Modeling Viral Genome Fitness Evolution Associated with Serial Bottleneck Events: Evidence of Stationary States of Fitness

Evolution of fitness values upon replication of viral populationsis strongly influenced by the size of the virus population thatparticipates in the infections. While large population passagesoften result in fitness gains, repeated plaque-to-plaque transfersresult in average fitness losses. Here we develop a numericalmodel that describes fitness evolution of viral clones subjectedto serial bottleneck events. The model predicts a biphasic evolutionof fitness values in that a period of exponential decrease isfollowed by a stationary state in which fitness values displaylarge fluctuations around an average constant value. This biphasicevolution is in agreement with experimental results of serialplaque-to-plaque transfers carried out with foot-and-mouth diseasevirus (FMDV) in cell culture. The existence of a stationaryphase of fitness values has been further documented by serialplaque-to-plaque transfers of FMDV clones that had reached verylow relative fitness values. The statistical properties of thestationary state depend on several parameters of the model,such as the probability of advantageous versus deleterious mutations,initial fitness, and the number of replication rounds. In particular,the size of the bottleneck is critical for determining the trendof fitness evolution.

INTRODUCTION

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Introduction

The initial steps in virus evolution are generation of diversity(through mutation, recombination, and genome segment reassortmentin multipartite genomes), competition among the generated variants,and selection of those mutants showing the largest phenotypicadvantage in a given environment (see overviews in references9, 14, 17, 28, 30, and 40). Because of high mutation rates duringviral RNA biosynthesis (2, 18), RNA viruses replicate as complexmutant swarms termed viral quasispecies (14, 21-24). The degreeof adaptation of a viral quasispecies to a given environmentis often quantitated by a relative fitness value, which measuresthe replication capacity of a viral population relative to areference mutant distinguishable either genotypically or phenotypically(15, 26, 33, 37). The long-term survival probability of a virusshould consider parameters other than replication capacity (suchas particle stability, transmissibility, etc. [11, 12, 15]).Despite their limitations, relative fitness values, determinedby growth competition experiments between two viral populationsin cell culture and in vivo, are providing insights into basicfeatures of quasispecies evolution as well as viral diseaseprogression (5, 15, 49).

Because of the large variations in viral population size duringinfections in vivo, a focus of interest has been the study ofthe influence of virus population size on the evolution of fitnessvalues (reviewed in reference 15). Experimental results withseveral RNA viruses have documented that large population passagesoften result in fitness gains (7, 26, 43, 45, 58) while repeatedbottleneck events (serial plaque-to-plaque transfers being anextreme example) lead to average fitness losses (6, 19, 25,27, 59, 60), as predicted by the operation of Muller's ratchet(38, 41). According to this mechanism, asexual populations oforganisms will tend to accumulate deleterious mutations in anirreversible fashion unless accumulation is retarded by recombination.Studies with vesicular stomatitis virus (VSV) established thatthe size of the population bottleneck that led to either anincrease, a decrease, or maintenance of a fitness value wasdetermined by the initial fitness of the population (44). Consistentwith this observation, exponential fitness gains observed uponlarge population passages were eventually limited by the populationsize, resulting in stochastic fitness variations (46).

In a recent study of the fitness evolution of foot-and-mouthdisease virus (FMDV) clones subjected to at least 100 successiveplaque-to-plaque transfers, a linear accumulation of mutationstogether with a biphasic fitness decrease was observed (27).The second phase showed fitness fluctuations around a fitnessmean value without perceivable fitness loss. This fact is remarkablesince it could underlie a mechanism for low-fitness viral populationsto elude extinction. For the present report we developed a numericalmodel that investigates fitness losses of fast-replicating genomesdisplaying high mutation rates and subjected to plaque-to-plaquetransfers. The results with this new numerical model are inagreement with experimental results showing a biphasic fitnessevolution of FMDV clones and fitness stability upon plaque transfersof very low fitness clones (27). The model predicts also theeffect of transmission size on fitness evolution, as documentedpreviously with experiments using VSV (44). Given its relevanceto virus survival, the fitness stability of low-fitness cloneshas been further supported by 30 additional plaque-to-plaquetransfers of highly debilitated FMDV clones. An essential featureof the model is the consideration of advantageous compensatorymutations as a molecular mechanism to cause fitness recovery,a feature adopted on the basis of experimental observationsmade with FMDV (1, 26) and also with unrelated systems suchas human immunodeficiency virus (HIV) type 1 (4, 42) and someantibiotic-resistant bacteria (3, 50).

