studies of direct reciprocity it is assumed that both players explore the same space of possible strategies. In contrast, here we study interactions between players that use different strategy spaces and therefore utilize different memory capacities. Surprisingly, we find that more complex strategy spaces often lose out against simpler ones. The social optimum, however, is achieved if all players use the more complex space. Therefore, the game between strategy spaces becomes a higher order social dilemma.
Collapse
Affiliation(s)
| | - Christian Hilbe
- Max Planck Research Group Dynamics of Social Behavior, Max Planck Institute for Evolutionary Biology, Plön, Germany
| | | | - Martin A. Nowak
- Department of Mathematics, Department of Organismic and Evolutionary Biology, Harvard University, Cambridge, Massachusetts, United States of America
| |
Collapse
|
14
|
Lobinska G, Pauzner A, Traulsen A, Pilpel Y, Nowak MA. Evolution of resistance to COVID-19 vaccination with dynamic social distancing. Nat Hum Behav 2022; 6:193-206. [PMID: 35210582 DOI: 10.1038/s41562-021-01281-8] [Citation(s) in RCA: 10] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/02/2021] [Accepted: 12/14/2021] [Indexed: 01/05/2023]
Abstract
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 presence of dynamic contact reduction and in response to vaccination. We use infection and vaccination data from six different countries. We show that under slow vaccination, resistance is very likely to appear even if social distancing is maintained. Under fast vaccination, the emergence of mutants can be prevented if social distancing is maintained during vaccination. We analyse 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.
Collapse
Affiliation(s)
- Gabriela Lobinska
- Department of Molecular Genetics, Weizmann Institute of Science, Rehovot, Israel
| | - Ady Pauzner
- Berglas School of Economics, Tel Aviv University, Tel Aviv, Israel
| | - Arne Traulsen
- Department of Evolutionary Theory, Max-Planck-Institute for Evolutionary Biology, Ploen, Germany
| | - Yitzhak Pilpel
- Department of Molecular Genetics, Weizmann Institute of Science, Rehovot, Israel.
| | - Martin A Nowak
- Department of Mathematics, Harvard University, Cambridge, MA, USA. .,Department of Organismic and Evolutionary Biology, Harvard University, Cambridge, MA, USA.
| |
Collapse
|
15
|
Svoboda J, Tkadlec J, Pavlogiannis A, Chatterjee K, Nowak MA. Infection dynamics of COVID-19 virus under lockdown and reopening. Sci Rep 2022; 12:1526. [PMID: 35087091 PMCID: PMC8795434 DOI: 10.1038/s41598-022-05333-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/23/2021] [Accepted: 01/05/2022] [Indexed: 01/08/2023] Open
Abstract
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 slowing down and reopening society and we compare their efficiency in mitigating the spread of the virus from several different points of view. We find that in order to avoid overwhelming of the hospital system, a policy must impose a harsh lockdown or it must react swiftly (or both). While reacting swiftly is universally beneficial, being harsh pays off only when the country is patient about reopening and when the neighboring countries coordinate their mitigation efforts. Our work highlights the importance of acting decisively when closing down and the importance of patience and coordination between neighboring countries when reopening.
Collapse
Affiliation(s)
| | - Josef Tkadlec
- Department of Mathematics, Harvard University, Cambridge, MA, 02138, USA
| | | | | | - Martin A Nowak
- Department of Mathematics, Harvard University, Cambridge, MA, 02138, USA.
- Department of Organismic and Evolutionary Biology, Harvard University, Cambridge, MA, 02138, USA.
| |
Collapse
|
16
|
Abstract
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, extensive research has produced remarkable structures called strong amplifiers which guarantee that every beneficial mutation fixates with high probability. But strong amplification has come at the cost of considerably delaying the fixation event, which can slow down the overall rate of evolution. However, the precise relationship between fixation probability and time has remained elusive. Here we characterize the slowdown effect of strong amplification. First, we prove that all strong amplifiers must delay the fixation event at least to some extent. Second, we construct strong amplifiers that delay the fixation event only marginally as compared to the well-mixed populations. Our results thus establish a tight relationship between fixation probability and time: Strong amplification always comes at a cost of a slowdown, but more than a marginal slowdown is not needed.
Collapse
Affiliation(s)
- Josef Tkadlec
- grid.38142.3c000000041936754XDepartment of Mathematics, Harvard University, Cambridge, MA 02138 USA
| | - Andreas Pavlogiannis
- grid.7048.b0000 0001 1956 2722Department of Computer Science, Aarhus University, Aabogade 34, 8200 Aarhus, Denmark
| | - Krishnendu Chatterjee
- grid.33565.360000000404312247Institute of Science and Technology Austria, Am Campus 1, 3400 Klosterneuburg, Austria
| | - Martin A. Nowak
- grid.38142.3c000000041936754XDepartment of Mathematics, Harvard University, Cambridge, MA 02138 USA
| |
Collapse
|
17
|
Olejarz J, Iwasa Y, Knoll AH, Nowak MA. The Great Oxygenation Event as a consequence of ecological dynamics modulated by planetary change. Nat Commun 2021; 12:3985. [PMID: 34183660 PMCID: PMC8238953 DOI: 10.1038/s41467-021-23286-7] [Citation(s) in RCA: 13] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/04/2020] [Accepted: 04/21/2021] [Indexed: 11/09/2022] Open
Abstract
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 availability of suitable electron donors that are vulnerable to oxidation. The GOE is triggered when the difference between the influxes of relevant reductants and phosphate falls below a critical value that is an increasing function of the reproductive rate of cyanobacteria. The transition can be either gradual and reversible or sudden and irreversible, depending on sources and sinks of oxygen. Increasing sources and decreasing sinks of oxygen can also trigger the GOE, but this possibility depends strongly on migration of cyanobacteria from privileged sites. Our model links ecological dynamics to planetary change, with geophysical evolution determining the relevant time scales. The Great Oxygenation Event (GOE) 2.4 billion years ago is believed to have been critical for the evolution of complex life. Here, Olejarz et al. propose a model suggesting that competition between major bacterial groups could have triggered the GOE in a feedback loop with geophysical processes.
Collapse
Affiliation(s)
- Jason Olejarz
- Department of Organismic and Evolutionary Biology, Harvard University, Cambridge, MA, USA.
| | - Yoh Iwasa
- Department of Bioscience, School of Science and Technology, Kwansei Gakuin University, Sanda-shi, Hyogo, Japan
| | - Andrew H Knoll
- Department of Organismic and Evolutionary Biology, Harvard University, Cambridge, MA, USA
| | - Martin A Nowak
- Department of Organismic and Evolutionary Biology, Harvard University, Cambridge, MA, USA.,Department of Mathematics, Harvard University, Cambridge, MA, USA
| |
Collapse
|
18
|
Liu D, Lin JR, Robitschek EJ, Kasumova GG, Heyde A, Shi A, Kraya A, Zhang G, Moll T, Frederick DT, Chen YA, Wang S, Schapiro D, Ho LL, Bi K, Sahu A, Mei S, Miao B, Sharova T, Alvarez-Breckenridge C, Stocking JH, Kim T, Fadden R, Lawrence D, Hoang MP, Cahill DP, Malehmir M, Nowak MA, Brastianos PK, Lian CG, Ruppin E, Izar B, Herlyn M, Van Allen EM, Nathanson K, Flaherty KT, Sullivan RJ, Kellis M, Sorger PK, Boland GM. Evolution of delayed resistance to immunotherapy in a melanoma responder. Nat Med 2021; 27:985-992. [PMID: 33941922 PMCID: PMC8474080 DOI: 10.1038/s41591-021-01331-8] [Citation(s) in RCA: 54] [Impact Index Per Article: 18.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/21/2019] [Accepted: 03/24/2021] [Indexed: 02/02/2023]
Abstract
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-evolution of seven lineages with multiple convergent, but independent resistance-associated alterations. 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 RNA sequencing and highly multiplexed immunofluorescence (t-CyCIF) revealed differences in immune composition among different lineages. Imaging revealed a vasculogenic mimicry phenotype in NGFRhi tumor cells with high PD-L1 expression in close proximity to immune cells. Rapid autopsy demonstrated two 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 patient with melanoma with an unusual clinical course.
