COMMENTARY COMMENTARY Measuring ruggedness in landscapes Jeremy Van Clevea,1 and Daniel B. Weissmanb,2 Fitness aDepartment of Biology, University of Kentucky, Lexington, KY 40506; and bInstitute for A Quantitative Biosciences, University of California, Berkeley, CA 94720

How important are interactions among mu- current , the population should fo- tations for ? Obviously, no gene cus its exploration in this region and there is functions in isolation, but it is possible that no point in maintaining diversity elsewhere. assuming that have independent Such smooth landscapes may seem unlikely, effects could still give a good prediction for but precisely this pattern has been found in Genotype sp how adaptation proceeds. In PNAS, Nahum some experimental yeast populations (5). ace et al. (1) use an elegant combination of sim- In contrast, there is accumulating evi- ulations and experiments with Escherichia dence from experiments in E. coli (6–8) and B Fitness coli to show that even in adaptation over other microorganisms (reviewed in ref. 9) the course of a few weeks involving only a that genetic interactions and rugged fitness handful of mutations, interactions among landscapes are common. Wright was an those mutations can have very large effects. early proponent of the importance of rugged The authors detect these effects using a fitness landscapes and proposed in his “shift- clever indirect method based on the effect ing balance theory” (SBT) (2, 10) that spa- of spatial mixing on the of their tial population structure is crucial for popu- experimental populations. lations evolving in rugged landscapes from Interactions among mutations are typi- low peaks to higher peaks. Although the SBT Genoty pe sp cally visualized using the “” was influential among involved in ace metaphor introduced by (2), the “modern evolutionary synthesis” in the which analogizes contours of organismal fit- first half of the 20th century (11), it later was Fig. 1. Fitness landscapes. The horizontal axes represent ness with the contours of physical topogra- criticized in an influential review (12) for the space of different combinations of , and the vertical axis is individual fitness as a function of genotype. phy. Most commonly, the horizontal axes of having important conceptual problems. (A) Smooth fitness landscape with a single peak and no the landscape represent the space of possible A crucial observation of Nahum et al. (1) fitness interactions among genes. Different evolutionary genotypes with the height of the landscape and others (5) is that the advantage of pop- trajectories lead to the same peak. (B) Rugged fitness representing the fitness of the correspond- ulation structure for adaptation on rugged landscape with multiple peaks and pervasive interactions ing genotype (3, 4) (Fig. 1). The ruggedness landscapes is both simpler and more gen- among genes. Different evolutionary trajectories can reach different peaks even from the same initial genotype. The of the fitness landscape is a measure of the eral than Wright (2) had originally proposed blue highlighted region shows that each peak in the rug- prevalence of fitness interactions among in the SBT. Population structure has the ged landscape still looks like a smooth, single-peaked genes: in smooth landscapes with a single more general effect of slowing down the spread landscape locally. peak, each has a fixed effect on fit- of beneficial mutations, temporarily shield- ness (Fig. 1A), whereas in rugged landscapes ing . This extra variation structured populations initially adapt faster with multiple peaks (Fig. 1B), the effect of allows for a broader search of genotype space, but are overtaken by the strongly structured each mutation can depend on the other mu- which may be important for adaptation on populations, which reach a higher final fit- tations an individual has. rugged fitness landscapes. Crucially, this gen- On any fitness landscape, adaptation starts eral effect is largely free from the issues that ness (figure 2 of ref. 1). This pattern holds for with beneficial genotypes arising and pro- plague the SBT. increasing levels of fitness landscape rug- ceeds as these types increase in frequency and Nahum et al. (1) confirm that population gedness K. The simulations also showed that take over the population. The first step, gen- structure can allow a broader search of rug- the strongly structured populations accumu- erating beneficial types, requires genetic di- ged landscapes by using the classic NK model lated more mutations when the fitness land- versity, but the second step tends to reduce of Kauffman and Levin (3). The NK model scape was rugged. that diversity as the population converges on uses a parameter K to measure landscape To test whether the theoretical results the fittest existing type. There is thus a po- ruggedness, where larger values of K imply might be relevant to real organisms, Nahum tential trade-off between exploration and more ruggedness. Nahum et al. (1) evolve et al. (1) conducted evolution experiments exploitation, with populations actually adapt- populations with either unrestricted migra- ing slower if the best immediate mutations tion (weak population structure) or restricted Author contributions: J.V.C. and D.B.W. wrote the paper. spread too quickly and wipe out others that migration (strong population structure). When The authors declare no conflict of interest.

lead in more productive directions. On smooth fitness landscapes are smooth, they find that See companion article on page 7530. landscapes, however, there is no trade-off both the weakly and strongly structured pop- 1To whom correspondence should be addressed. Email: jvancleve@ because the best single mutations lead in the ulations evolve the same final fitness, but the uky.edu. A best directions (Fig. 1 ). In this case, because weakly structured populations adapt faster. 2Present address: Department of , Emory University, Atlanta, the best new genotype is always near the best When landscapes are rugged, the weakly GA 30322.