MATERIALS AND METHODS

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Materials and Methods

Plaque-to-plaque transfers of FMDV clones. The origin of BHK-21 cells, procedures for cell culture, andplaque assays with FMDV have been previously described (25-27).Relative fitness values of FMDV clones were estimated from theaverage number of PFU present in a plaque grown on a BHK-21cell monolayer, determined upon triplicate platings; this procedureis identical to that used in previous studies (27) and differsfrom the standard measurement based on growth competition experiments(33). FMDV clone

was obtained after subjecting clone

to 130 plaque-to-plaque transfers as previously described (27).

is a clone derived from C-S8c1, the standard FMDV clone used in our laboratoryand which was obtained from natural isolate C-Sta. Pau Sp/70(53); the isolation of

was described in reference 25. In the present experiments four subclones derived from clone

were subjected to 30 additional plaque-to-plaque transfers following the plating procedure described previously(27).

Numerical model. The model developed in the present study delineates fitnessevolution upon plaque-to-plaque transfers, mimicking the experimentscarried out elsewhere with RNA viruses and in particular withFMDV (25, 27). To study the effect of population size on fitnessvariation, transfers involving pools of virus from a number(Np) of plaques to Np plaques in the way described by Novellaet al. (44) have also been modeled. The model is divided intotwo main steps.

Step 1: simulation of the development of a lytic plaque. The process starts with a "virtual" single virus genome whichafter several replication cycles (denoted by r) will generateprogeny, in a way analogous to the viral population producedin a lytic plaque. Each individual virus is characterized onlyby a parameter, W, standing for its fitness, which can takediscrete values ranging from 1 to ${infty}$ . Fitness values are takenas the mean direct progeny per individual, which is proportionalto the replication rate. Other factors that may have an influenceon fitness (11, 12) are not considered. Individuals in the modelare referred to as sequences or genomes instead of viruses.Each sequence has a certain probability of generating a numberk (k = 1, 2, 3,...) of direct descendants after replication.The probability P(k) of generating k descendants is given bya Poisson distribution, {P(k) = [(W)^k e^-W]/k!}, in which W isthe viral fitness, given here as the mean number of direct descendants(54).

During progeny formation, mutations take place, giving riseto genomes with the same fitness as, or lower or higher fitnessthan, the starting one. Each time that a deleterious mutationoccurs (probability of occurrence of deleterious mutation =p), the fitness of the new genome decreases by one unit, andwhen the mutations are advantageous (compensatory and back mutations)the fitness increases by one unit (probability of increase offitness = q). In the model, q << p < 1 and the highestprobability (1 - p - q) corresponds to occurrence of mutationswith no discernible effects on fitness. As only phenotypic variationsare observed, the model does not distinguish between sequenceswith neutral mutations and those with no mutations. The firstreplication cycle (r = 1) corresponds to the replication ofthe founder sequence to give a number (k) of progeny with probabilityP(k). Each new sequence can also initiate its own replication,originating a new ensemble of daughter sequences whose numberis also described by a Poisson distribution. The process isperformed for a given number of replication cycles (r), r beingproportional to the time of plaque development (24 to 48 h inthe experiments with FMDV [27]).

Step 2: selection of the sequences for the subsequent transfers. In the previous step, an ensemble of sequences with differentfitness values was generated. Fitness always has a positivevalue, as sequences with W $<=$ 0 do not replicate and are lost.The transition to W $<=$ 0 defines an extinction threshold whichis parallel to the case of the experimental system when viruseswhich have accumulated many deleterious mutations or a lethalmutation do not originate plaques and do not participate inthe next round of plaque formation. One of the plaque-forminggenomes is randomly chosen and used as input for repetitionof step 1. Steps 1 and 2 are then repeated a number of times(T), analogous to a number of plaque-to-plaque transfers carriedout in the laboratory. Each time that a simulated lytic plaquedevelops, it is possible to determine the distribution of fitnessvalues of the genomes composing the plaque and the number ofgenomes generated from the parental one.

Numerical computations. The computer programs were written in FORTRAN language. Shortruns were carried out on a Pentium 3, and long runs were performedon an Alpha 64-bit DS10 466 MHz, computer.