Collapse
MESH Headings
- B7-H1 Antigen/antagonists & inhibitors
- B7-H1 Antigen/genetics
- B7-H1 Antigen/immunology
- Chromosomes, Human, Pair 15/genetics
- Drug Resistance, Neoplasm/drug effects
- Female
- Gene Expression Regulation, Neoplastic
- Humans
- Immune Checkpoint Inhibitors/adverse effects
- Immune Checkpoint Inhibitors/therapeutic use
- Immunotherapy/adverse effects
- Male
- Melanoma/genetics
- Melanoma/immunology
- Melanoma/pathology
- Melanoma/therapy
- Neoplasm Metastasis
- Neoplasm Recurrence, Local/genetics
- Neoplasm Recurrence, Local/immunology
- Neoplasm Recurrence, Local/pathology
- Neoplasm Recurrence, Local/therapy
- Nerve Tissue Proteins/genetics
- Nerve Tissue Proteins/immunology
- Phylogeny
- Receptors, Nerve Growth Factor/genetics
- Receptors, Nerve Growth Factor/immunology
- Tumor Microenvironment/drug effects
Collapse
Affiliation(s)
- David Liu
- Dana-Farber Cancer Institute, Boston, MA, USA
- Broad Institute of Harvard and MIT, Cambridge, MA, USA
| | - Jia-Ren Lin
- Laboratory of Systems Pharmacology, Harvard Medical School, Boston, MA, USA
| | - Emily J Robitschek
- Dana-Farber Cancer Institute, Boston, MA, USA
- Broad Institute of Harvard and MIT, Cambridge, MA, USA
| | - Gyulnara G Kasumova
- Division of Surgical Oncology, Department of Surgery, Massachusetts General Hospital, Boston, MA, USA
| | - Alex Heyde
- Program for Evolutionary Dynamics, Harvard University, Cambridge, MA, USA
- Department of Organismic and Evolutionary Biology, Harvard University, Cambridge, MA, USA
| | - Alvin Shi
- Broad Institute of Harvard and MIT, Cambridge, MA, USA
- Computer Science and Artificial Intelligence Lab, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - Adam Kraya
- Division of Translational Medicine and Human Genetics, Department of Medicine, Perelman School of Medicine at the University of Pennsylvania, Philadelphia, PA, USA
| | - Gao Zhang
- Molecular and Cellular Oncogenesis Program, The Wistar Institute, Philadelphia, PA, USA
- Preston Robert Tisch Brain Tumor Center, Department of Neurosurgery, Department of Pathology, Duke University School of Medicine, Durham, NC, USA
| | - Tabea Moll
- Division of Medical Oncology, Department of Medicine, Massachusetts General Hospital Cancer Center, Harvard Medical School, Boston, MA, USA
| | - Dennie T Frederick
- Division of Medical Oncology, Department of Medicine, Massachusetts General Hospital Cancer Center, Harvard Medical School, Boston, MA, USA
| | - Yu-An Chen
- Laboratory of Systems Pharmacology, Harvard Medical School, Boston, MA, USA
| | - Shu Wang
- Laboratory of Systems Pharmacology, Harvard Medical School, Boston, MA, USA
| | - Denis Schapiro
- Laboratory of Systems Pharmacology, Harvard Medical School, Boston, MA, USA
- Klarman Cell Observatory, Broad Institute of MIT and Harvard, Cambridge, MA, USA
| | - Li-Lun Ho
- Broad Institute of Harvard and MIT, Cambridge, MA, USA
- Computer Science and Artificial Intelligence Lab, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - Kevin Bi
- Dana-Farber Cancer Institute, Boston, MA, USA
- Broad Institute of Harvard and MIT, Cambridge, MA, USA
| | | | - Shaolin Mei
- Dana-Farber Cancer Institute, Boston, MA, USA
- Laboratory of Systems Pharmacology, Harvard Medical School, Boston, MA, USA
| | - Benchun Miao
- Division of Medical Oncology, Department of Medicine, Massachusetts General Hospital Cancer Center, Harvard Medical School, Boston, MA, USA
| | - Tatyana Sharova
- Division of Surgical Oncology, Department of Surgery, Massachusetts General Hospital, Boston, MA, USA
| | | | - Jackson H Stocking
- Division of Medical Oncology, Department of Medicine, Massachusetts General Hospital Cancer Center, Harvard Medical School, Boston, MA, USA
| | - Tommy Kim
- Division of Surgical Oncology, Department of Surgery, Massachusetts General Hospital, Boston, MA, USA
| | - Riley Fadden
- Division of Medical Oncology, Department of Medicine, Massachusetts General Hospital Cancer Center, Harvard Medical School, Boston, MA, USA
| | - Donald Lawrence
- Division of Medical Oncology, Department of Medicine, Massachusetts General Hospital Cancer Center, Harvard Medical School, Boston, MA, USA
| | - Mai P Hoang
- Department of Pathology, Harvard Medical School, Massachusetts General Hospital, Boston, MA, USA
| | - Daniel P Cahill
- Department of Neurosurgery, Harvard Medical School, Massachusetts General Hospital, Boston, MA, USA
| | - Mohsen Malehmir
- Broad Institute of Harvard and MIT, Cambridge, MA, USA
- Division of Surgical Oncology, Department of Surgery, Massachusetts General Hospital, Boston, MA, USA
| | - Martin A Nowak
- Program for Evolutionary Dynamics, Harvard University, Cambridge, MA, USA
- Department of Organismic and Evolutionary Biology, Harvard University, Cambridge, MA, USA
- Department of Mathematics, Harvard University, Cambridge, MA, USA
| | - Priscilla K Brastianos
- Division of Medical Oncology, Department of Medicine, Massachusetts General Hospital Cancer Center, Harvard Medical School, Boston, MA, USA
| | - Christine G Lian
- Department of Pathology, Harvard Medical School, Brigham and Woman's Hospital, Boston, MA, USA
| | - Eytan Ruppin
- Cancer Data Science Lab, National Cancer Institute, National Institutes of Health, Bethesda, MD, USA
| | - Benjamin Izar
- Division of Hematology and Oncology, Columbia University Irving Medical Center, New York, NY, USA
- Columbia Center for Translation Immunology, New York, NY, USA
| | - Meenhard Herlyn
- Molecular and Cellular Oncogenesis Program, The Wistar Institute, Philadelphia, PA, USA
| | - Eliezer M Van Allen
- Dana-Farber Cancer Institute, Boston, MA, USA
- Broad Institute of Harvard and MIT, Cambridge, MA, USA
| | - Katherine Nathanson
- Division of Translational Medicine and Human Genetics, Department of Medicine, Perelman School of Medicine at the University of Pennsylvania, Philadelphia, PA, USA
- Basser Center for BRCA, Perelman School of Medicine at the University of Pennsylvania, Philadelphia, PA, USA
- Abramson Cancer Center, Perelman School of Medicine at the University of Pennsylvania, Philadelphia, PA, USA
| | - Keith T Flaherty
- Division of Medical Oncology, Department of Medicine, Massachusetts General Hospital Cancer Center, Harvard Medical School, Boston, MA, USA
| | - Ryan J Sullivan
- Division of Medical Oncology, Department of Medicine, Massachusetts General Hospital Cancer Center, Harvard Medical School, Boston, MA, USA
| | - Manolis Kellis
- Broad Institute of Harvard and MIT, Cambridge, MA, USA
- Computer Science and Artificial Intelligence Lab, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - Peter K Sorger
- Laboratory of Systems Pharmacology, Harvard Medical School, Boston, MA, USA
- Department of Systems Biology, Harvard Medical School, Cambridge, MA, USA
| | - Genevieve M Boland
- Broad Institute of Harvard and MIT, Cambridge, MA, USA.
- Division of Surgical Oncology, Department of Surgery, Massachusetts General Hospital, Boston, MA, USA.
| |
Collapse
|
19
|
Veller C, Edelman NB, Muralidhar P, Nowak MA. Variation in Genetic Relatedness Is Determined by the Aggregate Recombination Process. Genetics 2020; 216:985-994. [PMID: 33109528 PMCID: PMC7768252 DOI: 10.1534/genetics.120.303680] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/09/2020] [Accepted: 10/21/2020] [Indexed: 12/25/2022] Open
Abstract
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, and have neglected crossover interference and sex differences in recombination. Here, we consider genetic relatedness as the proportion of the total physical genome (bp) shared by relatives, and calculate its variance for general pedigree relationships, making no assumptions about the recombination process. For the relationships of grandparent-grandoffspring and siblings, the variance of genetic relatedness is a simple decreasing function of [Formula: see text], the average proportion of locus pairs that recombine in meiosis. For general pedigree relationships, the variance of genetic relatedness is a function of metrics analogous to [Formula: see text] Therefore, features of the aggregate recombination process that affect [Formula: see text] and analogs also affect variance in genetic relatedness. Such features include the number of chromosomes and heterogeneity in their size, the number of crossovers and their spatial organization along chromosomes, and sex differences in recombination. Our calculations help to explain several recent observations about variance in genetic relatedness, including that it is reduced by crossover interference (which is known to increase [Formula: see text]). Our methods further allow us to calculate the neutral variance of ancestry among F2s in a hybrid cross, enabling precise statistical inference in F2-based tests for various kinds of selection.
Collapse
Affiliation(s)
- Carl Veller
- Department of Organismic and Evolutionary Biology, Harvard University, Cambridge, Massachusetts 02138
| | - Nathaniel B Edelman
- Department of Organismic and Evolutionary Biology, Harvard University, Cambridge, Massachusetts 02138
| | - Pavitra Muralidhar
- Department of Organismic and Evolutionary Biology, Harvard University, Cambridge, Massachusetts 02138
| | - Martin A Nowak
- Department of Organismic and Evolutionary Biology, Harvard University, Cambridge, Massachusetts 02138
- Department of Mathematics, Harvard University, Cambridge, Massachusetts 02138
| |
Collapse
|
20
|
Abstract
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 node is poorer. More colors can represent a broader spectrum of resource qualities. For a population evolving according to the birth-death Moran model, the first question we address is which structures, identified by graph connectivity and graph coloring, are evolutionarily equivalent. We prove that all properly two-colored, undirected, regular graphs are evolutionarily equivalent (where “properly colored” means that no two neighbors have the same color). We then compare the effects of background heterogeneity on properly two-colored graphs to those with alternative schemes in which the colors are permuted. Finally, we discuss dynamic coloring as a model for spatiotemporal resource fluctuations, and we illustrate that random dynamic colorings often diminish the effects of background heterogeneity relative to a proper two-coloring. Heterogeneity in environmental conditions can have profound effects on long-term evolutionary outcomes in structured populations. We consider a population evolving on a colored graph, wherein the color of a node represents the resources at that location. Using a combination of analytical and numerical methods, we quantify the effects of background heterogeneity on a population’s dynamics. In addition to considering the notion of an “optimal” coloring with respect to mutant invasion, we also study the effects of dynamic spatial redistribution of resources as the population evolves. Although the effects of static background heterogeneity can be quite striking, these effects are often attenuated by the movement (or “flow”) of the underlying resources.
Collapse
Affiliation(s)
- Kamran Kaveh
- Department of Mathematics, Dartmouth College, Hanover, New Hampshire, United States
- * E-mail: (KK); (AM)
| | - Alex McAvoy
- Department of Mathematics, University of Pennsylvania, Philadelphia, Pennsylvania, United States
- * E-mail: (KK); (AM)
| | | | - Martin A. Nowak
- Department of Mathematics, Harvard University, Cambridge, Massachusetts, United States
- Department of Organismic and Evolutionary Biology, Harvard University, Cambridge, Massachusetts, United States
| |
Collapse
|
21
|
Burum B, Nowak MA, Hoffman M. An evolutionary explanation for ineffective altruism. Nat Hum Behav 2020; 4:1245-1257. [DOI: 10.1038/s41562-020-00950-4] [Citation(s) in RCA: 12] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/20/2020] [Accepted: 08/11/2020] [Indexed: 11/09/2022]
|
22
|
Krieger MS, Denison CE, Anderson TL, Nowak MA, Hill AL. Population structure across scales facilitates coexistence and spatial heterogeneity of antibiotic-resistant infections. PLoS Comput Biol 2020; 16:e1008010. [PMID: 32628660 PMCID: PMC7365476 DOI: 10.1371/journal.pcbi.1008010] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/18/2020] [Revised: 07/16/2020] [Accepted: 06/02/2020] [Indexed: 12/31/2022] Open
Abstract
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 that accounting for structured or spatially-heterogeneous host populations and variability in antibiotic consumption can lead to persistent coexistence over a wide range of treatment coverages, drug efficacies, costs of resistance, and mixing patterns. Moreover, this mechanism can explain other puzzling spatiotemporal features of drug-resistance epidemiology that have received less attention, such as large differences in the prevalence of resistance between geographical regions with similar antibiotic consumption or that neighbor one another. We find that the same amount of antibiotic use can lead to very different levels of resistance depending on how treatment is distributed in a transmission network. We also identify parameter regimes in which population structure alone cannot support coexistence, suggesting the need for other mechanisms to explain the epidemiology of antibiotic resistance. Our analysis identifies key features of host population structure that can be used to assess resistance risk and highlights the need to include spatial or demographic heterogeneity in models to guide resistance management.
