Benjamin Good is a theoretical biophysicist with a background in experimental evolution and population genetics. He is interested in the short-term evolutionary dynamics that emerge in rapidly evolving microbial populations like the gut microbiome. Technological advances are revolutionizing our ability to peer into these evolving ecosystems, providing us with an increasingly detailed catalog of their component species, genes, and pathways. Yet a vast gap still remains in understanding the population-level processes that control their emergent structure and function. Our group uses tools from statistical physics, population genetics, and computational biology to understand how microscopic growth processes and genome dynamics at the single cell level give rise to the collective behaviors that can be observed at the population level. Projects range from basic theoretical investigations of non-equilibrium processes in microbial evolution and ecology, to the development of new computational tools for measuring these processes in situ in both natural and experimental microbial communities. Through these specific examples, we seek to uncover unifying theoretical principles that could help us understand, forecast, and eventually control the ecological and evolutionary dynamics that take place in these diverse scenarios.

Academic Appointments

Honors & Awards

  • Chan Zuckerberg Biohub Investigator Award, Chan Zuckerberg Biohub (2022-2027)
  • Alfred P. Sloan Research Fellowship, Alfred P . Sloan Foundation (2021-2023)
  • Terman Fellowship, Stanford University (2019)
  • Miller Research Fellowship, Miller Institute for Basic Research in Science (2016-2019)

Professional Education

  • Ph. D., Harvard University, Physics (2016)
  • B.A., Swarthmore College, Physics/Mathematics (2010)

2023-24 Courses

Stanford Advisees

All Publications

  • Eco-evolutionary feedbacks in the human gut microbiome Good, B. H., Rosenfeld, L. B. biorxiv. 2022
  • Quantifying the Adaptive Potential of a Nascent Bacterial Community Ascensao, J. A., Wetmore, K. M., Good, B. H., Arkin, A. P., Hallatschek, O. biorxiv. 2022
  • Linkage disequilibrium between rare mutations. Genetics Good, B. H. 2022


    The statistical associations between mutations, collectively known as linkage disequilibrium (LD), encode important information about the evolutionary forces acting within a population. Yet in contrast to single-site analogues like the site frequency spectrum, our theoretical understanding of linkage disequilibrium remains limited. In particular, little is currently known about how mutations with different ages and fitness costs contribute to expected patterns of LD, even in simple settings where recombination and genetic drift are the major evolutionary forces. Here, I introduce a forward-time framework for predicting linkage disequilibrium between pairs of neutral and deleterious mutations as a function of their present-day frequencies. I show that the dynamics of linkage disequilibrium become much simpler in the limit that mutations are rare, where they admit a simple heuristic picture based on the trajectories of the underlying lineages. I use this approach to derive analytical expressions for a family of frequency-weighted LD statistics as a function of the recombination rate, the frequency scale, and the additive and epistatic fitness costs of the mutations. I find that the frequency scale can have a dramatic impact on the shapes of the resulting LD curves, reflecting the broad range of time scales over which these correlations arise. I also show that the differences between neutral and deleterious LD are not purely driven by differences in their mutation frequencies, and can instead display qualitative features that are reminiscent of epistasis. I conclude by discussing the implications of these results for recent LD measurements in bacteria. This forward-time approach may provide a useful framework for predicting linkage disequilibrium across a range of evolutionary scenarios.

    View details for DOI 10.1093/genetics/iyac004

    View details for PubMedID 35100407

  • Quantifying rapid bacterial evolution and transmission within the mouse intestine. Cell host & microbe Vasquez, K. S., Willis, L., Cira, N. J., Ng, K. M., Pedro, M. F., Aranda-Diaz, A., Rajendram, M., Yu, F. B., Higginbottom, S. K., Neff, N., Sherlock, G., Xavier, K. B., Quake, S. R., Sonnenburg, J. L., Good, B. H., Huang, K. C. 2021


