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Downloaded by guest on October 6, 2021 www.pnas.org/cgi/doi/10.1073/pnas.1807530115 competition resource similar selection. diversifying that and with models directional argue of of range mixture wide We a a in ecosystems. emerge should saturated features dynamical in com- effective even lower with petition, resources to toward pressures effort metabolic selection find shift emergent we generate Interestingly, differences flux. fitness in the frequen- that constantly below ecotype are the pinned genealogies while and be ecosystem, cies can the ecotypes of capacity extant in maximum balance, of diversification–selection number of the fitness state which a ongoing to and leads diversification Com- ecological community. between the within petition emerge that dynamics and structure fitness evolutionary ecological accumulated the the influence dramatically that can show are differences we invade, beneficial overall to favored constitutively the trivially these increasing While by rate. or growth resources shifting between by effort either rates, metabolic uptake resource heri- alter acquire that mutations Individuals table resources. empiri- the substitutable on simple, for based a a feedback competition eco-evolutionary introduce within of we model dynamics motivated gap, cally this evolutionary to address and To combine community. ecological selection directional the known and determine is diversification little nor- relevance, how would empirical about on their exclusion despite selection competitive Yet directional apply. where mally of traits, backdrop microbial a other amid diversifi- occurs spontaneous 2018) often This 1, May niches. cation review ecological for diver- distinct (received by 2018 into exclusion 21, sifying competitive September approved evade and can CA, communities Barbara, Microbial Santa California, of University Shraiman, I. Boris by Edited c a Good H. Benjamin resources substitutable competition for the during tinkering ecological promotes and diversification ecological limits h hfigpplto rqece ftetoeoye 5 13). (5, ecotypes two the of in ecologi- observed frequencies as population the timescales, shifting cause longer the over can wander are to evolution fixations equilibrium additional cal population-wide This when (11–13). accumulate even rare to ecotype, continue each mutations stud- adaptive within Sequencing that shown achieved. once have niches. been evolution ies temporal their has or cease diversification spatial rarely ecological utilization privileged microbes resource of these in coexis- accessibility Interestingly, differences of the to mechanism to traced The or be of due often 8–10). breakdown other can 6, a tence each (5, to with exclusion leading coexist competitive selection, stably frequency-dependent that to “ecotypes,” or eages, even and (6), months (7). (5), years days over ancestor single a of from assumed forms evolve primitive often which labo- in in is experiments, observed evolution than been ratory have process examples is striking malleable Particularly assump- exclusion and (2–4). competitive this common of challenge more breakdown a to the that started suggesting has tion, populations plant, specialized animal microbial, from highly and evidence empirical under Recent while only (1). exclusion, conditions occurs competitive to diversification subject ecological are mutations new most E eateto nertv ilg,Uiest fClfri,Bree,C 94720 CA Berkeley, California, of University Biology, Integrative of Department eateto hsc,Uiest fClfri,Bree,C 94720; CA Berkeley, California, of University Physics, of Department ntesmls ae,tepplto pisit aro lin- of pair a into splits population the cases, simplest the In n vltoayfre.Cnetoa idmsget that suggests wisdom Conventional forces. evolutionary oppos- ing are exclusion competitive and diversification cological | a,b,1 sxa evolution asexual tpe Martis Stephen , | coexistence a n sa Hallatschek Oskar and , b eateto iegneig nvriyo aiona ekly A970 and 94720; CA Berkeley, California, of University Bioengineering, of Department 1073/pnas.1807530115/-/DCSupplemental ulse nieOtbr1,2018. 15, October online Published at online information supporting contains article This 1 the under Published Submission. y Direct PNAS a is article This interest.y of conflict no declare authors The uhrcnrbtos ... .. n ..dsge eerh efre eerh and research, performed paper. research, the designed wrote O.H. and S.M., B.H.G., contributions: Author reproduce can approaches both while Yet the (23–29). evolve to which time allowed in are over model simulations, ecological diversi- particular computer ecological a of using on parameters stability evolution of and have effects fication studies the Numerous inter- investigated diversification. ecological of also to of point class the thought wide near a are actions of behavior models which limiting how evolution, general the describe showed trait very (22) frequency-dependent under dynamics theoretical of adaptive emerges comparison. of our in diversification field limited empirically, ecological the in remains important work process be Early this to of known understanding are ogy well as populations natural (19–21). these evo- well in short-term occur less can similar processes that lutionary are suggests communities work the recent these Although characterized, various within (16–18). in dynamics coexistence engaged and evolutionary ecotypes competition of com- of hundreds in degrees or evolve tens populations with microbial munities previously natural that (13). many experiments likely existing is Moreover, in it present and be 15), may ecotypes 14, undetected (7, ecotypes into more diversify complex or experiments more three laboratory in Some observed well. been as have communities dynamics similar but ture, (12). ecotype individuals of opposing invasion the the from by mutate out- or that (9) the niche through the either of , elimination to right lineages drive original even the can of perturbations one evolutionary these cases, certain In owo orsodnesol eadesd mi:[email protected] Email: addressed. be should correspondence whom To a,c lya motn oei hpn h tutr fmicrobial of structure the shaping in These communities. role could alone. important processes an ecology evolutionary play or short-term that evolution suggest of departures results models dramatic produce existing can from exclusion generaliz- competitive diversification By between and interact. beneficial interactions that heritable they show populations, include we how mutations, to microbial about theory large types consumer-resource known in exclu- ing Both is found competitive niche. little be ecological evade yet can different may mutations a mutant of exploiting a by cases, sion Their extinct. special go exclusion: or population In competitive the over take to either will subject descendants are mutations Most Significance hl h neatosbtenmcoilaatto n ecol- and adaptation microbial between interactions the While struc- community of form simplest the is coexistence Pairwise y NSlicense.y PNAS PNAS . y | o.115 vol. www.pnas.org/lookup/suppl/doi:10. | o 44 no. | E10407–E10416