RESULTS AND DISCUSSION

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Results and Discussion

Effect of initial fitness. The objective of the present study is to develop a model thatsimulates the evolution of fitness values of viral populationssubjected to serial plaque-to-plaque transfers, by using parametervalues derived directly from experimental results. In the numericalmodel the process is started with genomes of different initialfitness values (W₀). In all cases studied, there was a timeinterval, corresponding to the first transfers, in which thenumber of infectious individuals generated (which is proportionalto the fitness of the population at each transfer) decreasedin a roughly exponential manner. After a variable number oftransfers (T $~$ 200 for W₀ = 5 and T $~$ 500 for W₀ = 15 [Fig. 1]), the decreasing trend stopped and a statistically stationarystate of fitness values was reached. In this second phase, thenumber of individuals generated at each passage showed largefluctuations around a mean value which was independent of thefitness of the sequence which started the process. The valuesof the slopes of fitness decrease and the mean values attainedat the stationary state were calculated for different W₀. Whenthe parameters p and q were kept constant throughout the successivetransfers, there were no variations, either in the rate of fitnessdecrease or in the mean fitness value reached at the stationarystate (Fig. 1). To attain a more realistic description of theprocess of fitness evolution, some modifications were introducedin the numerical simulations. In the real experimental processof serial plaque transfers, the higher the fitness of the initialquasispecies, the higher the probability of obtaining variantswith deleterious mutations (44); thus, the effects of populationbottlenecks leading to a fitness decrease were more drastic.This was introduced in the simulation by making the probabilityof fitness decrease (p) proportional to the fitness (p = 0.01W). In this case, the model shows that the higher the fitnessof the starting genome, the higher the absolute value of theslope of the decreasing phase (Table 1). However, the averagefitness value reached in the stationary state and the passagenumber at which the stationary state started were essentiallyindependent of the initial fitness (Table 1).

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FIG. 1. Numerical simulation of the evolution of the number of infectious units produced as a function of the number of plaque-to-plaque transfers. The parameters kept constant in the simulations are p = 0.01, q = 0.001, and r = 5; three different initial fitness values for the founder sequence (W₀ = 5, 10, or 15) were assayed. Each curve represents an average of five independent runs. The numerical model and computer programs used are described in Materials and Methods.

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TABLE 1. Effect of the initial fitness on the process of fitness evolution through plaque-to-plaque transfers

Effect of the frequency of deleterious mutations. The reductions in fitness upon successive transfers and thetime span before the stationary state was achieved were closelyrelated to the frequency of deleterious mutations (Table 2).The rate of decrease in the number of infectious individualsat each plaque transfer (proportional to the average fitness)increased with p. Both the mean fitness value at the stationaryphase and the number of passages required to reach the stationaryfitness level decreased as p increased (Table 2).

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TABLE 2. Effect of the probability of occurrence of deleterious mutations (p) on the process of fitness evolution through plaque-to-plaque transfers

Basis for a stationary state of fitness equilibrium. To investigate the possible origin of fitness equilibrium, thestatistical distribution of fitness values at different transfers(W_T) was analyzed (Fig. 2). The initial sequence was given afitness of 5, and during a certain number of transfers the averagefitness of the distributions decreased (W₁₀ = 4.97, W₁₀₀ = 4.78,and W₆₀₀ = 2.75) until a constant average value was obtained(W₆₀₀ = W_1,000 $~$ 2.7). The results show that the shape of thedistributions changes with the transfer number. At the stageof fitness decrease (i.e., T = 10 and T = 100) the distributionsare quite symmetric, indicating that during the developmentof a lytic plaque similar amounts of genomes with fitness loweror higher than the average were generated. A distribution offitness values was previously reported for subclones of VSV(20). However, the distribution of fitness values at the stationarystage (i.e., T = 600 and T = 1,000) is more asymmetric, reflectingthe existence of a boundary on the lower values of fitness indicativeof an extinction threshold, which causes the distributions tobe skewed toward higher fitness values (Fig. 2). The distributionsat T = 600 and T = 1,000 were very similar, suggesting thatin the stationary state the probability of choosing a genomewith a given fitness for the next transfer does not change withtime, and consequently, the average number of infectious individualsgenerated when the process has reached this point is the sameat different transfers. Due to the broad distribution of fitnessobtained, large fluctuations in fitness values at differenttransfers are observed.