    Due to limitations on high-resolution strain tracking, selection dynamics during gut microbiota colonization and transmission between hosts remain mostly mysterious. Here, we introduced hundreds of barcoded Escherichiacoli strains into germ-free mice and quantified strain-level dynamics and metagenomic changes. Mutations in genes involved in motility and metabolite utilization are reproducibly selected within days. Even with rapid selection, coprophagy enforced similar barcode distributions across co-housed mice. Whole-genome sequencing of hundreds of isolates revealed linked alleles that demonstrate between-host transmission. A population-genetics model predicts substantial fitness advantages for certain mutants and that migration accounted for 10% of the resident microbiota each day. Treatment with ciprofloxacin suggests interplay between selection and transmission. While initial colonization was mostly uniform, in two mice a bottleneck reduced diversity and selected for ciprofloxacin resistance in the absence of drug. These findings highlight the interplay between environmental transmission and rapid, deterministic selection during evolution of the intestinal microbiota.

    View details for DOI 10.1016/j.chom.2021.08.003

    View details for PubMedID 34473943

  • Longitudinal linked-read sequencing reveals ecological and evolutionary responses of a human gut microbiome during antibiotic treatment. Genome research Roodgar, M., Good, B. H., Garud, N. R., Martis, S., Avula, M., Zhou, W., Lancaster, S. M., Lee, H., Babveyh, A., Nesamoney, S., Pollard, K. S., Snyder, M. P. 2021


    Gut microbial communities can respond to antibiotic perturbations by rapidly altering their taxonomic and functional composition. However, little is known about the strain-level processes that drive this collective response. Here, we characterize the gut microbiome of a single individual at high temporal and genetic resolution through a period of health, disease, antibiotic treatment, and recovery. We used deep, linked-read metagenomic sequencing to track the longitudinal trajectories of thousands of single nucleotide variants within 36 species, which allowed us to contrast these genetic dynamics with the ecological fluctuations at the species level. We found that antibiotics can drive rapid shifts in the genetic composition of individual species, often involving incomplete genome-wide sweeps of pre-existing variants. These genetic changes were frequently observed in species without obvious changes in species abundance, emphasizing the importance of monitoring diversity below the species level. We also found that many sweeping variants quickly reverted to their baseline levels once antibiotic treatment had concluded, demonstrating that the ecological resilience of the microbiota can sometimes extend all the way down to the genetic level. Our results provide new insights into the population genetic forces that shape individual microbiomes on therapeutically relevant timescales, with potential implications for personalized health and disease.

    View details for DOI 10.1101/gr.265058.120

    View details for PubMedID 34301627

  • Competition for fluctuating resources reproduces statistics of species abundance over time across wide-ranging microbiotas Ho, P., Good, B. H., Huang, K. C. biorxiv. 2021
  • Emergent evolutionary forces in spatial models of microbial growth in the human gut microbiota Ghosh, O. M., Good, B. H. biorxiv. 2021
  • Population genetics of polymorphism and divergence in rapidly evolving populations Melissa, M. J., Good, B. H., Fisher, D. S., Desai, M. M. biorxiv. 2021
  • Evolutionary dynamics of bacteria in the gut microbiome within and across hosts. PLoS biology Garud, N. R., Good, B. H., Hallatschek, O., Pollard, K. S. 2019; 17 (1): e3000102


    Gut microbiota are shaped by a combination of ecological and evolutionary forces. While the ecological dynamics have been extensively studied, much less is known about how species of gut bacteria evolve over time. Here, we introduce a model-based framework for quantifying evolutionary dynamics within and across hosts using a panel of metagenomic samples. We use this approach to study evolution in approximately 40 prevalent species in the human gut. Although the patterns of between-host diversity are consistent with quasi-sexual evolution and purifying selection on long timescales, we identify new genealogical signatures that challenge standard population genetic models of these processes. Within hosts, we find that genetic differences that accumulate over 6-month timescales are only rarely attributable to replacement by distantly related strains. Instead, the resident strains more commonly acquire a smaller number of putative evolutionary changes, in which nucleotide variants or gene gains or losses rapidly sweep to high frequency. By comparing these mutations with the typical between-host differences, we find evidence that some sweeps may be seeded by recombination, in addition to new mutations. However, comparisons of adult twins suggest that replacement eventually overwhelms evolution over multi-decade timescales, hinting at fundamental limits to the extent of local adaptation. Together, our results suggest that gut bacteria can evolve on human-relevant timescales, and they highlight the connections between these short-term evolutionary dynamics and longer-term evolution across hosts.