PHYSICS EVOLUTION some of the qualitative behaviors observed in experiments, it has uptake rates, which can either divert metabolic effort between been difficult to forge a more quantitative connection between resources or increase the growth rate on all resources. The latter these models and the large amount of molecular data that is now class of mutations provides a natural way to model adaptation at available. linked genomic loci. One reason that quantitative comparisons have been difficult Constitutively beneficial mutations might seem like an ecolog- is that evolution also selects for other traits that are not directly ically trivial addition to the model, since they are always favored involved in diversification. For example, always to invade on short timescales. On longer timescales, however, works to maintain essential cellular functions, and there may we show that these accumulated fitness differences can dramati- be a benefit to removing costly functions that are not needed cally influence both the ecological structure and the evolutionary in the current environment. As a result, mutations that influ- dynamics that take place within the community. By focusing on ence an ecologically relevant phenotype like acetate the weak limit, we derive analytical expressions for might have to compete with constitutively beneficial mutations these dynamics in the two-resource case, and we show how our that are only tangentially related to metabolism [e.g., the loss results extend to larger communities as well. These analytical of the yeast mating pathway (30)]. In some experiments, these results provide a general framework for integrating ecological constitutively beneficial mutations may even compose the bulk and population-genetic processes in evolving microbial com- of the mutations that reach observable frequencies (12, 13, 31). munities and suggest ways in which these processes might be Although many models exist for describing constitutively benefi- inferred from time-resolved molecular data. cial or deleterious mutations in the absence of ecology (32), we lack even a basic theoretical understanding of how they behave Evolutionary Model of Resource Competition when they are linked to ecological phenotypes and vice versa. To investigate the interactions between ecological diversification The absence of quantitative theoretical predictions makes it dif- and directional selection, we focus on a simple ecological model ficult to draw any inferences from the vast molecular data that in which individuals compete for an assortment of externally are now available. supplied resources in a well-mixed, chemostat-like environment To start to bridge this gap, we introduce a simple, empirically (Fig. 1). This resource-based model aims to capture some of motivated model that describes the interplay between ecologi- the key ecological features observed in certain microbial evo- cal diversification and directional selection at a large number of lution experiments (5, 8), as well as more complex ecosystems linked loci. The ecological interactions derive from a well-studied such as the gut microbiome (18), while remaining as analytically class of consumer resource models (33–36), in which individu- tractable as possible. als compete for multiple substitutable resources (e.g., different In our idealized setting, individuals compete for R substi- carbon sources) in a well-mixed environment. We extend this tutable resources, which are supplied by the environment at ecological model to allow for heritable mutations in resource fixed rates (Fig. 1). Individuals are characterized by a resource

A C

D

E

B F

Fig. 1. Ecological and evolutionary dynamics in a simplified consumer-resource model. (A) Schematic depiction of ecological dynamics. Substitutable P resources are supplied to the chemostat at constant rates βi (i = 1, ... , R), measured in units of biomass ( i βi = 1). Cells import resources at geneti- P P cally encoded rates, ri, which define a normalized resource strategy αi = ri/ j rj and overall fitness X = log i ri.(B) Schematic depiction of evolutionary dynamics. Mutations that alter resource strategies (~α) occur at rate Uα, while mutations that alter overall fitness (X) occur at rate UX .(C–F) Simulated ecological and evolutionary dynamics, starting from a clonal ancestor, in an environment with R = 2 resources. C–F represent independent populations evolved under different sets of parameters, which differ only in the mutation rates and fitness benefits of pure fitness mutations (SI Appendix, section 5.1). Lines denote the population frequency trajectories of all mutations that reached frequency ≥10% in at least one time point. Resource strategy mutations are shown in red, while pure fitness mutations are shown in blue.