Collapse
Affiliation(s)
- Madison S. Krieger
- Department of Organismic & Evolutionary Biology, Harvard University, Cambridge, Massachusetts, United States of America
| | - Carson E. Denison
- Department of Organismic & Evolutionary Biology, Harvard University, Cambridge, Massachusetts, United States of America
| | - Thayer L. Anderson
- Department of Organismic & Evolutionary Biology, Harvard University, Cambridge, Massachusetts, United States of America
| | - Martin A. Nowak
- Department of Organismic & Evolutionary Biology, Harvard University, Cambridge, Massachusetts, United States of America
| | - Alison L. Hill
- Department of Organismic & Evolutionary Biology, Harvard University, Cambridge, Massachusetts, United States of America
| |
Collapse
|
23
|
Sakamoto H, Attiyeh MA, Gerold JM, Makohon-Moore AP, Hayashi A, Hong J, Kappagantula R, Zhang L, Melchor JP, Reiter JG, Heyde A, Bielski CM, Penson AV, Gönen M, Chakravarty D, O'Reilly EM, Wood LD, Hruban RH, Nowak MA, Socci ND, Taylor BS, Iacobuzio-Donahue CA. The Evolutionary Origins of Recurrent Pancreatic Cancer. Cancer Discov 2020; 10:792-805. [PMID: 32193223 PMCID: PMC7323937 DOI: 10.1158/2159-8290.cd-19-1508] [Citation(s) in RCA: 56] [Impact Index Per Article: 14.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/19/2019] [Revised: 03/06/2020] [Accepted: 03/16/2020] [Indexed: 11/16/2022]
Abstract
Surgery is the only curative option for stage I/II pancreatic cancer; nonetheless, most patients will experience a recurrence 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 distant metastases. We identified that recurrent disease after adjuvant or first-line platinum therapy corresponds to an increased mutational burden. Recurrent disease is enriched for genetic alterations predicted to activate MAPK/ERK and PI3K-AKT signaling and develops from a monophyletic or polyphyletic origin. Treatment-induced genetic bottlenecks lead to a modified genetic landscape and subclonal heterogeneity for driver gene alterations in part due to intermetastatic seeding. In 1 patient what was believed to be recurrent disease was an independent (second) primary tumor. These findings suggest routine post-treatment sampling may have value in the management of recurrent pancreatic cancer. SIGNIFICANCE: The biological features or clinical vulnerabilities of recurrent pancreatic cancer after pancreaticoduodenectomy are unknown. Using whole-exome sequencing we find that recurrent disease has a distinct genomic landscape, intermetastatic genetic heterogeneity, diverse clonal origins, and higher mutational burden than found for treatment-naïve disease.See related commentary by Bednar and Pasca di Magliano, p. 762.This article is highlighted in the In This Issue feature, p. 747.
Collapse
Affiliation(s)
- Hitomi Sakamoto
- Sloan Kettering Institute, Memorial Sloan Kettering Cancer Center, New York, New York
| | - Marc A Attiyeh
- Sloan Kettering Institute, Memorial Sloan Kettering Cancer Center, New York, New York
| | - Jeffrey M Gerold
- Program for Evolutionary Dynamics, Harvard University, Cambridge, Massachusetts
- Department of Mathematics and Department of Organismic and Evolutionary Biology, Harvard University, Cambridge, Massachusetts
| | - Alvin P Makohon-Moore
- Sloan Kettering Institute, Memorial Sloan Kettering Cancer Center, New York, New York
- Human Oncology and Pathogenesis Program, Memorial Sloan Kettering Cancer Center, New York, New York
| | - Akimasa Hayashi
- Sloan Kettering Institute, Memorial Sloan Kettering Cancer Center, New York, New York
| | - Jungeui Hong
- Sloan Kettering Institute, Memorial Sloan Kettering Cancer Center, New York, New York
| | - Rajya Kappagantula
- Sloan Kettering Institute, Memorial Sloan Kettering Cancer Center, New York, New York
- Department of Pathology, Memorial Sloan Kettering Cancer Center, New York, New York
| | - Lance Zhang
- Sloan Kettering Institute, Memorial Sloan Kettering Cancer Center, New York, New York
| | - Jerry P Melchor
- Sloan Kettering Institute, Memorial Sloan Kettering Cancer Center, New York, New York
| | - Johannes G Reiter
- Canary Center for Cancer Early Detection, Department of Radiology, Stanford University, Palo Alto, California
| | - Alexander Heyde
- Program for Evolutionary Dynamics, Harvard University, Cambridge, Massachusetts
- Department of Mathematics and Department of Organismic and Evolutionary Biology, Harvard University, Cambridge, Massachusetts
| | - Craig M Bielski
- Marie-Josee and Henry R. Kravis Center for Molecular Oncology, Memorial Sloan Kettering Cancer Center, New York, New York
| | - Alexander V Penson
- Human Oncology and Pathogenesis Program, Memorial Sloan Kettering Cancer Center, New York, New York
- Department of Epidemiology and Biostatistics, Memorial Sloan Kettering Cancer Center, New York, New York
| | - Mithat Gönen
- Department of Epidemiology and Biostatistics, Memorial Sloan Kettering Cancer Center, New York, New York
| | - Debyani Chakravarty
- Marie-Josee and Henry R. Kravis Center for Molecular Oncology, Memorial Sloan Kettering Cancer Center, New York, New York
| | - Eileen M O'Reilly
- Human Oncology and Pathogenesis Program, Memorial Sloan Kettering Cancer Center, New York, New York
- Department of Medicine, Memorial Sloan Kettering Cancer Center, New York, New York
| | - Laura D Wood
- Department of Pathology, Johns Hopkins Medical Institutions, Baltimore, Maryland
- Sol Goldman Pancreatic Cancer Research Center, Baltimore, Maryland
| | - Ralph H Hruban
- Department of Pathology, Johns Hopkins Medical Institutions, Baltimore, Maryland
- Sol Goldman Pancreatic Cancer Research Center, Baltimore, Maryland
| | - Martin A Nowak
- Program for Evolutionary Dynamics, Harvard University, Cambridge, Massachusetts
- Department of Mathematics and Department of Organismic and Evolutionary Biology, Harvard University, Cambridge, Massachusetts
| | - Nicholas D Socci
- Bioinformatics Core, Memorial Sloan Kettering Cancer Center, New York, New York
- David M. Rubenstein Center for Pancreatic Cancer Research, Memorial Sloan Kettering Cancer Center, New York, New York
| | - Barry S Taylor
- Human Oncology and Pathogenesis Program, Memorial Sloan Kettering Cancer Center, New York, New York
- Marie-Josee and Henry R. Kravis Center for Molecular Oncology, Memorial Sloan Kettering Cancer Center, New York, New York
- Department of Epidemiology and Biostatistics, Memorial Sloan Kettering Cancer Center, New York, New York
| | - Christine A Iacobuzio-Donahue
- Human Oncology and Pathogenesis Program, Memorial Sloan Kettering Cancer Center, New York, New York.
- Department of Pathology, Memorial Sloan Kettering Cancer Center, New York, New York
- David M. Rubenstein Center for Pancreatic Cancer Research, Memorial Sloan Kettering Cancer Center, New York, New York
| |
Collapse
|
24
|
Tkadlec J, Pavlogiannis A, Chatterjee K, Nowak MA. Limits on amplifiers of natural selection under death-Birth updating. PLoS Comput Biol 2020; 16:e1007494. [PMID: 31951609 PMCID: PMC6968837 DOI: 10.1371/journal.pcbi.1007494] [Citation(s) in RCA: 24] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/03/2019] [Accepted: 10/18/2019] [Indexed: 12/29/2022] Open
Abstract
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 amplifiers exist for the Birth-death Moran process, some of them substantially increasing the fixation probability or even guaranteeing fixation in the limit of large population size. On the other hand, no amplifiers are known for the death-Birth Moran process, and computer-assisted exhaustive searches have failed to discover amplification. In this work we resolve this disparity, by showing that any amplification under death-Birth updating is necessarily bounded and transient. Our boundedness result states that even if a population structure does amplify selection, the resulting fixation probability is close to that of the well-mixed population. Our transience result states that for any population structure there exists a threshold r⋆ such that the population structure ceases to amplify selection if the mutant fitness advantage r is larger than r⋆. Finally, we also extend the above results to δ-death-Birth updating, which is a combination of Birth-death and death-Birth updating. On the positive side, we identify population structures that maintain amplification for a wide range of values r and δ. These results demonstrate that amplification of natural selection depends on the specific mechanisms of the evolutionary process. Extensive literature exists on amplifiers of natural selection for the Birth-death Moran process, but no amplifiers are known for the death-Birth Moran process. Here we show that if amplifiers exist under death-Birth updating, they must be bounded and transient. Boundedness implies weak amplification, and transience implies amplification for only a limited range of the mutant fitness advantage. These results demonstrate that amplification depends on the specific mechanisms of the evolutionary process.
Collapse
Affiliation(s)
| | | | | | - Martin A. Nowak
- Program for Evolutionary Dynamics, Department of Organismic and Evolutionary Biology, Department of Mathematics, Harvard University, Cambridge, Massachusetts, United States of America
- * E-mail:
| |
Collapse
|
25
|
Abstract
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 that they play in one time step influence the games to be played in the next time step. Within this model, we study the evolution of cooperation in structured populations and find a simple rule: Weak selection favors cooperation over defection if the ratio of the benefit provided by an altruistic behavior, b, to the corresponding cost, c, exceeds [Formula: see text], where k is the average number of neighbors of an individual and [Formula: see text] captures the effects of the game transitions. Even if cooperation cannot be favored in each individual game, allowing for a transition to a relatively valuable game after mutual cooperation and to a less valuable game after defection can result in a favorable outcome for cooperation. In particular, small variations in different games being played can promote cooperation markedly. Our results suggest that simple game transitions can serve as a mechanism for supporting prosocial behaviors in highly connected populations.