    View details for DOI 10.1371/journal.pbio.3000102

    View details for PubMedID 30673701

    View details for PubMedCentralID PMC6361464

  • Adaptation limits ecological diversification and promotes ecological tinkering during the competition for substitutable resources PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA Good, B. H., Martis, S., Hallatschek, O. 2018; 115 (44): E10407–E10416


    Microbial communities can evade competitive exclusion by diversifying into distinct ecological niches. This spontaneous diversification often occurs amid a backdrop of directional selection on other microbial traits, where competitive exclusion would normally apply. Yet despite their empirical relevance, little is known about how diversification and directional selection combine to determine the ecological and evolutionary dynamics within a community. To address this gap, we introduce a simple, empirically motivated model of eco-evolutionary feedback based on the competition for substitutable resources. Individuals acquire heritable mutations that alter resource uptake rates, either by shifting metabolic effort between resources or by increasing the overall growth rate. While these constitutively beneficial mutations are trivially favored to invade, we show that the accumulated fitness differences can dramatically influence the ecological structure and evolutionary dynamics that emerge within the community. Competition between ecological diversification and ongoing fitness evolution leads to a state of diversification-selection balance, in which the number of extant ecotypes can be pinned below the maximum capacity of the ecosystem, while the ecotype frequencies and genealogies are constantly in flux. Interestingly, we find that fitness differences generate emergent selection pressures to shift metabolic effort toward resources with lower effective competition, even in saturated ecosystems. We argue that similar dynamical features should emerge in a wide range of models with a mixture of directional and diversifying selection.

    View details for DOI 10.1073/pnas.1807530115

    View details for Web of Science ID 000448713200014

    View details for PubMedID 30322918

    View details for PubMedCentralID PMC6217437

  • Effective models and the search for quantitative principles in microbial evolution CURRENT OPINION IN MICROBIOLOGY Good, B. H., Hallatschek, O. 2018; 45: 203–12


    Microbes evolve rapidly. Yet they do so in idiosyncratic ways, which depend on the specific mutations that are beneficial or deleterious in a given situation. At the same time, some population-level patterns of adaptation are strikingly similar across different microbial systems, suggesting that there may also be simple, quantitative principles that unite these diverse scenarios. We review the search for simple principles in microbial evolution, ranging from the biophysical level to emergent evolutionary dynamics. A key theme has been the use of effective models, which coarse-grain over molecular and cellular details to obtain a simpler description in terms of a few effective parameters. Collectively, these theoretical approaches provide a set of quantitative principles that facilitate understanding, prediction, and potentially control of evolutionary phenomena, though formidable challenges remain due to the ecological complexity of natural populations.

    View details for DOI 10.1016/j.mib.2018.11.005

    View details for Web of Science ID 000454972700029

    View details for PubMedID 30530175

    View details for PubMedCentralID PMC6599682

  • The Effect of Strong Purifying Selection on Genetic Diversity GENETICS Cvijovic, I., Good, B. H., Desai, M. M. 2018; 209 (4): 1235–78