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, (t µ µ r 1 µ X R P ) and − eargue we 1.4, section Appendix, SI 1 tl osse ovxLyapunov convex a possesses still − µ X sasohsi otiuinaris- contribution stochastic a is hc ecie o elthey well how describes which ), ,wihipisthat implies which ), µ ecie nytecompetition the only describes X i ( ~ r onie ihtestandard the with coincides α X t i ) µ,i β (t noanraie portion normalized a into i − i f ) r ohsalcompared small both are e µ 1  X f 1 i = µ µ f r o iie othis to limited not are µ X f n + 3 µ + µ a lob viewed be also can ! log( = ξ /N √ µ , ξ √ µ (t N X (t ~α N sterelative the is ) i µ . ) .Ti san is This ). P R , X n fitness and f X i µ intensive r (t remains i resem- The ). ∂ ) i t must Eq. . f 1 µ [1] [2] [3] to = .I hscase, this In by 2.1 ). given section is fitness Appendix, invasion (SI the fitness” “invasion the rate as growth with process branching type of α population clonal a in fitness introduce we when it results and these below. fit- on 34, differences build ref. of to in useful described absence be recently will the were scenario in “neutral” dynamics this (U the differences considering ness Coexistence. by Stable begin Environment, Match We to Ecosystem for Selection Analysis scenario. additional complicated the more this on to comment unique and are that resources features of numbers larger In to tractability. maximiz- analytical while qualitative involved, key ing the timescales of fundamental many and elucidate behaviors to sufficient scalar already is by case described supply be environmental can the strategies parameters case, uptake this resource In and rates resources. environment two an in just evolve simplest with strains the the analyzing which by in scenario, start nontrivial we parameters, underlying the on evolution microbial resem- some superficially in least observed experiments. dynamics at Eq. complex which in the behaviors, model ble of simple range 1F seemingly diverse (Fig. the a coexistence evolution way, of this disruption within-clade permanent In rapid the coexistence and or renewed 1E), coexistence (Fig. continually stable and but 1D), diversification unstable fitness (Fig. rapid of 1C), include supply (Fig. can the stasis behaviors on Depending the 5.1). mutations, section supply of Appendix , same depicts values different the (SI have 1 and but conditions mutations, Fig. strategy environmental of population. same sub- the given are to evolution- which a ject populations, the four in of and arise simulations structure individual-based that dramatic ecological dynamics a the have ary that both still show on can simulations differences influence always fitness computer are accumulated they However, these because invade. model, to the favored to addition trivial logically model. our of behavior which the tool, into conceptual insight useful additional a provides be to prove will axes fundamental that so (39), fitness for epistasis macroscopic no ρ is there that htaentpeeti h urn niomn ie,toewith those (i.e., environment current the in β present resources not from are pure away a that effort simulate metabolic can shifting one by and mutation cost, fitness fitness resource a in incur also changes may Some strategy unambiguous. nor exhaustive neither effects, rate fitness per-genome of a distribution at arise mutations We U fitness strategy. these utilization that resource the assume be to may which related genome, a tangentially the at only throughout selection loci other directional of of number effects large the the capture alter mutations which These mutations,” fitness “pure fitness of overall class second a sider rate per-genome a at occur mutations U strategy that assume We distribution X i 2 X α ebgnb osdrn igesrtg uainta occurs that mutation strategy single a considering by begin We oudrtn hs ifrn eair n o hydepend they how and behaviors different these understand To eco- an like seem might mutations fitness pure example, For ent htti iiinit tesadsrtg uain is mutations strategy and fitness into division this that note We 0 = h nta yaiso hsmtto a edsrbdb a by described be can mutation this of dynamics initial The . (s n euti e eorestrategy resource new a in result and n htte increment they that and ) .Nvrhls,cnieigteeielzdcssa our as cases idealized these considering Nevertheless, ). ean h aefralgntcbackgrounds. genetic all for same the remains β ρ ~ α (β = ( X ~α 0 u ev h eorestrategy resource the leave but | 1 , nadto osrtg uain,w con- we mutations, strategy to ~α addition In ). X − 0 = S inv β ) , = and X µ ∆ X α 0 = ρ eetn hsanalysis this extend we Analysis, α(β α 1 ~α X ya amount an by (1 PNAS 1 1 (α, = (s raiganwsri ftype of strain new a creating , .Teeooia yaisin dynamics ecological The ). − − o ipiiy eassume we simplicity, For ). S α α | inv 1 1 ) o.115 vol. ) − = , epciey This respectively. α), ~α h∂ 0 t rw rmsome from drawn s f | i/f rw rmthe from drawn 1 U o 44 no. ~α loknown also , a produce can X unchanged. and | ρ E10409 X [4] (s ). )

PHYSICS EVOLUTION where ∆α = α2 − α1 is the difference between the mutant and A wild-type uptake rates. The invasion fitness is positive whenever ∆α and β − α1 have the same sign: If α1 < β, then selection will favor mutations that increase α, while if α1 > β, selection will favor mutations that decrease α. In this way, selection tries to tune the population uptake rate to match the environmental supply rate. If α1 = β, then the invasion fitness vanishes for all further strategy mutants. This constitutes a marginal evolution- arily stable state (ESS). Using the definition of X i (t) in Eq. 2, we can see that the universal dynamics in Eq. 3 correspond to a near-ESS limit, where the resource uptake rates remain close to β. For the sake of generality, we focus on this limit for the remainder of the main text. The full expressions for the micro- B scopic model in Eq. 1 are listed in SI Appendix. When α1 and α2 are both close to β, Eq. 4 reduces to the quadratic form,

∆α(β − α ) S ≈ 1 . [5] inv β(1 − β)