www.pnas.org/cgi/doi/10.1073/pnas.1507916112 PNAS | June 16, 2015 | vol. 112 | no. 24 | 7345–7346 Downloaded by guest on September 27, 2021 with E. coli. They created replicate popula- thefitnesslandscapewillbeimportantfor to measure more than a tiny fraction of it. tions starting from the same ancestral strain large but not small increases in fitness. Nahum et al.’s (1) approach, inferring some and let them adapt to the same environment Nahum et al.’s (1) results emphasize how aspects of the landscape from adaptive with weak and strong population structure understanding and predicting adaptation re- trajectories under different conditions, of- treatments that paralleled the simulations. quires understanding something about the fers a possible solution to this problem by The experimental results matched the pat- structure of fitness landscapes. Currently, focusing on just the limited set of features tern seen in the simulations of rugged land- however, we know very little about the shape that are relevant to adaptation. Encourag- scapes. At first, the weakly structured popu- ingly, an increasing number of experiments lations adapted faster, as beneficial mutations Nahum et al.’s results rapidly swept through. As time went on how- emphasize how under- are being done along these lines (e.g., ref. ever, the strongly structured populations 16), and we can hope that general patterns caught up and then overtook the weakly standing and predicting will begin to emerge. structured populations as their increased di- adaptation requires un- Crucially, this work will need to be ex- versity allowed them to find the best com- derstanding something tended to natural populations, whose fit- binations of mutations (which apparently ness landscapes may be quite different from involved mutations that were less beneficial about the structure of those in the laboratory. Pathogens may be individually). Whole- sequencing of fitness landscapes. the best natural populations to consider first. clones from the final populations showed There is a desperate need to predict how they of these landscapes. A number of studies have that the strongly structured populations had will evolve, and we are beginning to have the addressed this problem by exhaustively mea- indeed acquired more mutations than the data and theoretical tools to make such pre- weakly structured ones. suring small regions of landscapes (e.g., refs. 6 and 13–15). This approach has dictions (17, 18). In fact, one of the most im- These results stand in clear contrast to portant , drug resistance, often in- those of a similar experiment done in yeast yielded important insights, but it faces a volves multiple interacting mutations (6, 19), by Kryazhimskiy et al. (5), which found that fundamental limitation: because the full so understanding natural fitness landscapes spatial structure always slowed adaptation, fitness landscape is exponentially large in suggesting a smooth fitness landscape. That the size of the genome, we can never hope is essential. these two experiments gave opposite results raises the depressing prospect that each ex- periment’s results may be specific to the par- 1 Nahum JR, et al. (2015) A tortoise–hare pattern seen in 10 Wright S (1931) Evolution in Mendelian populations. Genetics ticular and studied, with adapting structured and unstructured populations suggests a 16(2):97–159. rugged fitness landscape in bacteria. Proc Natl Acad Sci USA 11 Dobzhansky T (1937) Genetics and the Origin of Species – only a limited ability to extrapolate. How- 112:7530 7535. (Columbia Univ Press, New York). ever, Nahum et al. (1) suggest a more encour- 2 Wright S (1932) The roles of mutation, , crossbreeding 12 Coyne JA, Barton NH, Turelli M (1997) Perspective: A critique of and selection in evolution. Proceedings of the Sixth International Sewall Wright’s shifting balance theory of evolution. Evolution 51(3): aging possibility: they note that near a fitness Congress on Genetics, ed Jones DF (Brooklyn Botanic Garden, 643–671. Brooklyn, NY), Vol 1, pp 356–366. peak, all landscapes look smooth regardless 13 Costanzo M, et al. (2010) The genetic landscape of a cell. 3 Kauffman S, Levin S (1987) Towards a general theory of adaptive B – of their overall roughness (Fig. 1 ), so we walks on rugged landscapes. J Theor Biol 128(1):11–45. Science 327(5964):425 431. might expect that experiments starting from 4 Gavrilets S (1997) Evolution and on holey adaptive 14 Acevedo A, Brodsky L, Andino R (2014) Mutational and fitness better-adapted organisms would tend to find landscapes. Trends Ecol Evol 12(8):307–312. landscapes of an RNA revealed through population sequencing. 5 Kryazhimskiy S, Rice DP, Desai MM (2012) Population subdivision Nature 505(7485):686–690. smoother landscapes. And indeed, although and adaptation in asexual populations of Saccharomyces cerevisiae. 15 Bank C, Ewing GB, Ferrer-Admettla A, Foll M, Jensen JD (2014) Kryazhimskiy et al. (5) started from a fairly Evolution 66(6):1931–1941. Thinking too positive? Revisiting current methods of population well-adapted ancestor whose fitness increased 6 Weinreich DM, Delaney NF, Depristo MA, Hartl DL (2006) genetic selection inference. Trends Genet 30(12):540–546. Darwinian evolution can follow only very few mutational paths 16 Levy SF, et al. (2015) Quantitative evolutionary dynamics using by no more than 10% over 500 generations, to fitter proteins. Science 312(5770):111–114. high-resolution lineage tracking. Nature 519(7542):181–186. 7 Khan AI, Dinh DM, Schneider D, Lenski RE, Cooper TF (2011) Nahum et al. (1) deliberately created an an- 17 Luksza M, Lässig M (2014) A predictive fitness model for Negative between beneficial mutations in an evolving influenza. Nature 507(7490):57–61. cestor carrying costly mutations and saw fit- bacterial population. Science 332(6034):1193–1196. 18 Neher RA, Russell CA, Shraiman BI (2014) Predicting evolution ness gains of more than 70% in fewer than 8 Woods RJ, et al. (2011) Second-order selection for in a 200 generations, suggesting that they started large Escherichia coli population. Science 331(6023):1433–1436. from the shape of genealogical trees. eLife 3:e03568. 9 Szendro IG, Schenk MF, Franke J, Krug J, de Visser JAGM (2013) 19 Bloom JD, Gong LI, Baltimore D (2010) Permissive secondary much farther from a fitness peak. Thus, we Quantitative analyses of empirical fitness landscapes. J Stat Mech mutations enable the evolution of influenza oseltamivir resistance. might generally expect that the roughness of Theory Exp 2013(01):P01005. Science 328(5983):1272–1275.

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