Collapse
Affiliation(s)
- Qi Su
- Center for Systems and Control, College of Engineering, Peking University, Beijing 100871, China
- Program for Evolutionary Dynamics, Harvard University, Cambridge, MA 02138
| | - Alex McAvoy
- Department of Organismic and Evolutionary Biology, Harvard University, Cambridge, MA 02138;
| | - Long Wang
- Center for Systems and Control, College of Engineering, Peking University, Beijing 100871, China;
| | - Martin A Nowak
- Program for Evolutionary Dynamics, Harvard University, Cambridge, MA 02138;
- Department of Organismic and Evolutionary Biology, Harvard University, Cambridge, MA 02138
- Department of Mathematics, Harvard University, Cambridge, MA 02138
| |
Collapse
|
26
|
Gudowska-Nowak E, Nowak MA, Chialvo DR, Ochab JK, Tarnowski W. From Synaptic Interactions to Collective Dynamics in Random Neuronal Networks Models: Critical Role of Eigenvectors and Transient Behavior. Neural Comput 2019; 32:395-423. [PMID: 31835001 DOI: 10.1162/neco_a_01253] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/04/2022]
Abstract
The study of neuronal interactions is at the center of several big collaborative neuroscience projects (including the Human Connectome Project, the Blue Brain Project, and the Brainome) that attempt to obtain a detailed map of the entire brain. Under certain constraints, mathematical theory can advance predictions of the expected neural dynamics based solely on the statistical properties of the synaptic interaction matrix. This work explores the application of free random variables to the study of large synaptic interaction matrices. Besides recovering in a straightforward way known results on eigenspectra in types of models of neural networks proposed by Rajan and Abbott (2006), we extend them to heavy-tailed distributions of interactions. More important, we analytically derive the behavior of eigenvector overlaps, which determine the stability of the spectra. We observe that on imposing the neuronal excitation/inhibition balance, despite the eigenvalues remaining unchanged, their stability dramatically decreases due to the strong nonorthogonality of associated eigenvectors. This leads us to the conclusion that understanding the temporal evolution of asymmetric neural networks requires considering the entangled dynamics of both eigenvectors and eigenvalues, which might bear consequences for learning and memory processes in these models. Considering the success of free random variables theory in a wide variety of disciplines, we hope that the results presented here foster the additional application of these ideas in the area of brain sciences.
Collapse
Affiliation(s)
- E Gudowska-Nowak
- Marian Smoluchowski Institute of Physics and Mark Kac Complex Systems Research Center, Jagiellonian University, PL 30-348 Kraków, Poland
| | - M A Nowak
- Marian Smoluchowski Institute of Physics and Mark Kac Complex Systems Research Center, Jagiellonian University, PL 30-348 Kraków, Poland
| | - D R Chialvo
- Center for Complex Systems and Brain Sciences, Escuela de Ciencia y Tecnología, Universidad Nacional de San Martín, San Martín, 1650 Buenos Aires, Argentina and Consejo Nacional de Investigaciones Científicas y Tecnológicas, 1650 Buenos Aires, Argentina
| | - J K Ochab
- Marian Smoluchowski Institute of Physics and Mark Kac Complex Systems Research Center, Jagiellonian University, PL 30-348 Kraków, Poland
| | - W Tarnowski
- Marian Smoluchowski Institute of Physics and Mark Kac Complex Systems Research Center, Jagiellonian University, PL 30-348 Kraków, Poland
| |
Collapse
|
27
|
Reiter JG, Baretti M, Gerold JM, Makohon-Moore AP, Daud A, Iacobuzio-Donahue CA, Azad NS, Kinzler KW, Nowak MA, Vogelstein B. An analysis of genetic heterogeneity in untreated cancers. Nat Rev Cancer 2019; 19:639-650. [PMID: 31455892 PMCID: PMC6816333 DOI: 10.1038/s41568-019-0185-x] [Citation(s) in RCA: 120] [Impact Index Per Article: 24.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Accepted: 07/23/2019] [Indexed: 12/12/2022]
Abstract
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 epithelial cancers, with particular regard to its clinical relevance. We find that the homogeneity of predicted functional mutations in driver genes is the rule rather than the exception. In primary tumours with multiple samples, 97% of driver-gene mutations in 38 patients were homogeneous. Moreover, among metastases from the same primary tumour, 100% of the driver mutations in 17 patients were homogeneous. With a single biopsy of a primary tumour in 14 patients, the likelihood of missing a functional driver-gene mutation that was present in all metastases was 2.6%. Furthermore, all functional driver-gene mutations detected in these 14 primary tumours were present among all their metastases. Finally, we found that individual metastatic lesions responded concordantly to targeted therapies in 91% of 44 patients. These analyses indicate that the cells within the primary tumours that gave rise to metastases are genetically homogeneous with respect to functional driver-gene mutations, and we suggest that future efforts to develop combination therapies have the potential to be curative.
Collapse
Affiliation(s)
- Johannes G Reiter
- Canary Center for Cancer Early Detection, Department of Radiology, Stanford University School of Medicine, Palo Alto, CA, USA.
| | - Marina Baretti
- The Sidney Kimmel Cancer Center, Johns Hopkins University School of Medicine, Baltimore, MD, USA
| | - Jeffrey M Gerold
- Program for Evolutionary Dynamics, Harvard University, Cambridge, MA, USA
| | - Alvin P Makohon-Moore
- The David M. Rubenstein Center for Pancreatic Cancer Research, Human Oncology and Pathogenesis Program, Memorial Sloan Kettering Cancer Center, New York, NY, USA
| | - Adil Daud
- University of California, San Francisco, San Francisco, CA, USA
| | - Christine A Iacobuzio-Donahue
- The David M. Rubenstein Center for Pancreatic Cancer Research, Human Oncology and Pathogenesis Program, Memorial Sloan Kettering Cancer Center, New York, NY, USA
- Department of Pathology, Memorial Sloan Kettering Cancer Center, New York, NY, USA
| | - Nilofer S Azad
- The Sidney Kimmel Cancer Center, Johns Hopkins University School of Medicine, Baltimore, MD, USA
| | - Kenneth W Kinzler
- The Sidney Kimmel Cancer Center, Johns Hopkins University School of Medicine, Baltimore, MD, USA
- The Ludwig Center, Johns Hopkins University School of Medicine, Baltimore, MD, USA
- The Sol Goldman Pancreatic Cancer Research Center, Johns Hopkins University School of Medicine, Baltimore, MD, USA
| | - Martin A Nowak
- Program for Evolutionary Dynamics, Harvard University, Cambridge, MA, USA.
- Department of Organismic and Evolutionary Biology, Harvard University, Cambridge, MA, USA.
- Department of Mathematics, Harvard University, Cambridge, MA, USA.
| | - Bert Vogelstein
- The Sidney Kimmel Cancer Center, Johns Hopkins University School of Medicine, Baltimore, MD, USA.
- The Ludwig Center, Johns Hopkins University School of Medicine, Baltimore, MD, USA.
- The Sol Goldman Pancreatic Cancer Research Center, Johns Hopkins University School of Medicine, Baltimore, MD, USA.
- Howard Hughes Medical Institute, Johns Hopkins University School of Medicine, Baltimore, MD, USA.
| |
Collapse
|
28
|
Abstract
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 cooperation and welfare7-10. Most previous models of reciprocity do not include inequality11-15. 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.
Collapse
Affiliation(s)
- Oliver P Hauser
- Department of Economics, University of Exeter Business School, Exeter, UK.
| | | | | | - Martin A Nowak
- Program for Evolutionary Dynamics, Harvard University, Cambridge, MA, USA. .,Department of Organismic and Evolutionary Biology, Harvard University, Cambridge, MA, USA. .,Department of Mathematics, Harvard University, Cambridge, MA, USA.
| |
Collapse
|
29
|
Abstract
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 none of the diversity in the primary tumor is transmitted to the metastasis. In contrast, if a metastasis is seeded by multiple cells, then some genetic diversity in the primary tumor can be transmitted. We study a multitype branching process of metastasis growth that originates from a single cell but over time receives additional cells. We derive a surprisingly simple formula that relates the expected diversity of a metastasis to the diversity in the pool of seeding cells. We calculate the probability that a metastasis is polyclonal. We apply our framework to published datasets for which polyclonality has been previously reported, analyzing 68 ovarian cancer samples, 31 breast cancer samples, and 8 colorectal cancer samples from 15 patients. For these clonally diverse metastases, under typical metastasis growth conditions, we find that 10 to 150 cells seeded each metastasis and left surviving lineages between initial formation and clinical detection.
Collapse
Affiliation(s)
- Alexander Heyde
- Program for Evolutionary Dynamics, Harvard University, Cambridge, MA 02138;
- Department of Organismic and Evolutionary Biology, Harvard University, Cambridge, MA 02138
| | - Johannes G Reiter
- Canary Center for Cancer Early Detection, Department of Radiology, Stanford University School of Medicine, Palo Alto, CA 94304
| | - Kamila Naxerova
- Center for Systems Biology, Massachusetts General Hospital and Harvard Medical School, Boston, MA 02114
- Department of Radiology, Massachusetts General Hospital and Harvard Medical School, Boston, MA 02114
| | - Martin A Nowak
- Program for Evolutionary Dynamics, Harvard University, Cambridge, MA 02138;
- Department of Organismic and Evolutionary Biology, Harvard University, Cambridge, MA 02138
- Department of Mathematics, Harvard University, Cambridge, MA 02138
| |
Collapse
|
30
|
Sinai S, Olejarz J, Neagu IA, Nowak MA. Primordial sex facilitates the emergence of evolution. J R Soc Interface 2019; 15:rsif.2018.0003. [PMID: 29491181 DOI: 10.1098/rsif.2018.0003] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/02/2018] [Accepted: 02/05/2018] [Indexed: 12/22/2022] Open
Abstract
Compartments are ubiquitous throughout biology, and they have very likely played a crucial role at the origin of life. Here we assume that a protocell, which is a compartment enclosing functional components, requires N such components in order to be evolvable. We calculate the timescale in which a minimal evolvable protocell is produced. We show that when protocells fuse and share information, the timescales polynomially in N By contrast, in the absence of fusion, the worst-case scenario is exponential in N We discuss the implications of this result for the origin of life and other biological processes.
