{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,20]],"date-time":"2026-03-20T04:54:28Z","timestamp":1773982468676,"version":"3.50.1"},"reference-count":56,"publisher":"Springer Science and Business Media LLC","issue":"5","license":[{"start":{"date-parts":[[2018,9,6]],"date-time":"2018-09-06T00:00:00Z","timestamp":1536192000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100001871","name":"Ministry of Education and Science | Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia (Portuguese Science and Technology Founation)","doi-asserted-by":"publisher","award":["Investigador FCT IF\/00019\/2013"],"award-info":[{"award-number":["Investigador FCT IF\/00019\/2013"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001871","name":"Ministry of Education and Science | Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia (Portuguese Science and Technology Founation)","doi-asserted-by":"publisher","award":["EXPL\/BIA-EVF\/0129\/2013"],"award-info":[{"award-number":["EXPL\/BIA-EVF\/0129\/2013"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Heredity"],"published-print":{"date-parts":[[2018,11]]},"DOI":"10.1038\/s41437-018-0143-5","type":"journal-article","created":{"date-parts":[[2018,9,6]],"date-time":"2018-09-06T10:29:03Z","timestamp":1536229743000},"page":"482-498","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Power law fitness landscapes and their ability to predict fitness"],"prefix":"10.1038","volume":"121","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9114-7873","authenticated-orcid":false,"given":"Diogo","family":"Passagem-Santos","sequence":"first","affiliation":[]},{"given":"Simone","family":"Zacarias","sequence":"additional","affiliation":[]},{"given":"Lilia","family":"Perfeito","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2018,9,6]]},"reference":[{"key":"143_CR1","doi-asserted-by":"publisher","first-page":"229","DOI":"10.1093\/molbev\/msu301","volume":"32","author":"C Bank","year":"2015","unstructured":"Bank C, Hietpas RT, Jensen JD, Bolon DNA (2015) A Systematic Survey of an Intragenic Epistatic Landscape Mol Biol Evol 32:229\u2013238","journal-title":"Mol Biol Evol"},{"key":"143_CR2","doi-asserted-by":"publisher","first-page":"14085","DOI":"10.1073\/pnas.1612676113","volume":"113","author":"C Bank","year":"2016","unstructured":"Bank C, Matuszewski S, Hietpas RT, Jensen JD (2016) On the (un)predictability of a large intragenic fitness landscape. Proc Natl Acad Sci USA 113:14085\u201314090","journal-title":"Proc Natl Acad Sci USA"},{"key":"143_CR3","unstructured":"Bengtsson H (2017) matrixStats: functions that apply to rows and columns of matrices (and to vectors). https:\/\/cran.r-project.org\/package=matrixStats"},{"key":"143_CR4","doi-asserted-by":"publisher","first-page":"847","DOI":"10.1534\/genetics.115.182691","volume":"203","author":"F Blanquart","year":"2016","unstructured":"Blanquart F, Bataillon T (2016) Epistasis and the structure of fitness landscapes: are experimental fitness landscapes compatible with Fisher\u2019s geometric model? Genetics 203:847\u2013862","journal-title":"Genetics"},{"key":"143_CR5","doi-asserted-by":"publisher","first-page":"7899","DOI":"10.1073\/pnas.0803151105","volume":"105","author":"ZD Blount","year":"2008","unstructured":"Blount ZD, Borland CZ, Lenski RE (2008) Historical contingency and the evolution of a key innovation in an experimental population of Escherichia coli Proc Natl Acad Sci USA 105:7899\u2013906","journal-title":"Proc Natl Acad Sci USA"},{"key":"143_CR6","doi-asserted-by":"publisher","first-page":"63","DOI":"10.1007\/s11222-009-9116-0","volume":"20","author":"MGB Blum","year":"2010","unstructured":"Blum MGB, Fran\u00e7ois O (2010) Non-linear regression models for Approximate Bayesian Computation Stat Comput 20:63\u201373","journal-title":"Stat Comput"},{"key":"143_CR7","unstructured":"Canty A, Ripley B (2012) boot: Bootstrap R (S-Plus) functions. R package version 13\u201317 pp. 