    Purifying selection reduces genetic diversity, both at sites under direct selection and at linked neutral sites. This process, known as background selection, is thought to play an important role in shaping genomic diversity in natural populations. Yet despite its importance, the effects of background selection are not fully understood. Previous theoretical analyses of this process have taken a backward-time approach based on the structured coalescent. While they provide some insight, these methods are either limited to very small samples or are computationally prohibitive. Here, we present a new forward-time analysis of the trajectories of both neutral and deleterious mutations at a nonrecombining locus. We find that strong purifying selection leads to remarkably rich dynamics: neutral mutations can exhibit sweep-like behavior, and deleterious mutations can reach substantial frequencies even when they are guaranteed to eventually go extinct. Our analysis of these dynamics allows us to calculate analytical expressions for the full site frequency spectrum. We find that whenever background selection is strong enough to lead to a reduction in genetic diversity, it also results in substantial distortions to the site frequency spectrum, which can mimic the effects of population expansions or positive selection. Because these distortions are most pronounced in the low and high frequency ends of the spectrum, they become particularly important in larger samples, but may have small effects in smaller samples. We also apply our forward-time framework to calculate other quantities, such as the ultimate fates of polymorphisms or the fitnesses of their ancestral backgrounds.

    View details for DOI 10.1534/genetics.118.301058

    View details for Web of Science ID 000440014100019

    View details for PubMedID 29844134

    View details for PubMedCentralID PMC6063222

  • The dynamics of molecular evolution over 60,000 generations NATURE Good, B. H., McDonald, M. J., Barrick, J. E., Lenski, R. E., Desai, M. M. 2017; 551 (7678): 45-+


    The outcomes of evolution are determined by a stochastic dynamical process that governs how mutations arise and spread through a population. However, it is difficult to observe these dynamics directly over long periods and across entire genomes. Here we analyse the dynamics of molecular evolution in twelve experimental populations of Escherichia coli, using whole-genome metagenomic sequencing at five hundred-generation intervals through sixty thousand generations. Although the rate of fitness gain declines over time, molecular evolution is characterized by signatures of rapid adaptation throughout the duration of the experiment, with multiple beneficial variants simultaneously competing for dominance in each population. Interactions between ecological and evolutionary processes play an important role, as long-term quasi-stable coexistence arises spontaneously in most populations, and evolution continues within each clade. We also present evidence that the targets of natural selection change over time, as epistasis and historical contingency alter the strength of selection on different genes. Together, these results show that long-term adaptation to a constant environment can be a more complex and dynamic process than is often assumed.

    View details for DOI 10.1038/nature24287

    View details for Web of Science ID 000414222900041

    View details for PubMedID 29045390

    View details for PubMedCentralID PMC5788700

  • Evolution of Mutation Rates in Rapidly Adapting Asexual Populations GENETICS Good, B. H., Desai, M. M. 2016; 204 (3): 1249–66


    Mutator and antimutator alleles often arise and spread in both natural microbial populations and laboratory evolution experiments. The evolutionary dynamics of these mutation rate modifiers are determined by indirect selection on linked beneficial and deleterious mutations. These indirect selection pressures have been the focus of much earlier theoretical and empirical work, but we still have a limited analytical understanding of how the interplay between hitchhiking and deleterious load influences the fates of modifier alleles. Our understanding is particularly limited when clonal interference is common, which is the regime of primary interest in laboratory microbial evolution experiments. Here, we calculate the fixation probability of a mutator or antimutator allele in a rapidly adapting asexual population, and we show how this quantity depends on the population size, the beneficial and deleterious mutation rates, and the strength of a typical driver mutation. In the absence of deleterious mutations, we find that clonal interference enhances the fixation probability of mutators, even as they provide a diminishing benefit to the overall rate of adaptation. When deleterious mutations are included, natural selection pushes the population toward a stable mutation rate that can be suboptimal for the adaptation of the population as a whole. The approach to this stable mutation rate is not necessarily monotonic: even in the absence of epistasis, selection can favor mutator and antimutator alleles that "overshoot" the stable mutation rate by substantial amounts.