Collapse
Affiliation(s)
- Sam Sinai
- Program for Evolutionary Dynamics, Harvard University, Cambridge, MA 02138, USA .,Department of Organismic and Evolutionary Biology, Harvard University, Cambridge, MA 02138, USA
| | - Jason Olejarz
- Program for Evolutionary Dynamics, Harvard University, Cambridge, MA 02138, USA
| | - Iulia A Neagu
- Program for Evolutionary Dynamics, Harvard University, Cambridge, MA 02138, USA.,Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - Martin A Nowak
- Program for Evolutionary Dynamics, Harvard University, Cambridge, MA 02138, USA .,Department of Organismic and Evolutionary Biology, Harvard University, Cambridge, MA 02138, USA.,Department of Mathematics, Harvard University, Cambridge, MA 02138, USA
| |
Collapse
|
31
|
Gruber M, Bozic I, Leshchiner I, Livitz D, Stevenson K, Rassenti L, Rosebrock D, Taylor-Weiner A, Olive O, Goyetche R, Fernandes SM, Sun J, Stewart C, Wong A, Cibulskis C, Zhang W, Reiter JG, Gerold JM, Gribben JG, Rai KR, Keating MJ, Brown JR, Neuberg D, Kipps TJ, Nowak MA, Getz G, Wu CJ. Growth dynamics in naturally progressing chronic lymphocytic leukaemia. Nature 2019; 570:474-479. [PMID: 31142838 PMCID: PMC6630176 DOI: 10.1038/s41586-019-1252-x] [Citation(s) in RCA: 69] [Impact Index Per Article: 13.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/26/2017] [Accepted: 05/01/2019] [Indexed: 01/01/2023]
Abstract
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 that CLL commonly demonstrates not only exponential expansion but also logistic growth, which is sigmoidal and reaches a certain steady-state level. Each growth pattern was associated with marked differences in genetic composition, the pace of disease progression and the extent of clonal evolution. In a subset of patients, whose serial samples underwent next-generation sequencing, we found that dynamic changes in the disease course of CLL were shaped by the genetic events that were already present in the early slow-growing stages. Finally, by analysing the growth rates of subclones compared with their parental clones, we quantified the growth advantage conferred by putative CLL drivers in vivo.
Collapse
MESH Headings
- Cell Proliferation/drug effects
- Clone Cells/drug effects
- Clone Cells/pathology
- Cohort Studies
- Disease Progression
- Evolution, Molecular
- Female
- High-Throughput Nucleotide Sequencing
- Humans
- Leukemia, Lymphocytic, Chronic, B-Cell/drug therapy
- Leukemia, Lymphocytic, Chronic, B-Cell/genetics
- Leukemia, Lymphocytic, Chronic, B-Cell/pathology
- Male
- Neoplasm Recurrence, Local/genetics
- Neoplasm Recurrence, Local/pathology
- Recurrence
- Reproducibility of Results
Collapse
Affiliation(s)
- Michaela Gruber
- Department of Medical Oncology, Dana-Farber Cancer Institute, Boston, MA, USA
- Broad Institute of MIT and Harvard, Cambridge, MA, USA
- Department of Internal Medicine I, Division of Haematology and Haemostaseology, Comprehensive Cancer Center, Medical University of Vienna, Vienna, Austria
- CeMM Research Center for Molecular Medicine of the Austrian Academy of Sciences, Vienna, Austria
| | - Ivana Bozic
- Department of Applied Mathematics, University of Washington, Seattle, WA, USA
| | | | | | - Kristen Stevenson
- Department of Biostatistics and Computational Biology, Dana Farber Cancer Institute, Boston, MA, USA
| | - Laura Rassenti
- Department of Medicine, University of California at San Diego Moores Cancer Center, La Jolla, CA, USA
| | | | | | - Oriol Olive
- Department of Medical Oncology, Dana-Farber Cancer Institute, Boston, MA, USA
| | - Reaha Goyetche
- Department of Medical Oncology, Dana-Farber Cancer Institute, Boston, MA, USA
| | - Stacey M Fernandes
- Department of Medical Oncology, Dana-Farber Cancer Institute, Boston, MA, USA
| | - Jing Sun
- Department of Medical Oncology, Dana-Farber Cancer Institute, Boston, MA, USA
| | - Chip Stewart
- Broad Institute of MIT and Harvard, Cambridge, MA, USA
| | - Alicia Wong
- Broad Institute of MIT and Harvard, Cambridge, MA, USA
| | | | - Wandi Zhang
- Department of Medical Oncology, Dana-Farber Cancer Institute, Boston, MA, USA
| | - Johannes G Reiter
- Program for Evolutionary Dynamics, Harvard University, Cambridge, MA, USA
| | - Jeffrey M Gerold
- Program for Evolutionary Dynamics, Harvard University, Cambridge, MA, USA
| | - John G Gribben
- Barts Cancer Institute, Queen Mary, University of London, London, UK
| | - Kanti R Rai
- Hofstra North Shore-LIJ School of Medicine, Lake Success, NY, USA
| | | | - Jennifer R Brown
- Department of Medical Oncology, Dana-Farber Cancer Institute, Boston, MA, USA
- Department of Medicine, Brigham and Women's Hospital, Boston, MA, USA
- Harvard Medical School, Boston, MA, USA
| | - Donna Neuberg
- Department of Biostatistics and Computational Biology, Dana Farber Cancer Institute, Boston, MA, USA
| | - Thomas J Kipps
- Department of Medicine, University of California at San Diego Moores Cancer Center, La Jolla, CA, USA
| | - Martin A Nowak
- Program for Evolutionary Dynamics, Harvard University, Cambridge, MA, USA
- Department of Mathematics and Department of Organismic and Evolutionary Biology, Harvard University, Cambridge, MA, USA
| | - Gad Getz
- Broad Institute of MIT and Harvard, Cambridge, MA, USA.
- Harvard Medical School, Boston, MA, USA.
- Department of Pathology, Massachusetts General Hospital, Boston, MA, USA.
- Center for Cancer Research, Massachusetts General Hospital, Boston, MA, USA.
| | - Catherine J Wu
- Department of Medical Oncology, Dana-Farber Cancer Institute, Boston, MA, USA.
- Broad Institute of MIT and Harvard, Cambridge, MA, USA.
- Department of Medicine, Brigham and Women's Hospital, Boston, MA, USA.
- Harvard Medical School, Boston, MA, USA.
| |
Collapse
|
32
|
Tkadlec J, Pavlogiannis A, Chatterjee K, Nowak MA. Population structure determines the tradeoff between fixation probability and fixation time. Commun Biol 2019; 2:138. [PMID: 31044163 PMCID: PMC6478818 DOI: 10.1038/s42003-019-0373-y] [Citation(s) in RCA: 24] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/07/2018] [Accepted: 03/07/2019] [Indexed: 12/04/2022] Open
Abstract
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 structures that achieve a tradeoff between fixation probability and time. First, we show that no amplifiers can have an asymptotically lower absorption time than the well-mixed population. Then we design population structures that substantially augment the fixation probability with just a minor increase in fixation time. Finally, we show that those structures enable higher effective rate of evolution than the well-mixed population provided that the rate of generating advantageous mutants is relatively low. Our work sheds light on how population structure affects the rate of evolution. Moreover, our structures could be useful for lab-based, medical, or industrial applications of evolutionary optimization.
Collapse
Affiliation(s)
| | | | | | - Martin A. Nowak
- Program for Evolutionary Dynamics, Department of Organismic and Evolutionary Biology, Department of Mathematics, Harvard University, Cambridge, MA 02138 USA
| |
Collapse
|
33
|
Noble C, Min J, Olejarz J, Buchthal J, Chavez A, Smidler AL, DeBenedictis EA, Church GM, Nowak MA, Esvelt KM. Daisy-chain gene drives for the alteration of local populations. Proc Natl Acad Sci U S A 2019; 116:8275-8282. [PMID: 30940750 PMCID: PMC6486765 DOI: 10.1073/pnas.1716358116] [Citation(s) in RCA: 101] [Impact Index Per Article: 20.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022] Open
Abstract
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 comprising genetic elements arranged in a daisy chain such that each drives the next. "Daisy-drive" systems can locally duplicate any effect achievable by using an equivalent self-propagating drive system, but their capacity to spread is limited by the successive loss of nondriving elements from one end of the chain. Releasing daisy-drive organisms constituting a small fraction of the local wild population can drive a useful genetic element nearly to local fixation for a wide range of fitness parameters without self-propagating spread. We additionally report numerous highly active guide RNA sequences sharing minimal homology that may enable evolutionarily stable daisy drive as well as self-propagating CRISPR-based gene drive. Especially when combined with threshold dependence, daisy drives could simplify decision-making and promote ethical use by enabling local communities to decide whether, when, and how to alter local ecosystems.
Collapse
Affiliation(s)
- Charleston Noble
- Program for Evolutionary Dynamics, Harvard University, Cambridge, MA 02138
- Department of Genetics, Harvard Medical School, Boston, MA 02115
| | - John Min
- Department of Genetics, Harvard Medical School, Boston, MA 02115
- Media Laboratory, Massachusetts Institute of Technology, Cambridge, MA 02139
- Wyss Institute for Biologically Inspired Engineering, Harvard University, Cambridge, MA 02138
| | - Jason Olejarz
- Program for Evolutionary Dynamics, Harvard University, Cambridge, MA 02138
| | - Joanna Buchthal
- Media Laboratory, Massachusetts Institute of Technology, Cambridge, MA 02139
- Wyss Institute for Biologically Inspired Engineering, Harvard University, Cambridge, MA 02138
| | - Alejandro Chavez
- Department of Genetics, Harvard Medical School, Boston, MA 02115
- Wyss Institute for Biologically Inspired Engineering, Harvard University, Cambridge, MA 02138
- Department of Pathology, Massachusetts General Hospital, Boston, MA 02114
| | - Andrea L Smidler
- Department of Immunology and Infectious Diseases, Harvard School of Public Health, Boston, MA 02115
| | | | - George M Church
- Department of Genetics, Harvard Medical School, Boston, MA 02115;
- Wyss Institute for Biologically Inspired Engineering, Harvard University, Cambridge, MA 02138
| | - Martin A Nowak
- Program for Evolutionary Dynamics, Harvard University, Cambridge, MA 02138
- Department of Mathematics, Harvard University, Cambridge, MA 02138
- Department of Organismic and Evolutionary Biology, Harvard University, Cambridge, MA 02138
| | - Kevin M Esvelt
- Media Laboratory, Massachusetts Institute of Technology, Cambridge, MA 02139;
| |
Collapse
|
34
|
Fotouhi B, Momeni N, Allen B, Nowak MA. Evolution of cooperation on large networks with community structure. J R Soc Interface 2019; 16:20180677. [PMID: 30862280 PMCID: PMC6451403 DOI: 10.1098/rsif.2018.0677] [Citation(s) in RCA: 63] [Impact Index Per Article: 12.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/07/2018] [Accepted: 02/18/2019] [Indexed: 11/12/2022] Open
Abstract
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 composed of distinct modules. In this paper, we study analytically the evolutionary game dynamics on large modular networks in the limit of weak selection. We obtain novel analytical conditions such that natural selection favours cooperation over defection. We calculate the transition point for each community to favour cooperation. We find that a critical inter-community link creation probability exists for given group density, such that the overall network supports cooperation even if individual communities inhibit it. As a byproduct, we present solutions for the critical benefit-to-cost ratio which perform with remarkable accuracy for diverse generative network models, including those with community structure and heavy-tailed degree distributions. We also demonstrate the generalizability of the results to arbitrary two-player games.