3\u20137. https:\/\/cran.rproject.org\/web\/packages\/boot\/citation.html"},{"key":"143_CR8","doi-asserted-by":"publisher","first-page":"3213","DOI":"10.1111\/j.1558-5646.2010.01058.x","volume":"64","author":"LM Chevin","year":"2010","unstructured":"Chevin LM, Martin G, Lenormand T (2010) Fisher\u2019s model and the genomics of adaptation: restricted pleiotropy, heterogenous mutation, and parallel evolution. Evolution 64:3213\u20133231","journal-title":"Evolution"},{"key":"143_CR9","doi-asserted-by":"publisher","first-page":"4156","DOI":"10.1098\/rspb.2012.1449","volume":"279","author":"HC Chiu","year":"2012","unstructured":"Chiu HC, Marx CJ, Segre D (2012) Epistasis from functional dependence of fitness on underlying traits. Proc R Soc B Biol Sci 279:4156\u20134164","journal-title":"Proc R Soc B Biol Sci"},{"key":"143_CR10","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pgen.1000652","volume":"5","author":"HH Chou","year":"2009","unstructured":"Chou HH, Berthet J, Marx CJ (2009) Fast growth increases the selective advantage of a mutation arising recurrently during evolution under metal limitation. PLoS Genet 5:e1000652","journal-title":"PLoS Genet"},{"key":"143_CR11","doi-asserted-by":"publisher","first-page":"99","DOI":"10.3389\/fgene.2015.00099","volume":"6","author":"A Couce","year":"2015","unstructured":"Couce A, Tenaillon OA (2015) The rule of declining adaptability in microbial evolution experiments. Front Genet 6:99","journal-title":"Front Genet"},{"key":"143_CR12","doi-asserted-by":"publisher","first-page":"475","DOI":"10.1111\/j.2041-210X.2011.00179.x","volume":"3","author":"K Csillery","year":"2012","unstructured":"Csillery K, Fran\u00e7ois O, Blum MGB (2012) abc: an R package for approximate Bayesian computation (ABC). Methods Ecol Evol 3:475\u2013479","journal-title":"Methods Ecol Evol"},{"key":"143_CR13","unstructured":"Davison A (2006) Bootstrap methods and their application. Slides :1\u201395"},{"key":"143_CR14","doi-asserted-by":"publisher","first-page":"480","DOI":"10.1038\/nrg3744","volume":"15","author":"JAG Visser de","year":"2014","unstructured":"de Visser JAG, Krug J (2014) Empirical fitness landscapes and the predictability of evolution. Nature Rev Genet 15:480\u2013490","journal-title":"Nature Rev Genet"},{"key":"143_CR15","doi-asserted-by":"crossref","unstructured":"Fisher RA (1930) The genetical theory of natural selection. Oxford University Press, New York","DOI":"10.5962\/bhl.title.27468"},{"key":"143_CR16","first-page":"453","volume":"57","author":"D Freedman","year":"1981","unstructured":"Freedman D, Diaconis P (1981) On the histogram as a density estimator: L2 theory. Probab Theory Relat Fields 57:453\u2013476","journal-title":"Probab Theory Relat Fields"},{"key":"143_CR17","doi-asserted-by":"crossref","unstructured":"Gavrilets S (2004) Fitness landscapes and the origin of species. Monogr Popul Biol","DOI":"10.1515\/9780691187051"},{"key":"143_CR18","doi-asserted-by":"publisher","first-page":"1716","DOI":"10.1063\/1.1378322","volume":"115","author":"DT Gillespie","year":"2001","unstructured":"Gillespie DT (2001) Approximate accelerated stochastic simulation of chemically reacting systems. J Chem Phys 115:1716\u20131733","journal-title":"J Chem Phys"},{"key":"143_CR19","doi-asserted-by":"publisher","first-page":"177","DOI":"10.1534\/genetics.114.172460","volume":"199","author":"BH Good","year":"2015","unstructured":"Good BH, Desai MM (2015) The impact of macroscopic epistasis on long-term evolutionary dynamics. Genetics 199:177\u2013190","journal-title":"Genetics"},{"key":"143_CR20","doi-asserted-by":"publisher","first-page":"45","DOI":"10.1038\/nature24287","volume":"551","author":"BH Good","year":"2017","unstructured":"Good BH, McDonald MJ, Barrick JE, Lenski RE, Desai MM (2017) The dynamics of molecular evolution over 60,000 generations. Nature 551:45\u201350","journal-title":"Nature"},{"key":"143_CR21","doi-asserted-by":"publisher","first-page":"277","DOI":"10.1534\/genetics.108.099127","volume":"182","author":"PA Gros","year":"2009","unstructured":"Gros PA, Nagard HL, Tenaillon O (2009) The evolution of epistasis and its links with genetic robustness, complexity and drift in a phenotypic model of adaptation. Genetics 182:277\u2013293","journal-title":"Genetics"},{"key":"143_CR22","unstructured":"Harrell FE Jr, with contributions from Charles Dupont and many others (2018) Hmisc: Harrell Miscellaneous. https:\/\/cran.r-project.org\/package=Hmisc"},{"key":"143_CR23","unstructured":"Holm S (1979) A simple sequentially rejective multiple test procedure. https:\/\/www.jstor.org\/stable\/4615733"},{"key":"143_CR24","unstructured":"Intel (2018) Intel Python. https:\/\/software.intel.com\/en-us"},{"key":"143_CR25","doi-asserted-by":"publisher","first-page":"684","DOI":"10.1111\/2041-210X.12050","volume":"4","author":"F Jabot","year":"2013","unstructured":"Jabot F, Faure T, Dumoulin N (2013) EasyABC: performing efficient approximate Bayesian computation sampling schemes using R (RB O\u2019Hara, Ed.). Methods Ecol Evol 4:684\u2013687","journal-title":"Methods Ecol Evol"},{"key":"143_CR26","doi-asserted-by":"publisher","first-page":"13067","DOI":"10.1073\/pnas.1215206110","volume":"110","author":"H Jacquier","year":"2013","unstructured":"Jacquier H, Birgy A, Le Nagard H, Mechulam Y, Schmitt E, Glodt J et al (2013) Capturing the mutational landscape of the beta-lactamase TEM-1. Proc Natl Acad Sci 110:13067\u201313072","journal-title":"Proc Natl Acad Sci"},{"key":"143_CR27","doi-asserted-by":"publisher","DOI":"10.7554\/eLife.27167","volume":"6","author":"ER Jerison","year":"2017","unstructured":"Jerison ER, Kryazhimskiy S, Mitchell JK, Bloom JS, Kruglyak L, Desai MM (2017) Genetic variation in adaptability and pleiotropy in budding yeast. eLife 6:e27167","journal-title":"eLife"},{"key":"143_CR28","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pgen.1003600","volume":"9","author":"L Jiang","year":"2013","unstructured":"Jiang L, Mishra P, Hietpas RT, Zeldovich KB, Bolon DNA (2013) Latent Effects of Hsp90 Mutants Revealed at Reduced Expression Levels (TR Serio, Ed.). PLoS Genet 9:e1003600","journal-title":"PLoS Genet"},{"key":"143_CR29","unstructured":"Kelley K (2018) MBESS: the MBESS R package. https:\/\/cran.r-project.org\/package=MBESS"},{"key":"143_CR30","doi-asserted-by":"publisher","first-page":"1193","DOI":"10.1126\/science.1203801","volume":"332","author":"AI Khan","year":"2011","unstructured":"Khan AI, Dinh DM, Schneider D, Lenski RE, Cooper TF (2011) Negative epistasis between beneficial mutations in an evolving bacterial population. Science 332:1193\u20131196","journal-title":"Science"},{"key":"143_CR31","doi-asserted-by":"publisher","first-page":"694","DOI":"10.1038\/381694a0","volume":"381","author":"TT Kibota","year":"1996","unstructured":"Kibota TT, Lynch M (1996) Estimate of the genomic mutation rate deleterious to overall fitness in E. coll. Nature 381:694\u2013696","journal-title":"Nature"},{"key":"143_CR32","first-page":"1519","volume":"344","author":"S Kryazhimskiy","year":"2014","unstructured":"Kryazhimskiy S, Rice DP, Jerison ER, Desai MM (2014) Global epistasis makes adaptation predictable despite sequence-level stochasticity. bioRxiv 344:1519\u20131522","journal-title":"bioRxiv"},{"key":"143_CR33","doi-asserted-by":"publisher","first-page":"0077","DOI":"10.1038\/s41559-017-0077","volume":"1","author":"M L\u00e4ssig","year":"2017","unstructured":"L\u00e4ssig M, Mustonen V, Walczak AM (2017) Predicting evolution. Nat Ecol Evol 1:0077","journal-title":"Nat Ecol Evol"},{"key":"143_CR34","doi-asserted-by":"publisher","first-page":"1315","DOI":"10.1086\/285289","volume":"138","author":"RE Lenski","year":"1991","unstructured":"Lenski RE, Rose MR, Simpson SC, Tadler SC (1991) Long-term experimental evolution in Escherichia coli. I. Adaptation and divergence during 2,000 generations. Am Nat 138:1315\u20131341","journal-title":"Am Nat"},{"key":"143_CR35","doi-asserted-by":"publisher","first-page":"567","DOI":"10.1038\/nrg3937","volume":"16","author":"A Long","year":"2015","unstructured":"Long A, Liti G, Luptak A, Tenaillon O (2015) Elucidating the molecular architecture of adaptation via evolve and resequence experiments. Nat Rev Genet 16:567\u2013582","journal-title":"Nat Rev Genet"},{"key":"143_CR36","doi-asserted-by":"publisher","first-page":"499","DOI":"10.1126\/science.1115649","volume":"310","author":"M Lunzer","year":"2005","unstructured":"Lunzer M, Miller SP, Felsheim R, Dean AM (2005) The biochemical architecture of an ancient adaptive landscape. Science 310:499\u2013501","journal-title":"Science"},{"key":"143_CR37","doi-asserted-by":"publisher","first-page":"1345","DOI":"10.1534\/genetics.110.123083","volume":"186","author":"RC MacLean","year":"2010","unstructured":"MacLean RC, Perron GG, Gardner A (2010) Diminishing returns from beneficial mutations and pervasive epistasis shape the fitness landscape for rifampicin resistance in Pseudomonas aeruginosa. Genetics 186:1345\u20131354","journal-title":"Genetics"},{"key":"143_CR38","doi-asserted-by":"publisher","first-page":"655","DOI":"10.1534\/genetics.111.132134","volume":"190","author":"AC Nagel","year":"2012","unstructured":"Nagel AC, Joyce P, Wichman HA, Miller CR (2012) Stickbreaking: a novel fitness landscape model that harbors epistasis and is consistent with commonly observed patterns of adaptive evolution. Genetics 190:655\u2013667","journal-title":"Genetics"},{"key":"143_CR39","doi-asserted-by":"publisher","first-page":"252","DOI":"10.1038\/nrg761","volume":"3","author":"SP Otto","year":"2002","unstructured":"Otto SP, Lenormand T (2002) Resolving the paradox of sex and recombination. Nat Rev Genet 3:252\u2013261","journal-title":"Nat Rev Genet"},{"key":"143_CR40","doi-asserted-by":"publisher","first-page":"150","DOI":"10.1111\/evo.12234","volume":"68","author":"L Perfeito","year":"2014","unstructured":"Perfeito L, Sousa A, Bataillon T, Gordo I (2014) Rates of fitness decline and rebound suggest pervasive epistasis. Evolution 68:150\u2013162","journal-title":"Evolution"},{"key":"143_CR41","unstructured":"R Core Team (2015) R Core Team. http:\/\/www.mendeley.com\/research\/r-language-environment-statistical-computing-96\/%5Cnpapers2:\/\/publication\/uuid\/A1207DAB-22D3-4A04-82FB-D4DD5AD57C28"},{"key":"143_CR42","unstructured":"Sch\u00e4fer J, Opgen-Rhein R, Strimmer K (2014) corpcor: efficient estimation of covariance and (partial) correlation. R package version 167. https:\/\/cran.rproject.org\/web\/packages\/corpcor\/index.html"},{"key":"143_CR43","doi-asserted-by":"publisher","first-page":"20161376","DOI":"10.1098\/rspb.2016.1376","volume":"283","author":"S Schoustra","year":"2016","unstructured":"Schoustra S, Hwang S, Krug J, de Visser JAGM (2016) Diminishing-returns epistasis among random beneficial mutations in a multicellular fungus. Proc Biol Sci 283:20161376","journal-title":"Proc Biol Sci"},{"key":"143_CR44","doi-asserted-by":"publisher","first-page":"1204","DOI":"10.1002\/pro.2897","volume":"25","author":"TN Starr","year":"2016","unstructured":"Starr TN, Thornton JW (2016) Epistasis in protein evolution. Protein Sci 25:1204\u20131218","journal-title":"Protein Sci"},{"key":"143_CR45","doi-asserted-by":"publisher","first-page":"179","DOI":"10.1146\/annurev-ecolsys-120213-091846","volume":"45","author":"O Tenaillon","year":"2014","unstructured":"Tenaillon O (2014) The utility of Fisher\u2019s geometric model in evolutionary genetics. Annu Rev Ecol Evol Syst 45:179\u2013201","journal-title":"Annu Rev Ecol Evol Syst"},{"key":"143_CR46","doi-asserted-by":"publisher","DOI":"10.1038\/ncomms3235","volume":"4","author":"A Teresa Avelar","year":"2013","unstructured":"Teresa Avelar A, Perfeito L, Gordo I, Godinho Ferreira M (2013) Genome architecture is a selectable trait that can be maintained by antagonistic pleiotropy. Nat Commun 4:2235","journal-title":"Nat Commun"},{"key":"143_CR47","unstructured":"Terho P (2013) Flowing software. http:\/\/flowingsoftware.btk.fi\/index.php?page=1"},{"key":"143_CR48","unstructured":"Trautmann H, Steuer D, Mersmann O, Bornkamp B (2014) truncnorm: truncated normal