    View details for DOI 10.1534/genetics.116.193565

    View details for Web of Science ID 000388502900033

    View details for PubMedID 27646140

    View details for PubMedCentralID PMC5105855

  • Fate of a mutation in a fluctuating environment PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA Cvijovic, I., Good, B. H., Jerison, E. R., Desai, M. M. 2015; 112 (36): E5021–E5028


    Natural environments are never truly constant, but the evolutionary implications of temporally varying selection pressures remain poorly understood. Here we investigate how the fate of a new mutation in a fluctuating environment depends on the dynamics of environmental variation and on the selective pressures in each condition. We find that even when a mutation experiences many environmental epochs before fixing or going extinct, its fate is not necessarily determined by its time-averaged selective effect. Instead, environmental variability reduces the efficiency of selection across a broad parameter regime, rendering selection unable to distinguish between mutations that are substantially beneficial and substantially deleterious on average. Temporal fluctuations can also dramatically increase fixation probabilities, often making the details of these fluctuations more important than the average selection pressures acting on each new mutation. For example, mutations that result in a trade-off between conditions but are strongly deleterious on average can nevertheless be more likely to fix than mutations that are always neutral or beneficial. These effects can have important implications for patterns of molecular evolution in variable environments, and they suggest that it may often be difficult for populations to maintain specialist traits, even when their loss leads to a decline in time-averaged fitness.

    View details for DOI 10.1073/pnas.1505406112

    View details for Web of Science ID 000360994900009

    View details for PubMedID 26305937

    View details for PubMedCentralID PMC4568713

  • The Evolutionarily Stable Distribution of Fitness Effects GENETICS Rice, D. P., Good, B. H., Desai, M. M. 2015; 200 (1): 321–U599


    The distribution of fitness effects (DFE) of new mutations is a key parameter in determining the course of evolution. This fact has motivated extensive efforts to measure the DFE or to predict it from first principles. However, just as the DFE determines the course of evolution, the evolutionary process itself constrains the DFE. Here, we analyze a simple model of genome evolution in a constant environment in which natural selection drives the population toward a dynamic steady state where beneficial and deleterious substitutions balance. The distribution of fitness effects at this steady state is stable under further evolution and provides a natural null expectation for the DFE in a population that has evolved in a constant environment for a long time. We calculate how the shape of the evolutionarily stable DFE depends on the underlying population genetic parameters. We show that, in the absence of epistasis, the ratio of beneficial to deleterious mutations of a given fitness effect obeys a simple relationship independent of population genetic details. Finally, we analyze how the stable DFE changes in the presence of a simple form of diminishing-returns epistasis.

    View details for DOI 10.1534/genetics.114.173815

    View details for Web of Science ID 000354071000024

    View details for PubMedID 25762525

    View details for PubMedCentralID PMC4423373

  • The Impact of Macroscopic Epistasis on Long-Term Evolutionary Dynamics GENETICS Good, B. H., Desai, M. M. 2015; 199 (1): 177–U639


    Genetic interactions can strongly influence the fitness effects of individual mutations, yet the impact of these epistatic interactions on evolutionary dynamics remains poorly understood. Here we investigate the evolutionary role of epistasis over 50,000 generations in a well-studied laboratory evolution experiment in Escherichia coli. The extensive duration of this experiment provides a unique window into the effects of epistasis during long-term adaptation to a constant environment. Guided by analytical results in the weak-mutation limit, we develop a computational framework to assess the compatibility of a given epistatic model with the observed patterns of fitness gain and mutation accumulation through time. We find that a decelerating fitness trajectory alone provides little power to distinguish between competing models, including those that lack any direct epistatic interactions between mutations. However, when combined with the mutation trajectory, these observables place strong constraints on the set of possible models of epistasis, ruling out many existing explanations of the data. Instead, we find that the data are consistent with a "two-epoch" model of adaptation, in which an initial burst of diminishing-returns epistasis is followed by a steady accumulation of mutations under a constant distribution of fitness effects. Our results highlight the need for additional DNA sequencing of these populations, as well as for more sophisticated models of epistasis that are compatible with all of the experimental data.