Collapse
Affiliation(s)
- Babak Fotouhi
- Program for Evolutionary Dynamics, Harvard University, Cambridge, MA, USA
- Institute for Quantitative Social Sciences, Harvard University, Cambridge, MA, USA
| | - Naghmeh Momeni
- Program for Evolutionary Dynamics, Harvard University, Cambridge, MA, USA
- Massachusetts Institute of Technology (MIT) - Sloan School of Management, Cambridge, MA, USA
| | - Benjamin Allen
- Program for Evolutionary Dynamics, Harvard University, Cambridge, MA, USA
- Center for Mathematical Sciences and Applications, Harvard University, Cambridge, MA, USA
- Department of Mathematics, Emmanuel College, Boston, MA, USA
| | - Martin A. Nowak
- Program for Evolutionary Dynamics, Harvard University, Cambridge, MA, USA
- Department of Mathematics, Harvard University, Cambridge, MA, USA
- Department of Organismic and Evolutionary Biology, Harvard University, Cambridge, MA, USA
| |
Collapse
|
35
|
van der Heijden M, Miedema DM, Waclaw B, Veenstra VL, Lecca MC, Nijman LE, van Dijk E, van Neerven SM, Lodestijn SC, Lenos KJ, de Groot NE, Prasetyanti PR, Arricibita Varea A, Winton DJ, Medema JP, Morrissey E, Ylstra B, Nowak MA, Bijlsma MF, Vermeulen L. Spatiotemporal regulation of clonogenicity in colorectal cancer xenografts. Proc Natl Acad Sci U S A 2019; 116:6140-6145. [PMID: 30850544 PMCID: PMC6442578 DOI: 10.1073/pnas.1813417116] [Citation(s) in RCA: 45] [Impact Index Per Article: 9.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
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 and time by using a color-based clonal tracing method. This method involves lentiviral red-green-blue (RGB) marking of cell populations, which enabled us to track individual cells and their clonal outgrowth during tumor initiation and growth in a xenograft model. We found that clonal expansion largely depends on the location of a clone, as small clones reside in the center and large clones mostly drive tumor growth at the border. These dynamics are recapitulated in a computational model, which confirms that the clone position within a tumor rather than cell-intrinsic features, is crucial for clonal outgrowth. We also found that no significant clonal loss occurs during tumor growth and clonal dispersal is limited in most models. Our results imply that, in addition to molecular features of clones such as (epi-)genetic differences between cells, clone location and the geometry of tumor growth are crucial for clonal expansion. Our findings suggest that either microenvironmental signals on the tumor border or differences in physical properties within the tumor, are major contributors to explain heterogeneous clonal expansion. Thus, this study provides further insights into the dynamics of solid tumor growth and progression, as well as the origins of tumor cell heterogeneity in a relevant model system.
Collapse
Affiliation(s)
- Maartje van der Heijden
- Laboratory for Experimental Oncology and Radiobiology, Center for Experimental and Molecular Medicine, Cancer Center Amsterdam, Amsterdam Gastroenterology & Metabolism, Amsterdam UMC, University of Amsterdam, 1105 AZ Amsterdam, The Netherlands
| | - Daniël M Miedema
- Laboratory for Experimental Oncology and Radiobiology, Center for Experimental and Molecular Medicine, Cancer Center Amsterdam, Amsterdam Gastroenterology & Metabolism, Amsterdam UMC, University of Amsterdam, 1105 AZ Amsterdam, The Netherlands
| | - Bartlomiej Waclaw
- School of Physics and Astronomy, The University of Edinburgh, EH9 3FD Edinburgh, United Kingdom
| | - Veronique L Veenstra
- Laboratory for Experimental Oncology and Radiobiology, Center for Experimental and Molecular Medicine, Cancer Center Amsterdam, Amsterdam Gastroenterology & Metabolism, Amsterdam UMC, University of Amsterdam, 1105 AZ Amsterdam, The Netherlands
| | - Maria C Lecca
- Laboratory for Experimental Oncology and Radiobiology, Center for Experimental and Molecular Medicine, Cancer Center Amsterdam, Amsterdam Gastroenterology & Metabolism, Amsterdam UMC, University of Amsterdam, 1105 AZ Amsterdam, The Netherlands
| | - Lisanne E Nijman
- Laboratory for Experimental Oncology and Radiobiology, Center for Experimental and Molecular Medicine, Cancer Center Amsterdam, Amsterdam Gastroenterology & Metabolism, Amsterdam UMC, University of Amsterdam, 1105 AZ Amsterdam, The Netherlands
| | - Erik van Dijk
- Department of Pathology, Amsterdam UMC, Vrije Universiteit Amsterdam, 1081 HV Amsterdam, The Netherlands
| | - Sanne M van Neerven
- Laboratory for Experimental Oncology and Radiobiology, Center for Experimental and Molecular Medicine, Cancer Center Amsterdam, Amsterdam Gastroenterology & Metabolism, Amsterdam UMC, University of Amsterdam, 1105 AZ Amsterdam, The Netherlands
| | - Sophie C Lodestijn
- Laboratory for Experimental Oncology and Radiobiology, Center for Experimental and Molecular Medicine, Cancer Center Amsterdam, Amsterdam Gastroenterology & Metabolism, Amsterdam UMC, University of Amsterdam, 1105 AZ Amsterdam, The Netherlands
| | - Kristiaan J Lenos
- Laboratory for Experimental Oncology and Radiobiology, Center for Experimental and Molecular Medicine, Cancer Center Amsterdam, Amsterdam Gastroenterology & Metabolism, Amsterdam UMC, University of Amsterdam, 1105 AZ Amsterdam, The Netherlands
| | - Nina E de Groot
- Laboratory for Experimental Oncology and Radiobiology, Center for Experimental and Molecular Medicine, Cancer Center Amsterdam, Amsterdam Gastroenterology & Metabolism, Amsterdam UMC, University of Amsterdam, 1105 AZ Amsterdam, The Netherlands
| | - Pramudita R Prasetyanti
- Laboratory for Experimental Oncology and Radiobiology, Center for Experimental and Molecular Medicine, Cancer Center Amsterdam, Amsterdam Gastroenterology & Metabolism, Amsterdam UMC, University of Amsterdam, 1105 AZ Amsterdam, The Netherlands
| | - Andrea Arricibita Varea
- Laboratory for Experimental Oncology and Radiobiology, Center for Experimental and Molecular Medicine, Cancer Center Amsterdam, Amsterdam Gastroenterology & Metabolism, Amsterdam UMC, University of Amsterdam, 1105 AZ Amsterdam, The Netherlands
| | - Douglas J Winton
- Cancer Research UK, Cambridge Institute, University of Cambridge, CB2 0RE Cambridge, United Kingdom
| | - Jan Paul Medema
- Laboratory for Experimental Oncology and Radiobiology, Center for Experimental and Molecular Medicine, Cancer Center Amsterdam, Amsterdam Gastroenterology & Metabolism, Amsterdam UMC, University of Amsterdam, 1105 AZ Amsterdam, The Netherlands
| | - Edward Morrissey
- Medical Research Council Weatherall Institute of Molecular Medicine, University of Oxford, John Radcliffe Hospital, Headington, OX3 9DS Oxford, United Kingdom
| | - Bauke Ylstra
- Department of Pathology, Amsterdam UMC, Vrije Universiteit Amsterdam, 1081 HV Amsterdam, The Netherlands
| | - Martin A Nowak
- Program for Evolutionary Dynamics, Harvard University, Cambridge, MA 02138
| | - Maarten F Bijlsma
- Laboratory for Experimental Oncology and Radiobiology, Center for Experimental and Molecular Medicine, Cancer Center Amsterdam, Amsterdam Gastroenterology & Metabolism, Amsterdam UMC, University of Amsterdam, 1105 AZ Amsterdam, The Netherlands
| | - Louis Vermeulen
- Laboratory for Experimental Oncology and Radiobiology, Center for Experimental and Molecular Medicine, Cancer Center Amsterdam, Amsterdam Gastroenterology & Metabolism, Amsterdam UMC, University of Amsterdam, 1105 AZ Amsterdam, The Netherlands;
| |
Collapse
|
36
|
Abstract
In an iterated game between two players, there is much interest in characterizing the set of feasible pay-offs 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 specify the probabilities to take actions depending on the outcome of the previous round. Here, we consider 'reactive learning strategies', which gradually modify their propensity to take certain actions based on past actions of the opponent. Every linear reactive learning strategy, p *, corresponds to a memory one-strategy, p , and vice versa. We prove that for evaluating the region of feasible pay-offs against a memory-one strategy, C ( p ) , we need to check its performance against at most 11 other strategies. Thus, C ( p ) is the convex hull inR 2 of at most 11 points. Furthermore, if p is a memory-one strategy, with feasible pay-off region C ( p ) , and p * is the corresponding reactive learning strategy, with feasible pay-off region C ( p ∗ ) , then C ( p ∗ ) is a subset of C ( p ) . Reactive learning strategies are therefore powerful tools in restricting the outcomes of iterated games.