Since all mutations first arise in a single individual, many will be lost to , even when their invasion fitness is positive. With probability ∼Sinv  1, the mutant lineage will survive drift long enough to reach frequency f ∼ 1/NSinv and will then start to increase deterministically at rate Sinv. In sufficiently large pop- ulations, the transition to deterministic growth will occur long before the mutant starts to influence its own growth rate, so that C the constant invasion fitness assumption is justified (SI Appendix, section 2.1). At long times, the ecological dynamics will lead to one of two final states: Either the mutant will replace the wild type (com- petitive exclusion) or the two will coexist at some intermediate frequency (Fig. 2A). The latter scenario will occur if and only if the wild type can reinvade a population of mutants, which R requires that the reciprocal invasion fitness, Sinv ≈ ∆α(α2 − β)/β(1 − β), is also positive. By examining this expression, we see that the mutant will outcompete the wild type if its strat- egy lies between β and α1, while stable coexistence occurs when α1 and α2 span β (i.e., α1 < β < α2 or vice versa). When this Fig. 2. Schematic illustration of key eco-evolutionary processes in a two- condition for coexistence is met, the steady-state frequencies are resource ecosystem. (A) Ecological diversification from a clonal ancestor. In determined by the linear equation, the absence of fitness mutations, strains coexist at a stable equilibrium (f*) with fluctuations (δf) controlled by genetic drift. Further strategy mutations X ∗ are not favored to invade. (B) Pure fitness mutations that sweep within an α ≡ αµfµ = β, [6] ecotype shift the stable equilibrium by ∆f; accumulated fitness differences µ can ultimately drive ecotypes to extinction. Further strategy mutations allow the winning clade to rediversify at a later time. (C) Occupied niches can also ∗ ∗ whose solution is given by f /(1 − f ) = (β − α1)/(α2 − β) (34). be invaded by strategy mutations that arise in fitter genetic backgrounds. In other words, the relative frequencies of the strains are In this case, the original ecotype lineage is driven to extinction while the inversely proportional to their distance from the environmental ecological structure of the community is preserved. supply rate. According to Eq. 6, these frequencies are chosen P ∗ such that the population-averaged uptake rate α = µ αµfµ exactly balances the resource supply rate β. This provides an once the population diversifies to fill the two niches, the rate intuitive explanation for the cause of coexistence: By maintaining of evolution dramatically slows down (as in Fig. 1A), since the the strains at intermediate frequencies, the population is able to relevant timescales are controlled by genetic drift. In this way, a match the environmental supply rate more closely than it could large-effect mutation can allow the ecosystem as a whole to reach with either strain on its own. an effective ESS, long before any of the constituent strains reach Once this ecological equilibrium is attained, number fluctua- the ESS on their own. tions will continuously perturb the true frequency away from f ∗ (Fig. 2A), subject to a linearized restoring fitness ∼∆α2/β(1 − Diversification Load. We are now in a position to analyze how fit- β) (SI Appendix, section 2.1). The restoring force is strong com- ness alters the basic picture above. We begin by revisiting the pared with genetic drift when N ∆α2/β(1 − β)  1, which leads invasion of a mutant strain in an initially clonal population, this p 2 time allowing for a fitness difference ∆X between the mutant to linearized fluctuations of order δf ∼ β(1 − β)/N ∆√α and a 2 and wild type. In this case, the new invasion fitness is given by a lifetime for the stable state that is exponentially long in N ∆α . simple linear combination, At this point, additional strategy mutants are subject to very weak selection pressures: Fluctuations will induce momentary invasion S (∆α,∆X ) ≈ ∆X + S (∆α), [7] p inv inv fitnesses of order δSinv ∼ |α3 − α2|/ N β(1 − β) (which can be large compared with 1/N ), but these fitness effects are quickly where Sinv(∆α) is the invasion fitness for a pure strategy muta- averaged to zero during the ∼1/δSinv generations required for tion from Eq. 4. This result describes, in quantitative terms, such a mutation to establish (SI Appendix, section 2.2). Thus, how selection balances its ecological preferences (α → β) with

E10410 | www.pnas.org/cgi/doi/10.1073/pnas.1807530115 Good et al. 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NU ∆ s  τ s h tesdifference fitness the , p diversify  c α s s τ ttsi therefore is states ) c S X 2 diversify s swl,ecp that except well, as  inv s /β /s s c 3 tityspeaking, Strictly f c α (1 | ∼ if if α · ∗ h mutation the , 1 η (1 1 ie,we the when (i.e., o 44 no. s s s − (t c and and   ∼ − otecol- the so , ), β τ 1/NU l else All ). f s s collapse c c ∗ α α | . , then ), 2 2 τ E10411 and , when drift [12] [13] α U s  α ∼ c , .