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FIG. 2. Distribution of fitness values at different plaque transfers. The probability distributions P(W) were calculated at transfers T = 10, 100, 600, and 1,000, by using the following constant values for the parameters: W₀ = 5, p = 0.01, q = 0.001, and r = 5. Each distribution has been obtained as an average of 200 independent trials. The W value in each panel is the average fitness of the genome distribution (filled boxes). The numerical model and computer programs used are described in Materials and Methods.

Infective population size and fitness evolution. The effect of the transmission size (number of infectious unitsfrom a virus population used in successive infections) on fitnessevolution was studied by choosing different numbers of sequencesto initiate the replication in the next transfer. The transmissionsize was critical to determine the trend of fitness evolution.For W₀ = 6, fitness losses occurred when the transmission sizeNp was 1 or 2, whereas a transmission size of 3 or higher resultedin fitness gains (Fig. 3A). As expected from the results ofthe plaque transfers involving one genome, an initial phaseof fitness variation was followed by a stationary state whichwas more evident when the transmission size was small (Fig.3A). The average fitness value at the stationary state was completelydetermined by the transmission size of the population (keepingconstant the values of p, q, and r). This implies that, fora given transmission size, the fitness of the population mayincrease or decrease, depending on whether the initial fitnessis lower or higher than the characteristic fitness determinedby the transmission size (Fig. 3B). After a sufficient numberof transfers, all the populations converged toward a similaraverage fitness value which was independent of the initial fitness.

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FIG. 3. Evolution of fitness values during Np plaque-to-Np plaque transfers as a function of the population transmission size (Np) (A) or the initial fitness (B). In panel A the initial fitness was W₀ = 6 in all cases. In panel B the transmission size was Np = 3 in all cases, and the lines from bottom to top correspond to W = 1, 3, 5, 7, and 9, respectively. In all cases the values kept constant for the parameters were p = 0.01, q = 0.001, and r = 5. Values are the average of 200 independent trials. The numerical model and computer programs are as described in Materials and Methods.

Exploration of different parameter values and consistency with experimental results. The influence of p, q, and r on fitness evolution has also beenexplored. In all cases the qualitative behavior of the modelwas the same provided q << p < 1. The biphasic evolutionof fitness, the presence of a stationary state, and the statisticalproperties of the fluctuations did not depend on the particularparameters chosen. Some combinations of parameters gave quantitativeresults quite similar to those observed in the actual processof plaque-to-plaque transfers carried out with FMDV (Fig. 4).With p = 0.06 and q = 0.001, both the rate of decrease of fitnessas a function of plaque transfer and the transfer number atwhich the stationary state starts were very close to the valuesobtained experimentally (compare Fig. 4A and B). The stationaryfitness level with r = 8 was closer to the experimental valuethan was the level predicted with r = 5. As examples of grossdiscrepancy with experimental results, two simulations withp = q are included in Fig. 4A. When p = q = 0 (no mutations)(Fig. 4A, lower left panel), population fluctuations (due tothe distribution of fitness according to a Poisson distribution)without a transient phase of fitness change were observed. Whenp = q = 0.02 (Fig. 4A, lower right panel), an increase in thenumber of infectious units occurred due to the faster replicationof sequences that increase their fitness as a consequence ofbeneficial mutations. Longer simulations (data not shown) indicatedthat the average fitness grew in an unrestricted fashion andthat no stationary state was reached. We have also exploreda number of variations of the rules of our model (real valuesfor fitness instead of integer numbers, different values ofthe extinction threshold, continuous replication of sequencesinstead of discrete replication cycles, etc. [S. Manrubia, M.Arribas, and E. Lázaro, submitted for publication]).In all cases the qualitative behavior was unchanged, and theconclusions were not altered.