Collapse
Affiliation(s)
- Alex McAvoy
- Program for Evolutionary Dynamics, Harvard University, 1 Brattle Square, Suite 6, Cambridge, MA 02138, USA
| | | |
Collapse
|
37
|
Veller C, Kleckner N, Nowak MA. A rigorous measure of genome-wide genetic shuffling that takes into account crossover positions and Mendel's second law. Proc Natl Acad Sci U S A 2019; 116:1659-1668. [PMID: 30635424 PMCID: PMC6358705 DOI: 10.1073/pnas.1817482116] [Citation(s) in RCA: 39] [Impact Index Per Article: 7.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
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 is qualitatively inadequate, because the positions of crossovers along a chromosome are also critical: a crossover toward the middle of a chromosome causes more shuffling than a crossover toward the tip. Moreover, traditional measures fail to consider shuffling from independent assortment of homologous chromosomes (Mendel's second law). Here, we present a rigorous measure of genome-wide shuffling that does not suffer from these limitations. We define the parameter [Formula: see text] as the probability that the alleles at two randomly chosen loci are shuffled during gamete production. This measure can be decomposed into separate contributions from crossover number and position and from independent assortment. Intrinsic implications of this metric include the fact that [Formula: see text] is larger when crossovers are more evenly spaced, which suggests a selective advantage of crossover interference. Utilization of [Formula: see text] is enabled by powerful emergent methods for determining crossover positions either cytologically or by DNA sequencing. Application of our analysis to such data from human male and female reveals that (i) [Formula: see text] in humans is close to its maximum possible value of 1/2 and that (ii) this high level of shuffling is due almost entirely to independent assortment, the contribution of which is ∼30 times greater than that of crossovers.
Collapse
Affiliation(s)
- Carl Veller
- Department of Organismic and Evolutionary Biology, Harvard University, Cambridge, MA 02138
- Program for Evolutionary Dynamics, Harvard University, Cambridge, MA 02138
| | - Nancy Kleckner
- Department of Molecular and Cellular Biology, Harvard University, Cambridge, MA 02138;
| | - Martin A Nowak
- Department of Organismic and Evolutionary Biology, Harvard University, Cambridge, MA 02138
- Program for Evolutionary Dynamics, Harvard University, Cambridge, MA 02138
- Department of Mathematics, Harvard University, Cambridge, MA 02138
| |
Collapse
|
38
|
Kaveh K, McAvoy A, Nowak MA. Environmental fitness heterogeneity in the Moran process. R Soc Open Sci 2019; 6:181661. [PMID: 30800394 PMCID: PMC6366185 DOI: 10.1098/rsos.181661] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 10/02/2018] [Accepted: 11/30/2018] [Indexed: 06/09/2023]
Abstract
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 environment. We first calculate the condition for selection to favour the mutant relative to the resident wild-type. In large populations, the mutant is favoured if and only if the mutant's spatial average reproductive rate exceeds that of the resident. But environmental heterogeneity elucidates an interesting asymmetry between the mutant and the resident. Specifically, mutant heterogeneity suppresses its fixation probability; if this heterogeneity is strong enough, it can even completely offset the effects of selection (including in large populations). By contrast, resident heterogeneity has no effect on a mutant's fixation probability in large populations and can amplify it in small populations.
Collapse
|
39
|
Hilbe C, Schmid L, Tkadlec J, Chatterjee K, Nowak MA. Indirect reciprocity with private, noisy, and incomplete information. Proc Natl Acad Sci U S A 2018; 115:12241-12246. [PMID: 30429320 PMCID: PMC6275544 DOI: 10.1073/pnas.1810565115] [Citation(s) in RCA: 40] [Impact Index Per Article: 6.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
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 members agree on each other's reputation, previous research has highlighted eight crucial moral systems. These "leading-eight" strategies can maintain cooperation and resist invasion by defectors. However, in real populations individuals often hold their own private views of others. Once two individuals disagree about their opinion of some third party, they may also see its subsequent actions in a different light. Their opinions may further diverge over time. Herein, we explore indirect reciprocity when information transmission is private and noisy. We find that in the presence of perception errors, most leading-eight strategies cease to be stable. Even if a leading-eight strategy evolves, cooperation rates may drop considerably when errors are common. Our research highlights the role of reliable information and synchronized reputations to maintain stable moral systems.
Collapse
Affiliation(s)
- Christian Hilbe
- Institute of Science and Technology Austria, 3400 Klosterneuburg, Austria;
| | - Laura Schmid
- Institute of Science and Technology Austria, 3400 Klosterneuburg, Austria
| | - Josef Tkadlec
- Institute of Science and Technology Austria, 3400 Klosterneuburg, Austria
| | | | - Martin A Nowak
- Program for Evolutionary Dynamics, Harvard University, Cambridge, MA 02138
- Department of Organismic and Evolutionary Biology, Harvard University, Cambridge, MA 02138
- Department of Mathematics, Harvard University, Cambridge, MA 02138
| |
Collapse
|
40
|
Reiter JG, Makohon-Moore AP, Gerold JM, Heyde A, Attiyeh MA, Kohutek ZA, Tokheim CJ, Brown A, DeBlasio RM, Niyazov J, Zucker A, Karchin R, Kinzler KW, Iacobuzio-Donahue CA, Vogelstein B, Nowak MA. Minimal functional driver gene heterogeneity among untreated metastases. Science 2018; 361:1033-1037. [PMID: 30190408 DOI: 10.1126/science.aat7171] [Citation(s) in RCA: 181] [Impact Index Per Article: 30.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/27/2018] [Accepted: 08/02/2018] [Indexed: 12/31/2022]
Abstract
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 breast, colorectal, endometrial, gastric, lung, melanoma, pancreatic, and prostate cancers. We found that within individual patients, a large majority of driver gene mutations are common to all metastases. Further analysis revealed that the driver gene mutations that were not shared by all metastases are unlikely to have functional consequences. A mathematical model of tumor evolution and metastasis formation provides an explanation for the observed driver gene homogeneity. Thus, single biopsies capture most of the functionally important mutations in metastases and therefore provide essential information for therapeutic decision-making.
Collapse
Affiliation(s)
- Johannes G Reiter
- Canary Center for Cancer Early Detection, Department of Radiology, Stanford University School of Medicine, Palo Alto, CA 94305, USA. .,Program for Evolutionary Dynamics, Harvard University, Cambridge, MA 02138, USA
| | - Alvin P Makohon-Moore
- The David M. Rubenstein Center for Pancreatic Cancer Research, Human Oncology and Pathogenesis Program, Memorial Sloan Kettering Cancer Center, New York, NY 10065, USA
| | - Jeffrey M Gerold
- Program for Evolutionary Dynamics, Harvard University, Cambridge, MA 02138, USA
| | - Alexander Heyde
- Program for Evolutionary Dynamics, Harvard University, Cambridge, MA 02138, USA
| | - Marc A Attiyeh
- The David M. Rubenstein Center for Pancreatic Cancer Research, Human Oncology and Pathogenesis Program, Memorial Sloan Kettering Cancer Center, New York, NY 10065, USA
| | - Zachary A Kohutek
- Department of Radiation Oncology, Memorial Sloan Kettering Cancer Center, New York, NY 10065, USA
| | - Collin J Tokheim
- Department of Biomedical Engineering, Institute for Computational Medicine, Johns Hopkins University, Baltimore, MD 21218, USA
| | - Alexia Brown
- The David M. Rubenstein Center for Pancreatic Cancer Research, Human Oncology and Pathogenesis Program, Memorial Sloan Kettering Cancer Center, New York, NY 10065, USA
| | - Rayne M DeBlasio
- The David M. Rubenstein Center for Pancreatic Cancer Research, Human Oncology and Pathogenesis Program, Memorial Sloan Kettering Cancer Center, New York, NY 10065, USA
| | - Juliana Niyazov
- The David M. Rubenstein Center for Pancreatic Cancer Research, Human Oncology and Pathogenesis Program, Memorial Sloan Kettering Cancer Center, New York, NY 10065, USA
| | - Amanda Zucker
- The David M. Rubenstein Center for Pancreatic Cancer Research, Human Oncology and Pathogenesis Program, Memorial Sloan Kettering Cancer Center, New York, NY 10065, USA
| | - Rachel Karchin
- Department of Biomedical Engineering, Institute for Computational Medicine, Johns Hopkins University, Baltimore, MD 21218, USA.,Department of Oncology, Johns Hopkins University School of Medicine, Baltimore, MD 21287, USA
| | - Kenneth W Kinzler
- The Ludwig Center, Johns Hopkins University School of Medicine, Baltimore, MD 21287, USA.,The Sol Goldman Pancreatic Cancer Research Center, Johns Hopkins University School of Medicine, Baltimore, MD 21287, USA.,Sidney Kimmel Cancer Center, The Johns Hopkins University School of Medicine, Baltimore, MD 21205, USA
| | - Christine A Iacobuzio-Donahue
- The David M. Rubenstein Center for Pancreatic Cancer Research, Human Oncology and Pathogenesis Program, Memorial Sloan Kettering Cancer Center, New York, NY 10065, USA.,Department of Pathology, Memorial Sloan Kettering Cancer Center, New York, NY 10065, USA
| | - Bert Vogelstein
- The Ludwig Center, Johns Hopkins University School of Medicine, Baltimore, MD 21287, USA.,The Sol Goldman Pancreatic Cancer Research Center, Johns Hopkins University School of Medicine, Baltimore, MD 21287, USA.,Sidney Kimmel Cancer Center, The Johns Hopkins University School of Medicine, Baltimore, MD 21205, USA.,Howard Hughes Medical Institute, The Johns Hopkins University School of Medicine, Baltimore, MD 21205, USA
| | - Martin A Nowak
- Program for Evolutionary Dynamics, Harvard University, Cambridge, MA 02138, USA. .,Department of Organismic and Evolutionary Biology and Department of Mathematics, Harvard University, Cambridge, MA 02138, USA
| |
Collapse
|
41
|
Olejarz J, Kaveh K, Veller C, Nowak MA. Selection for synchronized cell division in simple multicellular organisms. J Theor Biol 2018; 457:170-179. [PMID: 30172691 PMCID: PMC6169303 DOI: 10.1016/j.jtbi.2018.08.038] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/15/2018] [Revised: 07/30/2018] [Accepted: 08/29/2018] [Indexed: 02/08/2023]
Abstract
The evolution of multicellularity was a major transition in the history of life on earth. Conditions under which multicellularity is favored have been studied theoretically and experimentally. But since the construction of a multicellular organism requires multiple rounds of cell division, a natural question is whether these cell divisions should be synchronous or not. We study a population model in which there compete simple multicellular organisms that grow by either synchronous or asynchronous cell divisions. We demonstrate that natural selection can act differently on synchronous and asynchronous cell division, and we offer intuition for why these phenotypes are generally not neutral variants of each other.