PHYSICS EVOLUTION ecosystem spends an appreciable amount of time in the satu- 10. We then consider strategy mutations that occur on the rated state), we must also account for mutations between the background of α2, altering its strategy to α3 while leaving two strategies that arise before the ecosystem collapses. Those its fitness intact. The invasion fitness for such a mutation is mutations that arise in the less-fit clade will have little chance of given by invading. However, a mutation from the more-fit to the less-fit (α − α )∆X S ≈ 2 3 . [15] strategy will establish with probability ∼|∆X |, where ∆X is the inv ∆α current fitness difference between the two clades. If this mutation is successful, it will outcompete the resident lineage with the cor- As anticipated, fitness differences create additional selection responding value of α and reset the fitness difference to ∆X = 0 pressure for strategy mutations beyond the simple switching (Fig. 2C). In this way, invasion from one ecotype to another behavior considered above. can significantly delay the process of ecosystem collapse, since it The direction of selection is determined by the sign of ∆X . In the background of the fitter clade (∆X > 0), selection favors relieves the tension between fitness maximization (X → ∞) and mutations that increase the strategy in the direction of β (a selection to match the environment (α → β). form of generalism), while simultaneously disfavoring muta- To analyze this process, we note that successful invasion tions that lead to increased specialization (Fig. 3). The oppo- events will occur as an inhomogeneous Poisson process with rate ∗ ∗ site behavior occurs in the less-fit background, with selection λ(t) ∼ NUαf |∆X |, where f (t) and ∆X (t) are again argmax(Xi ) favoring mutations that increase the distance from β, leading 12 determined by the diffusion model in Eq. . This leads to a to increased specialization. Both behaviors have an intuitive characteristic invasion timescale explanation in terms of individuals preferring to allocate their 1 metabolic energy toward the resource with the least-fit con-  if Uα  UX ,  NUX s sumers, thereby minimizing the effective competition that they   2/3  3/2  1 UX s  if Uα  UX , experience. NUX s Uα sc τinvade ∼ [14]  2 3   2 Once a successful strategy mutation arises, it will sweep  sc UX s s  2 log 2 3 if Uα  UX s , through part of the population and alter the ecological equilib-  NUX s Uαsc c ∞ else, rium (Fig. 3). Mutations in the less-fit clade are straightforward to analyze. Since these are always directed away from both β which is derived in SI Appendix, section 2.3. Each of these and α1, these mutants will sweep through their parent clade and regimes corresponds to a different intuitive picture of the dynam- increase the equilibrium frequency according to Eq. 10. Success- ics. In the first case, strategy mutations are frequent compared ful mutations in the fitter clade have a wider range of outcomes, with pure fitness mutations, and invasion occurs almost imme- since these are always directed toward β and α1. If α3 < β, the diately after the first fitness mutation arises. In the second mutant lineage will outcompete the less-fit strain α1 and will sta- bly coexist with its parent clade α2 at an equilibrium frequency case, invasion occurs after multiple fitness mutations have accu- ∗ mulated, but when the frequencies of the clades still wander f = (β − α2)/(α3 − α2). On the other hand, if β < α3 < α2, the α diffusively relative to each other [f ∗ ≈ 1/2 ± O ps/s ]. In the mutant lineage will always sweep through its parent clade 2. If c α α third regime, invasion occurs after one of the clades has grown 3 is sufficiently close to 2, this will simply lead to an increase 10 α to a sufficiently large frequency that it would have determin- in frequency according to Eq. . However, if 3 is close enough β ∆X (α ) istically led to ecosystem collapse. When the invading mutant to that max 3 becomes less than the actual fitness differ- ∆X establishes, it will therefore cause a rapid shift in the frequencies ence, , then the mutant will sweep out both clades and lead of the ecotypes as f ∗(∆X ) returns to f ∗(0). to an ecosystem collapse and subsequent rediversification. Thus, 2 in addition to creating a larger target for invasion events, these  s  Finally, when Uα  UX , strategy mutants are suffi- sc additional strategy mutations can also enhance the probability of ciently rare that the ecosystem will typically collapse and ecosystem collapse. The balance between these competing ten- rediversify before invasion can occur. This sets the region dencies will depend on the genetic architecture of the resource of validity of the diversification–selection balance in Eq. 13. Interestingly, Eq. 13 shows that collapse and rediversification can still dominate over invasion even when both niches are typically filled (Pr[S = 2]  Pr[S = 1]). In this case, both the genealogical structure and the typical state of the ecosystem will resemble the invasion regime, but the historical record would contain a series of punctuated extinction and diversifi- cation events, interspersed with long periods of gradual fitness evolution.

Fitness Differences Create Opportunities for Ecological Tinkering. Our derivation of Eqs. 12 and 14 assumed that the two eco- types were fixed by the genetic architecture of the organism. Individuals could mutate between α1 and α2, but mutations to other points in strategy space were forbidden. In the absence of fitness differences, we saw that selection for these additional strategy mutants is weak once both niches have been filled (Sinv . 1/N ), potentially justifying the single-locus assumption in terms of a priority effect. However, the previous analysis shows Fig. 3. Invasion fitness landscape for additional strategy mutations in a that there can be strong selection to switch strategies once fit- two-resource ecosystem. The two resident ecotypes are illustrated by blue circles, while red circles denote mutant strains created by strategy muta- ness mutations accumulate, so it is also plausible that fitness tions on one of the ecotype backgrounds. The solid black line denotes the differences could lead to selection for strategy mutations more P effective mean fitness, i αiXi, experienced by a given resource strategy. generally. Strains with overall fitness (X) above this line are favored to invade, while To investigate these selection pressures, we consider a pop- others are selected against. If a mutant successfully invades, its effect on the ulation that is currently described by the steady state in Eq. ecosystem is indicated by the text.