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FIG. 4. Comparison of the infectious units produced as a function of plaque transfer number according to the numerical model and in actual experiments. (A) Time series of the number of infectious units predicted by using several combinations of parameters. (Upper left) p = 0.06, q = 0.001, r = 5, and W₀ = 6. (Upper right) p = 0.06, q = 0.001, r = 8, and W₀ = 6. (Lower left) p = q = 0, r = 5, and W₀ = 6. (Lower right) p = q = 0.02, r = 5, and W₀ = 6. (B) Number of infectious units per plaque (plaque titer) of clone as a function of plaque transfer number. (Left) Plaque titers obtained when was subjected to 100 successive plaque-to-plaque transfers (27). (Right) Plaque titers obtained with four subclones (a, b, c, and d) were isolated from plaque transfer 100 and subjected to 30 transfers; the time of plaque development was 26 to 30 h. For some plaque transfers of clone plaque transfer 100c (marked with an asterisk), the time of plaque development was increased to 46 h, since plaque transfer 27 contained less than 10 PFU after 27 h of plaque development. Note that the scale of the ordinate in the four right panels is different from that in the left panel. Simulations and experimental procedures are described in Materials and Methods.

The robustness of average fitness stability has been furtherexplored experimentally by subjecting four subclones derivedfrom an FMDV clone which had already reached a stationary stateof fitness values to 30 additional plaque-to-plaque transfers(Fig. 4B). It is very remarkable that after 30 additional plaquetransfers—a total of 90 plaque-to-plaque transfers sincethe stationary state was reached (27)—the mean averagefitness of the virus remained constant. As also observed inthe numerical simulations, the successive fitness values determinedexperimentally showed large fluctuations. These are expectedfrom the broad fitness distribution of the individuals whichcompose the population ensemble and which are the origin ofthe single individual genome that participates in the subsequenttransfer. The presence within a plaque of genomes with differentfitness values was also documented experimentally by analyzingsubclones isolated from the same parental clone (27).

Main features of the model, biological implications, and connections with present views of RNA virus evolution. The numerical model proposed here includes as a main featurethe occurrence, with a low probability, of advantageous mutationsthat play a key role in reaching a stationary state of fitness,after a transient phase of variable fitness values. The modelincorporates also the likely higher frequency of neutral anddeleterious mutations than of advantageous mutations in thecourse of virus plaque formation. However, the frequency ofneutral mutations during virus evolution is unknown. Often synonymousmutations are the best candidates to be neutral. Yet the picornaviruscoding regions may contain cis-acting elements which conferon open reading frames a phenotypic involvement in additionto their protein coding function (31, 39). Evidence of a selectivevalue of synonymous replacements has been obtained with severalRNA viruses (13, 52). Therefore, synonymous mutations withinthese elements are unlikely to be neutral. Furthermore, recentevidence has shown that a corrected ratio of nonsynonymous tosynonymous mutations may be taken as indicative of positiveselection in an experimental setting in which positive selectionis impossible (56), making quantifications of neutral siteson the basis of the ratio of nonsynonymous to synonymous mutationsquestionable. Given also the contingent nature of some neutralmutations (48), it is likely that the number of truly neutralsites in RNA genomes with compact genetic information is limited,albeit the number is unknown and difficult to estimate. Thisuncertainty should not affect the numerical model proposed here,since one of its basic quantitative features is that the combinednumber of deleterious and neutral mutations largely exceedsthe number of advantageous mutations, irrespective of the proportionof deleterious to neutral mutations.

The stationary state of fitness values results from an equilibriumbetween the trend to eliminate individuals as their fitnessfalls below the extinction threshold and the probability ofselecting for the subsequent transfer individuals with compensatorymutations. This probability is higher in the stationary statethan in the transient phase, as a consequence of the increasednumber of individuals whose fitness becomes zero. The occurrenceof compensatory, advantageous mutations was not introduced inmost models of Muller's ratchet (32, 35), which considered thatback mutations (true reversions) constituted the only mechanismto compensate for the negative effects of deleterious mutations.Wagner and Gabriel (57) considered the effect of compensatorymutations in a model of fitness evolution in finite parthenogeneticpopulations subjected to random drift. They also observed abiphasic dynamics in which, after an initial transient phase,a stationary state was reached. That compensatory mutationsare far more frequent than back mutations has been directlydemonstrated experimentally by determining the entire genomicnucleotide sequences of FMDV produced within individual plaqueswithout any biological amplification (27). A similar absenceof back mutations was found in the process of fitness gain ofFMDV clones upon large population passages (1, 26). The molecularbasis for fitness increase by compensatory mutations includesrestoration of secondary and higher-order RNA structures inregulatory elements and recovery of catalytic activities inviral enzymes, among others (14). Even in models that did notincorporate the occurrence of beneficial mutations, the predictedspeed of the ratchet was higher when the number of deleteriousmutations accumulated in a population was low (35). When thenumber of deleterious mutations reached a certain value, thespeed of the ratchet could be dramatically decreased throughepistatic effects. In yet another theoretical model, it hasbeen recently shown that the time between successive clicksof the ratchet (corresponding to the total elimination of thefittest type) grew exponentially with any additional mutation(8). In the latter model, despite the fact that the system neverreached a truly stationary state, the ratchet was, in practice,arrested.