Collapse
Affiliation(s)
- Jason Olejarz
- Program for Evolutionary Dynamics, Harvard University, Cambridge, MA 02138, USA.
| | - Kamran Kaveh
- Program for Evolutionary Dynamics, Harvard University, Cambridge, MA 02138, USA.
| | - Carl Veller
- Program for Evolutionary Dynamics, Harvard University, Cambridge, MA 02138, USA; Department of Organismic and Evolutionary Biology, Harvard University, Cambridge, MA 02138, USA.
| | - Martin A Nowak
- Program for Evolutionary Dynamics, Harvard University, Cambridge, MA 02138, USA; Department of Organismic and Evolutionary Biology, Harvard University, Cambridge, MA 02138, USA; Department of Mathematics, Harvard University, Cambridge, MA 02138, USA.
| |
Collapse
|
42
|
McAvoy A, Adlam B, Allen B, Nowak MA. Stationary frequencies and mixing times for neutral drift processes with spatial structure. Proc Math Phys Eng Sci 2018; 474:20180238. [PMCID: PMC6237506 DOI: 10.1098/rspa.2018.0238] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/09/2018] [Accepted: 09/25/2018] [Indexed: 09/03/2023] Open
Abstract
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 probability that any given individual has a certain trait, all converge to the stationary distribution of the mutation process. In particular, the stationary frequencies of traits in the population are independent of its size, spatial structure and evolutionary update rule, and these frequencies can be calculated by evaluating a simple stochastic process describing a population of size one (i.e. the mutation process itself). We conclude by analysing mixing times, which characterize rates of convergence of the mutation process along the lineages, in terms of demographic variables of the evolutionary process.
Collapse
Affiliation(s)
- Alex McAvoy
- Program for Evolutionary Dynamics, Harvard University, Cambridge, MA 02138, USA
| | - Ben Adlam
- Program for Evolutionary Dynamics, Harvard University, Cambridge, MA 02138, USA
- School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138, USA
| | - Benjamin Allen
- Program for Evolutionary Dynamics, Harvard University, Cambridge, MA 02138, USA
- Department of Mathematics, Emmanuel College, Boston, MA 02115, USA
| | - Martin A. Nowak
- Program for Evolutionary Dynamics, Harvard University, Cambridge, MA 02138, USA
- Department of Organismic and Evolutionary Biology, Harvard University, Cambridge, MA 02138, USA
- Department of Mathematics, Harvard University, Cambridge, MA 02138, USA
| |
Collapse
|
43
|
Abstract
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 levels during infection and how they are altered by treatment. In this review, we summarize the contributions that virus dynamics models have made to understanding the pathophysiology of infection and to designing effective therapies. This includes studies of the multiphasic decay of viral load when antiretroviral therapy is given, the evolution of drug resistance, the long-term persistence latently infected cells, and the rebound of viremia when drugs are stopped. We additionally discuss new work applying viral dynamics models to new classes of investigational treatment for HIV, including latency-reversing agents and immunotherapy.
Collapse
Affiliation(s)
- Alison L. Hill
- Program for Evolutionary DynamicsHarvard UniversityCambridgeMassachusetts
| | - Daniel I. S. Rosenbloom
- Department of PharmacokineticsPharmacodynamics, & Drug MetabolismMerck Research LaboratoriesKenilworthNew Jersey
| | - Martin A. Nowak
- Program for Evolutionary DynamicsHarvard UniversityCambridgeMassachusetts
| | - Robert F. Siliciano
- Department of MedicineJohns Hopkins University School of MedicineBaltimoreMaryland
- Howard Hughes Medical InstituteBaltimoreMaryland
| |
Collapse
|
44
|
Abstract
Social dilemmas occur when incentives for individuals are misaligned with group interests1-7. According to the 'tragedy of the commons', these misalignments can lead to overexploitation and collapse of public resources. The resulting behaviours can be analysed with the tools of game theory8. The theory of direct reciprocity9-15 suggests that repeated interactions can alleviate such dilemmas, but previous work has assumed that the public resource remains constant over time. Here we introduce the idea that the public resource is instead changeable and depends on the strategic choices of individuals. An intuitive scenario is that cooperation increases the public resource, whereas defection decreases it. Thus, cooperation allows the possibility of playing a more valuable game with higher payoffs, whereas defection leads to a less valuable game. We analyse this idea using the theory of stochastic games16-19 and evolutionary game theory. We find that the dependence of the public resource on previous interactions can greatly enhance the propensity for cooperation. For these results, the interaction between reciprocity and payoff feedback is crucial: neither repeated interactions in a constant environment nor single interactions in a changing environment yield similar cooperation rates. Our framework shows which feedbacks between exploitation and environment-either naturally occurring or designed-help to overcome social dilemmas.
Collapse
Affiliation(s)
- Christian Hilbe
- Program for Evolutionary Dynamics, Harvard University, Cambridge, MA, USA. .,IST Austria, Klosterneuburg, Austria.
| | - Štěpán Šimsa
- Faculty of Mathematics and Physics, Charles University, Prague, Czech Republic
| | | | - Martin A Nowak
- Program for Evolutionary Dynamics, Harvard University, Cambridge, MA, USA. .,Department of Organismic and Evolutionary Biology, Department of Mathematics, Harvard University, Cambridge, MA, USA.
| |
Collapse
|
45
|
Fotouhi B, Momeni N, Allen B, Nowak MA. Conjoining uncooperative societies facilitates evolution of cooperation. Nat Hum Behav 2018; 2:492-499. [DOI: 10.1038/s41562-018-0368-6] [Citation(s) in RCA: 29] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/09/2017] [Accepted: 05/22/2018] [Indexed: 11/09/2022]
|
46
|
Noble C, Adlam B, Church GM, Esvelt KM, Nowak MA. Current CRISPR gene drive systems are likely to be highly invasive in wild populations. eLife 2018; 7:33423. [PMID: 29916367 PMCID: PMC6014726 DOI: 10.7554/elife.33423] [Citation(s) in RCA: 110] [Impact Index Per Article: 18.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/09/2017] [Accepted: 05/15/2018] [Indexed: 12/25/2022] Open
Abstract
Recent reports have suggested that self-propagating CRISPR-based gene drive systems are unlikely to efficiently invade wild populations due to drive-resistant alleles that prevent cutting. Here we develop mathematical models based on existing empirical data to explicitly test this assumption for population alteration drives. Our models show that although resistance prevents spread to fixation in large populations, even the least effective drive systems reported to date are likely to be highly invasive. Releasing a small number of organisms will often cause invasion of the local population, followed by invasion of additional populations connected by very low rates of gene flow. Hence, initiating contained field trials as tentatively endorsed by the National Academies report on gene drive could potentially result in unintended spread to additional populations. Our mathematical results suggest that self-propagating gene drive is best suited to applications such as malaria prevention that seek to affect all wild populations of the target species.
Collapse
Affiliation(s)
- Charleston Noble
- Program for Evolutionary Dynamics, Harvard University, Cambridge, United States.,Department of Genetics, Harvard Medical School, Harvard University, Boston, United States.,Wyss Institute for Biologically Inspired Engineering, Harvard University, Boston MA, United States
| | - Ben Adlam
- Program for Evolutionary Dynamics, Harvard University, Cambridge, United States.,School of Engineering and Applied Science, Harvard University, Cambridge, United States
| | - George M Church
- Department of Genetics, Harvard Medical School, Harvard University, Boston, United States.,Wyss Institute for Biologically Inspired Engineering, Harvard University, Boston MA, United States
| | - Kevin M Esvelt
- Massachusetts Institute of Technology Media Lab, Cambridge, United States
| | - Martin A Nowak
- Program for Evolutionary Dynamics, Harvard University, Cambridge, United States.,Department of Mathematics, Harvard University, Cambridge, United States.,Department of Organismic and Evolutionary Biology, Harvard University, Cambridge, United States
| |
Collapse
|
47
|
Pavlogiannis A, Tkadlec J, Chatterjee K, Nowak MA. Construction of arbitrarily strong amplifiers of natural selection using evolutionary graph theory. Commun Biol 2018; 1:71. [PMID: 30271952 PMCID: PMC6123726 DOI: 10.1038/s42003-018-0078-7] [Citation(s) in RCA: 29] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/28/2018] [Accepted: 05/25/2018] [Indexed: 11/08/2022] Open
Abstract
Because of the intrinsic randomness of the evolutionary process, a mutant with a fitness advantage has some chance to be selected but no certainty. Any experiment that searches for advantageous mutants will lose many of them due to random drift. It is therefore of great interest to find population structures that improve the odds of advantageous mutants. Such structures are called amplifiers of natural selection: they increase the probability that advantageous mutants are selected. Arbitrarily strong amplifiers guarantee the selection of advantageous mutants, even for very small fitness advantage. Despite intensive research over the past decade, arbitrarily strong amplifiers have remained rare. Here we show how to construct a large variety of them. Our amplifiers are so simple that they could be useful in biotechnology, when optimizing biological molecules, or as a diagnostic tool, when searching for faster dividing cells or viruses. They could also occur in natural population structures.
Collapse
Affiliation(s)
| | | | | | - Martin A Nowak
- Program for Evolutionary Dynamics, Department of Organismic and Evolutionary Biology, Department of Mathematics, Harvard University, Cambridge, MA, 02138, USA.
| |
Collapse
|
48
|
Hoffman M, Hilbe C, Nowak MA. The signal-burying game can explain why we obscure positive traits and good deeds. Nat Hum Behav 2018; 2:397-404. [DOI: 10.1038/s41562-018-0354-z] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/06/2018] [Accepted: 04/24/2018] [Indexed: 11/09/2022]
|
49
|
Ibsen-Jensen R, Tkadlec J, Chatterjee K, Nowak MA. Language acquisition with communication between learners. J R Soc Interface 2018; 15:rsif.2018.0073. [PMID: 29593089 DOI: 10.1098/rsif.2018.0073] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/25/2018] [Accepted: 03/02/2018] [Indexed: 11/12/2022] Open
Abstract
We consider a class of students learning a language from a teacher. The situation can be interpreted as a group of child learners receiving input from the linguistic environment. The teacher provides sample sentences. The students try to learn the grammar from the teacher. In addition to just listening to the teacher, the students can also communicate with each other. The students hold hypotheses about the grammar and change them if they receive counter evidence. The process stops when all students have converged to the correct grammar. We study how the time to convergence depends on the structure of the classroom by introducing and evaluating various complexity measures. We find that structured communication between students, although potentially introducing confusion, can greatly reduce some of the complexity measures. Our theory can also be interpreted as applying to the scientific process, where nature is the teacher and the scientists are the students.
Collapse
Affiliation(s)
| | | | | | - Martin A Nowak
- Program for Evolutionary Dynamics, Department of Organismic and Evolutionary Biology, Department of Mathematics, Harvard University, Cambridge, MA 02138, USA
| |
Collapse
|
50
|
|