E10412 | www.pnas.org/cgi/doi/10.1073/pnas.1807530115 Good et al. Downloaded by guest on October 6, 2021 Downloaded by guest on October 6, 2021 vrtenme fsriigseisi qa otenme of number the to equal is surviving resources. of number the ever where in Increases Eq. 3.1). frequencies in tion equilibrium fitnesses the at mean evaluated resource-specific the where ode al. et Good the in Eq. processes assembly [where obtained case community recently neutral were the findings for Similar to conditions. composition ronmental pressures their selection internal the adjust screen these dynamically Thus, equilibrium. ecosystems at coexist saturated that strategies resource of set vector supply cies resource the both of of expansions perturbation Moreover, α fitnesses. mean specific fitnesses strain the obtained Eq. directly of be inversion can matrix these a resources, by of is number strains the coexisting to of variables equal number intensive the where the ecosystem, through “saturated” only composition nity of in values directions, sense high beneficial a from still flow is that X there mutations case, favors two-resource selection the which to similar Thus, “effort-averaged” the strategies, ,smlrt h w-eorecs nEq. in of case values sec- two-resource equilibrium , Appendix the the that (SI to strategies similar the 3.2), between tion distance effective an the ecosystem, urated from strain resident a of phenotype higher in only know arise that to behaviors dimensions. useful new of fundamentally still scope are is the there beyond the extend it on results qualitative beyond Nevertheless, constraints our whether is case. with fewer compared two-resource even case parameters evolutionary are the this and there ecological of of as how space analysis work, ask full present to environments the A natural complicated more therefore well. these is as to It generalize results (41). hor- our through transfer rates uptake gene resource their izontal alter pools to environments gene them flexible in allow and that resources found potential of are How- numbers explicit large communities interest. with derive of microbial to quantities many use admit the evolutionary ever, could to case, many we enough for this which simple predictions solution, In was analytical equilibrium. ecosystem full at stable a at the coexist where of can resources, structure strains substitutable two two most only with environments Coexistence. Pairwise Beyond work. future remains for regimes topic potential interesting the of an exploration detailed A data. ing ∆ i −1 ~α) i ,µ h nainfins nEq. in fitness invasion The o eea clgcleulbim uainta lesthe alters that mutation a equilibrium, ecological general a For olwrvle of values lower to 17 f ugs httepeatri tl nesl rprinlto proportional inversely still is prefactor the that suggest ilhv nivso fitness invasion an have will µ ∗ α hs uniisinfluence quantities these ; hw htti sagnrcpoet htocr when- occurs that property generic a is this that shows i −1 ,µ ρ stelf nes of inverse left the is α (α 0 | hc spol aaeeie yexist- by parameterized poorly is which α), X µ S X utfigteritrrtto sresource- as interpretation their justifying , inv X X X X i α i → i ≈ i i i o h te eore n ieversa. vice and resources other the for lhuhteeaenow are there although , ≈ r aoe when favored are r ie ylna obntosof combinations linear by given are X s 1, X − X 16 u rvosaayi oue on focused analysis previous Our j µ X ahrta utone. just than rather , i X eed ntecretcommu- current the on depends α i 0 = i α µ,i r odtoal independent conditionally are i −1 X ,µ ∆α hs eseta nasat- a in that see we Thus, . β 3),a ela ncertain in as well as (34)], X i (X X i nytruhsaigthe shaping through only µ i X n h tanfrequen- strain the and , µ i ∞ → R , rmteetra envi- external the from i f ~α , µ ∗ µ ) R sec- Appendix, (SI X to 2 = i ii 3,36). (35, limit (X slwrthan lower is enote We 15. n whether and − R( µ 2 + X utbe must s i , na In . ~α 1)/2 [16] [17] µ + ls tani o culyfvrdb eeto.B ento,all definition, By selection. loss-of-function by favored gener- of the actually that entropy not is is case greater this strain in alist generalist the difference key the a by for However, mutants. preference balanced the is which strain in (40), 5 argument (Fig. load background generalist the and in mutations domi- (α from be variants descended to loss-of-function (α tends strain single ecosystem generalist steady-state a by the nated that show tions 4A). (Fig. order lowest at least that such strains “generalist” of tia can that when pressures To arise selection 4B). ecological (Fig. strong coexist the to for able compensate are the that constrain strategies can distinct mutations of fitness number pure of rate recapitu- high results sufficiently a The for uptake 3.3 ). observed behavior section individual qualitative , Appendix the use toggle late (SI not that off or and mutations use on with either rates can resource, individuals given which a strat- in binary model, a of space simulations egy computer performed we Eq. effect, in this balance diversification–selection the coex- of multiple harbor when case, now strains two-resource isting can the ecosystems” to species “unsaturated contrast surviving In these of value. number saturated the this the drive below can of mutations fitness square that the a to with strategies. resource proportional fitnesses, the between strain inversely distance the effective is two-resource of that combinations the prefactor linear in Eq. via equi- As ecological neutral librium of the 3.2). perturb differences section fitness generalization small case, , Appendix the (SI as resources serves which inversion, matrix similar a from R 4. Fig. rfco f1/ of Eq. prefactor in relation scaling the depicts capacity ecosystem in maximum the indi- SD denote The lines lines (A) solid replicate. maximum replicates; the independent and minimum three the from cate points time multiple ( in sup- model resource rates uniform resource-use nearly ply binary with limit, a mutation of weak strong-selection, simulations the from state steady long-term nanal nfr niomn [β environment uniform nearly a In above saw we simple, particularly is case saturated the While frequencies steady-state the limit, this In h ubro oxsigeoye.Teclrddashed colored The ecotypes. coexisting of number The (B) resources. .Ti srmnseto mutation- a of reminiscent is This S2–S4). Figs. Appendix, SI iesfiainslcinblnewhen balance Diversification–selection .Ec on eoe naeaeover average an denotes point Each 5.2). section Appendix , SI B A f µ h ouain r ocdt vleconsor- evolve to forced are populations the R,  S ∗ √ ≈ 2π X i nlddfrvisualization. for included R β i α > i −1 ,µ edn oacniuu generalization continuous a to leading 2, − X 19 i ,ν µ,i hc ple for applies which β PNAS i ∝ α P µ,i i −1 n olcinof collection a and 1) ,µ µ | α ∝ ~α S i −1 o.115 vol. ,ν µ R 1 = i  R f (X − µ ∝ h lc ahdline dashed black The R. 2 = ∗ f δ ssilcoeto close still is µ 1 µ ∗ µ,i ihan with R,  S oinvestigate To 13. .Crlsdpc the depict Circles 1. O ± − eore,i that in resources, 10 a eobtained be can | htrecently that ) X o 44 no. ν ,simula- ()], o multiple for ), X i costhe across | E10413 − S β ~ [18] O at , (1) 1