Kondrashov (35) discussed the case of truncation selection (anextreme form of epistasis), which is directly comparable toour model in the marginal case where beneficial mutations areabsent (q = 0). Indeed, if the fitness of a population takesa zero value when the number of mutations exceeds a threshold,the population reaches a "stationary" state where all individualshave the same positive minimum fitness level and have accumulatedin their genome exactly the maximum number of mutations compatiblewith viability. The population sits then precisely at the extinctionthreshold with no diversity in the system. Consequently, underthese conditions there is no possibility of fitness recovery.This threshold would be represented in our model by the minimumallowed fitness, thus mimicking a sort of truncation in thesense of the model proposed by Kondrashov (35). However, assoon as q is set to a positive value, the following effects,which have been indeed observed in experimental settings, areobtained: (i) the stationary state is not at the minimum valueof fitness; (ii) occasionally, the whole population can attainstates of higher fitness; and (iii) states with low fitnesscan be reversed through large population passages.

The model predicts that, in the case of HIV infections, low-fitnessvirus could be endowed with mechanisms to elude extinction.Prolonged survival of HIV could occur despite remarkable fitnessdecreases associated with incorporation of mutations that conferresistance to antiretroviral inhibitors (4, 42) and the effectof fitness decrease in delaying disease progression (49) anddespite reductions in population size following highly activeantiretroviral therapy (reviewed in reference 9).

There are ways, other than consecutive plaque transfers, topush a viral population toward accumulation of deleterious mutations.Among them, the use of drugs that increase the mutation frequencyis of special relevance (14, 34, 51). The use of mutagenic agentseither alone or in combination with antiviral inhibitors candrive viral populations to extinction (10, 36, 47). Our numericalmodel predicts that an increase in the rate of deleterious mutations(assumed to be directly related to the total mutation frequency)will drive the population to a stationary state with a loweraverage fitness level. This suggests that a high-enough deleteriousmutation rate could push the population toward extinction, sinceall the individual genomes would be eliminated due to the negativeselection. It is very intriguing how some organisms or simplereplicons such as viruses have evolutionarily selected for thereplication of their genomes an average mutation frequency whichallows them to adapt rapidly to environmental changes whileevading extinction despite the likely occurrence of bottleneckevents in the course of infections within hosts and in the processof viral transmissions between infected and susceptible hosts(29).

Both the biphasic fitness evolution accompanying serial plaquetransfers and the effect of transmission size and initial fitnesson fitness variations predicted by the numerical model describedhere are in complete agreement with experimental results (27,44). Such an agreement constitutes a proof of the validity ofour model and of the dynamics predicted at very high passagenumber, under conditions not yet explored in laboratory experiments.In particular, the model encourages additional experiments tostudy the molecular basis of long-term fitness stability uponmany additional plaque-to-plaque transfers, despite continuinghigh mutation rates. This equilibrium state offers an interestingcounterpart to the population equilibrium (constancy of consensusor average nucleotide sequence despite a complex and dynamicmutant spectrum) attained after many large population passages(16, 55). It would be extremely informative for an understandingof quasispecies dynamics to compare the composition of mutantspectra in low-fitness and in high-fitness equilibrium states.

ACKNOWLEDGMENTS

We are indebted to J. Pérez-Mercader for promoting interdisciplinaryprojects at CAB and F. Morán for valuable suggestions.

Work at CAB was supported by grants from INTA and CAM, and workat CBMSO was supported by grants PM 97-0060-C02-01 and BMC 2001-1823-C02-01and an institutional grant from the Fundación RamónAreces.

FOOTNOTES

* Corresponding author. Mailing address: Centro de Biología Molecular "Severo Ochoa" (CSIC-UAM), Universidad Autónoma de Madrid, Cantoblanco, 28049 Madrid, Spain. Phone: 34-91 3978485. Fax: 34-91 3974799. E-mail: edomingo{at}cbm.uam.es.

REFERENCES

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