    View details for DOI 10.1534/genetics.114.172460

    View details for Web of Science ID 000347712900015

    View details for PubMedID 25395665

    View details for PubMedCentralID PMC4286683

  • Deleterious Passengers in Adapting Populations GENETICS Good, B. H., Desai, M. M. 2014; 198 (3): 1183–1208


    Most new mutations are deleterious and are eventually eliminated by natural selection. But in an adapting population, the rapid amplification of beneficial mutations can hinder the removal of deleterious variants in nearby regions of the genome, altering the patterns of sequence evolution. Here, we analyze the interactions between beneficial "driver" mutations and linked deleterious "passengers" during the course of adaptation. We derive analytical expressions for the substitution rate of a deleterious mutation as a function of its fitness cost, as well as the reduction in the beneficial substitution rate due to the genetic load of the passengers. We find that the fate of each deleterious mutation varies dramatically with the rate and spectrum of beneficial mutations and the deleterious substitution rate depends nonmonotonically on the population size and the rate of adaptation. By quantifying this dependence, our results allow us to estimate which deleterious mutations will be likely to fix and how many of these mutations must arise before the progress of adaptation is significantly reduced.

    View details for DOI 10.1534/genetics.114.170233

    View details for Web of Science ID 000344373300028

    View details for PubMedID 25194161

    View details for PubMedCentralID PMC4224160

  • The Fates of Mutant Lineages and the Distribution of Fitness Effects of Beneficial Mutations in Laboratory Budding Yeast Populations GENETICS Frenkel, E. M., Good, B. H., Desai, M. M. 2014; 196 (4): 1217-+


    The outcomes of evolution are determined by which mutations occur and fix. In rapidly adapting microbial populations, this process is particularly hard to predict because lineages with different beneficial mutations often spread simultaneously and interfere with one another's fixation. Hence to predict the fate of any individual variant, we must know the rate at which new mutations create competing lineages of higher fitness. Here, we directly measured the effect of this interference on the fates of specific adaptive variants in laboratory Saccharomyces cerevisiae populations and used these measurements to infer the distribution of fitness effects of new beneficial mutations. To do so, we seeded marked lineages with different fitness advantages into replicate populations and tracked their subsequent frequencies for hundreds of generations. Our results illustrate the transition between strongly advantageous lineages that decisively sweep to fixation and more moderately advantageous lineages that are often outcompeted by new mutations arising during the course of the experiment. We developed an approximate likelihood framework to compare our data to simulations and found that the effects of these competing beneficial mutations were best approximated by an exponential distribution, rather than one with a single effect size. We then used this inferred distribution of fitness effects to predict the rate of adaptation in a set of independent control populations. Finally, we discuss how our experimental design can serve as a screen for rare, large-effect beneficial mutations.

    View details for DOI 10.1534/genetics.113.160069

    View details for Web of Science ID 000334179300025

    View details for PubMedID 24514901

    View details for PubMedCentralID PMC3982683

  • Genetic Diversity in the Interference Selection Limit PLOS GENETICS Good, B. H., Walczak, A. M., Neher, R. A., Desai, M. M. 2014; 10 (3): e1004222


    Pervasive natural selection can strongly influence observed patterns of genetic variation, but these effects remain poorly understood when multiple selected variants segregate in nearby regions of the genome. Classical population genetics fails to account for interference between linked mutations, which grows increasingly severe as the density of selected polymorphisms increases. Here, we describe a simple limit that emerges when interference is common, in which the fitness effects of individual mutations play a relatively minor role. Instead, similar to models of quantitative genetics, molecular evolution is determined by the variance in fitness within the population, defined over an effectively asexual segment of the genome (a "linkage block"). We exploit this insensitivity in a new "coarse-grained" coalescent framework, which approximates the effects of many weakly selected mutations with a smaller number of strongly selected mutations that create the same variance in fitness. This approximation generates accurate and efficient predictions for silent site variability when interference is common. However, these results suggest that there is reduced power to resolve individual selection pressures when interference is sufficiently widespread, since a broad range of parameters possess nearly identical patterns of silent site variability.