PHYSICS EVOLUTION ABall growth rate but leave the relative uptake rates unchanged. Strategy mutations enable ecological diversification, while fitness mutations capture the effects of directional selection at other genomic loci. This classification scheme is best viewed as a conceptual tool, rather than a statement about the underlying biology. We have mostly focused on mutations with either a perfect tradeoff or a perfect benefit, but Eqs. 7 and 16 apply equally well in more real- istic cases where a shift in resource strategy is accompanied by a change in the overall growth rate. These expressions can be used to predict when the costs of an opportunistic mutation will out- Fig. 5. (A and B) Schematic of (A) ecological and (B) genealogical struc- weigh its ecological benefits or vice versa. Similarly, true fitness ture at the evolutionary steady state described in Eq. 19. In B, blue circles mutations (e.g., an increase in ATP efficiency) are assumed to represent pure fitness mutations and red circles represent loss-of-function be rare in nature, since they could have fixed in the population strategy mutations. long ago. In practice, effective fitness mutations are more likely to correspond to strategy mutations whose tradeoffs are simply not exposed by the current environmental conditions. In this pic- of the transient states in Fig. 5 are ecologically stable, while the ture, the overall fitness Xµ can be viewed as an emergent trait preference for the generalist strain arises dynamically from the that arises whenever we project high-dimensional cellular pheno- race to acquire pure fitness mutations. types onto a restricted set of axes (SI Appendix, section 4.3). The The dynamics of this process can be characterized analytically presence of effective fitness mutations may therefore be a more in the weak mutation limit, yielding a simple heuristic expression general phenomenon than their name would seem to imply. for the diversification–selection balance, The creation of new strains via mutation bears a superficial resemblance to immigration from a fixed species pool, which is  2  1 Uα the traditional scenario considered in theoretical ecology. How- S ∼ 2 , [19] R UX s ever, this analogy is exact only in the absence of inheritance, when the phenotypes of nearby genotypes are uncorrelated from which is valid for S  R (SI Appendix, section 3.3). The transi- each other. In contrast, when the effects of mutations are herita- tion to the fully saturated state (S = R) requires an even more ble, we have seen that directional selection can produce dramatic stringent condition, which implies that unsaturated ecosystems departures from traditional ecological predictions. are obtained for a very broad parameter regime (Fig. 4B). In Similar to immigration (36, 42), strategy mutations allow an both cases, a larger number of substitutable resources will lead initially clonal population to diversify into stably coexisting eco- to a less diverse ecosystem at diversification–selection balance. types, whose upper bound is set by the number of resources. This is ultimately due to the fact that the difference between gen- Yet because fitness mutations are heritable, further evolution eralists and single loss-of-function variants becomes increasingly will lead to fitness differences between the clades, which can small as R → ∞. dynamically shift the ecological equilibrium over time and even- This suggests that the relative frailty of the diversification– tually drive less-fit clades to extinction. The mere observation selection balance in Eq. 19 may be a pathological feature of that selection can disrupt coexistence is not surprising, since the simple genetic architecture that we have assumed, in which drug resistance or other harsh selection regimes provide strik- fit generalist phenotypes are easily accessible. If we instead ing examples of this effect. However, our quantitative analysis impose an upper limit Rc  R on the number of resources shows that this collapse can happen long before any clade is that a strain can metabolize, heuristic calculations suggest that universally inferior to another and that it can result from the diversification–selection balance will be achieved for substan- compound effect of many small-effect mutations that would tially higher values of S, even for large R (SI Appendix, section not lead to extinction on their own. These results suggest that 3.4). In this case, the ecological and genealogical structures that ongoing directional selection may have a larger impact on the are attained at this evolutionary steady state will be consider- structure of microbial communities than is often assumed. In ably more complex than the shallow star-shaped genealogies in particular, while previous ecological analyses suggest that the Fig. 5. A detailed analysis of this steady state remains an number of ecotypes should meet (35, 36) or even exceed (34) the interesting topic for future work. number of resources, our results raise the possibility that they could also reside at a diversification–selection balance below the Discussion maximum capacity of the ecosystem. In microbial populations, primitive ecological interactions can In addition to their influence on coexistence, we also found evolve spontaneously over years (5), months (6), and even days that fitness differences accrued via directional selection will gen- (7). Yet this process rarely takes place in isolation. In rapidly erate emergent selection pressures for continual evolution of evolving populations, diversifying selection must compete with the ecological phenotypes, even in a saturated ecosystem. While directional selection acting on other loci throughout the genome. these internal selection pressures are reminiscent of the Red Here, we have introduced a simple mathematical framework to Queen effect (43), our quantitative analysis shows that they model the interactions between these two processes in asexually select for different phenotypes than in the standard predator– reproducing organisms. prey setting. In particular, less-fit clades do not experience The ecological interactions in our model emerge from the increased selection pressure to narrow their fitness deficit by competition for substitutable resources (e.g., different carbon accumulating fitness mutations. Instead, selection favors muta- sources), according to a well-studied class of models from theo- tions that divert metabolic effort toward resources with lower retical ecology (33–36). To incorporate evolution into this model, effective competition, even at the cost of widening the fitness we assumed that individuals can acquire mutations that alter deficit. Moreover, the direction of selection toward any given their resource uptake rates. We showed that it is useful to distin- resource can shift dynamically as the fitness differences and guish between two characteristic types of mutations: (i) strategy resource uptake strategies evolve over time. mutations, which divert metabolic effort from one resource to Most of our analysis focused on the strong-selection–weak- another, and (ii) fitness mutations, which increase the over- mutation regime, in which the current ecological equilibrium is