distribution. https:\/\/cran.r-project.org\/package=truncnorm"},{"key":"143_CR49","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pgen.1000578","volume":"5","author":"S Trindade","year":"2009","unstructured":"Trindade S, Sousa A, Xavier KB, Dionisio F, Ferreira MG, Gordo I (2009) Positive epistasis drives the acquisition of multidrug resistance. PLoS Genet 5:e1000578","journal-title":"PLoS Genet"},{"key":"143_CR50","doi-asserted-by":"publisher","first-page":"2606","DOI":"10.1111\/j.0014-3820.2001.tb00772.x","volume":"55","author":"LM Wahl","year":"2001","unstructured":"Wahl LM, Gerrish PJ (2001) The probability that beneficial mutations are lost in populations with periodic bottlenecks. Evolution 55:2606\u20132610","journal-title":"Evolution"},{"key":"143_CR51","doi-asserted-by":"crossref","first-page":"961","DOI":"10.1093\/genetics\/162.2.961","volume":"162","author":"LM Wahl","year":"2002","unstructured":"Wahl LM, Gerrish PJ, Saika-Voivod I (2002) Evaluating the impact of population bottlenecks in experimental evolution. Genetics 162:961\u2013971","journal-title":"Genetics"},{"key":"143_CR52","unstructured":"Wilhelm S, with contributions from Manjunath BG (2015) {tmvtnorm}: truncated multivariate normal and Student t distribution. http:\/\/cran.r-project.org\/package=tmvtnorm"},{"key":"143_CR53","doi-asserted-by":"publisher","first-page":"1364","DOI":"10.1126\/science.1243357","volume":"342","author":"MJ Wiser","year":"2013","unstructured":"Wiser MJ, Ribeck N, Lenski RE (2013) Long-term dynamics of adaptation in asexual populations. Science 342:1364\u20131367","journal-title":"Science"},{"key":"143_CR54","doi-asserted-by":"publisher","first-page":"1433","DOI":"10.1126\/science.1198914","volume":"331","author":"RJ Woods","year":"2011","unstructured":"Woods RJ, Barrick JE, Cooper TF, Shrestha U, Kauth MR, Lenski RE (2011) Second-order selection for evolvability in a large Escherichia coli population. Science 331:1433\u20131436","journal-title":"Science"},{"key":"143_CR55","first-page":"356","volume":"1","author":"S Wright","year":"1932","unstructured":"Wright S (1932) The roles of mutation, inbreeding, crossbreeding, and selection in evolution. Proc Sixth Int Congr Genet 1:356\u2013366","journal-title":"Proc Sixth Int Congr Genet"},{"key":"143_CR56","doi-asserted-by":"publisher","first-page":"1291","DOI":"10.1046\/j.1365-8711.2003.06633.x","volume":"342","author":"S Zucker","year":"2003","unstructured":"Zucker S (2003) Cross-correlation and maximum-likelihood analysis: a new approach to combining cross-correlation functions. Mon Not R Astron Soc 342:1291\u20131298","journal-title":"Mon Not R Astron Soc"}],"container-title":["Heredity"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/www.nature.com\/articles\/s41437-018-0143-5","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/www.nature.com\/articles\/s41437-018-0143-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/www.nature.com\/articles\/s41437-018-0143-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,5,20]],"date-time":"2023-05-20T21:17:04Z","timestamp":1684617424000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.nature.com\/articles\/s41437-018-0143-5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,9,6]]},"references-count":56,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2018,11]]}},"alternative-id":["143"],"URL":"https:\/\/doi.org\/10.1038\/s41437-018-0143-5","relation":{},"ISSN":["0018-067X","1365-2540"],"issn-type":[{"value":"0018-067X","type":"print"},{"value":"1365-2540","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,9,6]]},"assertion":[{"value":"2 February 2018","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"15 August 2018","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"16 August 2018","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"6 September 2018","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Compliance with ethical standards"}},{"value":"The authors declare that they have no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}