    View details for DOI 10.1371/journal.pgen.1004222

    View details for Web of Science ID 000337144700046

    View details for PubMedID 24675740

    View details for PubMedCentralID PMC3967937

  • Fluctuations in fitness distributions and the effects of weak linked selection on sequence evolution THEORETICAL POPULATION BIOLOGY Good, B. H., Desai, M. M. 2013; 85: 86–102


    Evolutionary dynamics and patterns of molecular evolution are strongly influenced by selection on linked regions of the genome, but our quantitative understanding of these effects remains incomplete. Recent work has focused on predicting the distribution of fitness within an evolving population, and this forms the basis for several methods that leverage the fitness distribution to predict the patterns of genetic diversity when selection is strong. However, in weakly selected populations random fluctuations due to genetic drift are more severe, and neither the distribution of fitness nor the sequence diversity within the population are well understood. Here, we briefly review the motivations behind the fitness-distribution picture, and summarize the general approaches that have been used to analyze this distribution in the strong-selection regime. We then extend these approaches to the case of weak selection, by outlining a perturbative treatment of selection at a large number of linked sites. This allows us to quantify the stochastic behavior of the fitness distribution and yields exact analytical predictions for the sequence diversity and substitution rate in the limit that selection is weak.

    View details for DOI 10.1016/j.tpb.2013.01.005

    View details for Web of Science ID 000322297600010

    View details for PubMedID 23337315

  • Distribution of fixed beneficial mutations and the rate of adaptation in asexual populations PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA Good, B. H., Rouzine, I. M., Balick, D. J., Hallatschek, O., Desai, M. M. 2012; 109 (13): 4950–55


    When large asexual populations adapt, competition between simultaneously segregating mutations slows the rate of adaptation and restricts the set of mutations that eventually fix. This phenomenon of interference arises from competition between mutations of different strengths as well as competition between mutations that arise on different fitness backgrounds. Previous work has explored each of these effects in isolation, but the way they combine to influence the dynamics of adaptation remains largely unknown. Here, we describe a theoretical model to treat both aspects of interference in large populations. We calculate the rate of adaptation and the distribution of fixed mutational effects accumulated by the population. We focus particular attention on the case when the effects of beneficial mutations are exponentially distributed, as well as on a more general class of exponential-like distributions. In both cases, we show that the rate of adaptation and the influence of genetic background on the fixation of new mutants is equivalent to an effective model with a single selection coefficient and rescaled mutation rate, and we explicitly calculate these effective parameters. We find that the effective selection coefficient exactly coincides with the most common fixed mutational effect. This equivalence leads to an intuitive picture of the relative importance of different types of interference effects, which can shift dramatically as a function of the population size, mutation rate, and the underlying distribution of fitness effects.

    View details for DOI 10.1073/pnas.1119910109

    View details for Web of Science ID 000302164200051

    View details for PubMedID 22371564

    View details for PubMedCentralID PMC3323973

  • Performance of modularity maximization in practical contexts PHYSICAL REVIEW E Good, B. H., de Montjoye, Y., Clauset, A. 2010; 81 (4): 046106


    Although widely used in practice, the behavior and accuracy of the popular module identification technique called modularity maximization is not well understood in practical contexts. Here, we present a broad characterization of its performance in such situations. First, we revisit and clarify the resolution limit phenomenon for modularity maximization. Second, we show that the modularity function Q exhibits extreme degeneracies: it typically admits an exponential number of distinct high-scoring solutions and typically lacks a clear global maximum. Third, we derive the limiting behavior of the maximum modularity Qmax for one model of infinitely modular networks, showing that it depends strongly both on the size of the network and on the number of modules it contains. Finally, using three real-world metabolic networks as examples, we show that the degenerate solutions can fundamentally disagree on many, but not all, partition properties such as the composition of the largest modules and the distribution of module sizes. These results imply that the output of any modularity maximization procedure should be interpreted cautiously in scientific contexts. They also explain why many heuristics are often successful at finding high-scoring partitions in practice and why different heuristics can disagree on the modular structure of the same network. We conclude by discussing avenues for mitigating some of these behaviors, such as combining information from many degenerate solutions or using generative models.

    View details for DOI 10.1103/PhysRevE.81.046106

    View details for Web of Science ID 000277265900009

    View details for PubMedID 20481785