E10414 | www.pnas.org/cgi/doi/10.1073/pnas.1807530115 Good et al. Downloaded by guest on October 6, 2021 Downloaded by guest on October 6, 2021 8 otrK,Shue ,CyeK,Rkf-aomS(07 h vlto ftehost coexisting the of of evolution The hundreds (2017) S reveals Rakoff-Nahoum KZ, genomics Coyte J, Single-cell Schluter KR, (2014) Foster al. 18. et N, Kashtan 17. after maintains evolution reverse Recurrent (2017) al. et A, Sousa 10. 9 edl L ta.(06 eoewd eetv wesadgn-pcfi wesin sweeps gene-specific and sweeps selective Genome-wide (2016) al. et ML, Bendall 19. prolonged during Øvre diversity V, Torsvik microbial evolved 16. experimentally long-term of in succession Ecological Evolution (2011) VS of Cooper (1999) SR, dynamics Poltak The R 15. (2017) Kolter MM Desai SE, RE, Lenski Finkel JE, 14. Barrick MJ, McDonald experi- BH, of Good bank Tangled 13. (2013) VS Cooper SR, Poltak LM, Mayo-Smith diversifica- CC, adaptive Traverse of dynamics 12. evolutionary Parallel (2013) M Doebeli MD, Herron 11. 1 au R odB,HlashkO olr S(07 vltoaydnmc of dynamics Evolutionary (2017) KS Pollard individual O, of Hallatschek microbiome BH, gut Good the NR, within evolution Garud Adaptive 21. (2017) al. et S, Zhao 20. ayo h aoaoyeprmnsta oiae hsstudy. this motivated that experiments by laboratory ( In violated limit the is mutation assumption of impor- this weak many convenient, particularly the analytically on A While focus settings. 1). our laboratory is expected limitation factors or tant complicating natural the either of in many omits which model, measur- (S by fitness or invasion (13) (∆ distribution perturbation timescales joint long the on fluctuations this ing analyzing frequencies constrain by ecotype to either in ways experimentally, potential (46). parameter in suggests implicated while key been analysis 45), have (9, present mutations mutation smaller Our large-effect of series single a a others, to architec- traced diversification be genetic ecological cases, can well-studied the dynamical few the a characterized practice, In poorly controlling empirically. remain In interactions in ecological role observe. most of key tures we a that play to behaviors out rates, uptake turn resource on which effects noninfinitesimal have that tions sec- and can dynamics S1 symmetry adaptive broken standard Fig. the simple picture. from , Appendix this deviations that dramatic (SI to show times lead far results all remain Our 4). to at tion constrained optimum effectively its additional is an from key as which The behaves dimension, resem- 44). selection trait closely (22, directional that dynamics that form is adaptive supply difference universal of the a models to on traditional close bles takes model sufficiently the our are when rates, limit, strategies this In uptake occurs. resource mutation next the before attained ode al. et Good .FeklE,e l 21)Coddgot ed otesotnosevolution spontaneous the to leads growth Crowded (2015) al. et EM, Frenkel 9. .FisnM,SxrG rvsn ,DeeiM(04 xeietleiec for evidence Experimental (2004) M Doebeli M, Travisano G, Saxer environment. 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University the the the of from development support the edges inspired that discussions ACKNOWLEDGMENTS. and ecology promising between a interactions generally. offer more the evolution may investigating tractability for analytical intensive avenue its of ecologi- number so, small of If a class by variables. broader mediated are a it that of that interactions behavior cal hypothesize limiting we the axes, popu- capture fitness Since of may multiple generalization discovered. simplest with be the genetics as to lation viewed whether yet be or can classes model interaction universality our ecological other of are modes there diverse more onto simulations to confined been mostly far. have so which investigate to effects, which in these framework analytical promising a time- provide cross-feeding, [e.g., of our model to effects basic additions other the and an explore recombination, environments, fully in varying also to [e.g., will required measurements work quantita- be Future evolutionary to (39)]. to required framework model approximate-likelihood is the regime fit this tively of more a investigation However, where limit. thorough mutation case weak the the from gleaned to intuition results our of ti loitrsigt s hte u eut a emapped be can results our whether ask to interesting also is It vltoaydynamics. evolutionary USA Sci Acad model. resource consumer MacArthur’s 2018:033406. to solution cavity ecosystem. diverse ecosystem. model a in Princeton). 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