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Here we model these evolutionary dynamics on two-dimensional phenotype spaces that leverage scaling relations between the drug-response surfaces of drug-sensitive (ancestral) and drug-resistant (mutant) populations. We show that evolved resistance to the component drugs \u2013 and in turn, the adaptation of growth rate \u2013 is governed by a Price equation whose covariance terms encode geometric features of both the two-drug-response surface (DI) in ancestral cells and the correlations between resistance levels to those drugs (CE). Within this framework, mean evolutionary trajectories reduce to a type of weighted gradient dynamics, with the drug interaction dictating the shape of the underlying landscape and the collateral effects constraining the motion on those landscapes. We also demonstrate how constraints on available mutational pathways can be incorporated into the framework, adding a third key driver of evolution. Our results clarify the complex relationship between drug interactions and collateral effects in multidrug environments and illustrate how specific dosage combinations can shift the weighting of these two effects, leading to different and temporally explicit selective outcomes.<\/jats:p>","DOI":"10.7554\/elife.64851","type":"journal-article","created":{"date-parts":[[2021,7,21]],"date-time":"2021-07-21T20:00:13Z","timestamp":1626897613000},"update-policy":"https:\/\/doi.org\/10.7554\/elife.64851","source":"Crossref","is-referenced-by-count":41,"title":["Price equation captures the role of drug interactions and collateral effects in the evolution of multidrug resistance"],"prefix":"10.7554","volume":"10","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0493-3102","authenticated-orcid":true,"given":"Erida","family":"Gjini","sequence":"first","affiliation":[{"name":"Center for Computational and Stochastic Mathematics, Instituto Superior Tecnico, University of Lisbon, Portugal, Lisbon, Portugal"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0985-7401","authenticated-orcid":true,"given":"Kevin B","family":"Wood","sequence":"additional","affiliation":[{"name":"Departments of Biophysics and Physics, University of Michigan, Ann Arbor, United States"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"4374","published-online":{"date-parts":[[2021,7,22]]},"reference":[{"key":"bib1","doi-asserted-by":"publisher","first-page":"982","DOI":"10.2307\/2410204","article-title":"On the relationship between quantitative genetic and ess models","volume":"47","author":"Abrams","year":"1993","journal-title":"Evolution"},{"key":"bib2","doi-asserted-by":"publisher","first-page":"2723","DOI":"10.1038\/s41396-018-0212-z","article-title":"Cross-feeding modulates antibiotic tolerance in bacterial communities","volume":"12","author":"Adamowicz","year":"2018","journal-title":"The ISME 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