The Fittest versus the Flattest: Experimental Confirmation of the Quasispecies Effect with Subviral Pathogens

The “survival of the fittest” is the paradigm of Darwinian evolution in which the best-adapted replicators are favored by natural selection. However, at high mutation rates, the fittest organisms are not necessarily the fastest replicators but rather are those that show the greatest robustness against deleterious mutational effects, even at the cost of a low replication rate. This scenario, dubbed the “survival of the flattest”, has so far only been shown to operate in digital organisms. We show that “survival of the flattest” can also occur in biological entities by analyzing the outcome of competition between two viroid species coinfecting the same plant. Under optimal growth conditions, a viroid species characterized by fast population growth and genetic homogeneity outcompeted a viroid species with slow population growth and a high degree of variation. In contrast, the slow-growth species was able to outcompete the fast species when the mutation rate was increased. These experimental results were supported by an in silico model of competing viroid quasispecies.


Introduction
The two most basic processes of evolution are mutation and selection. In the simplest Darwinian paradigm, natural selection acts on existing genetic variation and favors those genotypes with the higher fitness. High fitness is usually, but not always, associated with fast replication, but when the mutation rate is so high that each newly generated individual carries genetic defects, fitness can also be maximized by reducing the impact of these mutations on an individual's phenotype. Therefore, the selective advantage of genetically robust systems is their decreased susceptibility to deleterious mutations, regardless of their replication rate. Whether robustness (i.e., the reduced sensitivity of phenotypes to perturbations) is an evolved property or is intrinsic to genetic systems is largely unknown, because the mechanistic basis for robustness would depend on the peculiarities of each system. One of the simplest situations in which mutational robustness evolves at the population level is represented by the quasispecies model of molecular evolution [1][2][3][4]. According to this model, selection would maximize the average replication rate of the swarm of genotypes interconnected by mutation rather than favoring the genotype with the highest replication rate [1][2][3][4]. Hence, mutation acts as a selective agent and shapes the genome in a manner that causes the entire quasispecies to become robust against mutations. Thus, in a highly mutagenic environment, a quasispecies occupying a low but flat region in the fitness landscape should outcompete a quasispecies located at a higher but narrower fitness peak when most of its surrounding mutants are unfit [4][5][6]. This phenomenon has been called the quasispecies effect or, more recently, the ''survival of the flattest'' in clear reference to Darwin's ''survival of the fittest'' [7,8].
Despite the attractiveness of the survival of the flattest, empirical evidence directly supporting this theory has so far been restricted to the work of Wilke et al. with digital organisms [7] and of Wilke in simulated RNA evolution [9]. Here, we use an experimental system very well-suited for testing the applicability of the hypothesis to biological entities: two viroid species that infect the same host. Viroids are subviral plant pathogens whose genomes are composed of a small (246-401 nucleotides long) single-stranded circular RNA molecule that does not encode any protein but is able to replicate in susceptible host plants [10,11]. A very structured and characteristic RNA folding pattern represents the only ''phenotype'' of viroids. Rod-like structures are typical for the family Pospiviroidae, whereas more branched structures are typical for the family Avsunviroidae.
Twenty-five of the 29 known viroid species belong to the family Pospiviroidae (named after Potato spindle tuber viroid, the type species of the family). All of them contain a central conserved region, and depending on the degree of similarity within this region, members of the family are assigned to five different genera. Pospiviroidae replicate and accumulate in the nucleus [10,11]. The other four known viroids form the family Avsunviroidae (named after Avocado sunblotch viroid, the type species of the family). Avsunviroidae lack the characteristic structural motifs of the Pospiviroidae and contain hammerhead ribozymes. Apart from the common hammerhead structures, sequence similarities among Avsunviroidae are remarkably low. Avsunviroidae replicate and accumulate in chloroplasts [10,11]. Although viroids require cellular factors to complete their infectious cycle, Avsunviroidae exhibit ribozyme activities that self-process multimeric replicative intermediates [10].
The two viroid species chosen for this study were Chrysanthemum stunt pospiviroid (CSVd) [12] and Chrysanthemum chlorotic mottle avsunviroid (CChMVd) [13]. This choice was made based upon four biological properties. (i) In plants initially inoculated with equivalent amounts of each viroid and for which systemic infection was established for an extended period, the concentration of CChMVd per gram of fresh plant tissue was ;20 times lower than for CSVd (Table  1), suggesting a lower net population growth rate for CChMVd. (ii) In contrast, the genetic variability of the CChMVd quasispecies was much larger than for the CSVd quasispecies by all indexes examined (Table 1). (iii) Both viroid species invade the whole plant, and the presence of several Avsunviroidae and Pospiviroidae in the same cell types of infected leaves has been confirmed by in situ hybridization experiments [14][15][16], thus creating conditions that allow intracellular competition for resources. (iv) In silico, the neutral neighborhood (i.e., the fraction of all possible one-error mutants, including deletions, that do not change the minimum free energy secondary structure) for the CChMVd molecule is ;2 times larger than for the CSVd molecule [17][18][19] (Table 1). Consistent with this, sequencing of multiple clones of both viroids from systemically infected plants revealed that CChMVd quasispecies were composed of molecules more diverse in folding stability (ratio of standard deviations for minimum free energies: 3.234) and shape [20] (ratio of standard deviations for differences in shape: 27.462) than CSVd quasispecies (Table 1). Therefore, CChMVd quasispecies grow slowly, are genetically heterogeneous, and exhibit a remarkable diversity of RNA secondary structures. In contrast, CSVd quasispecies grow rapidly and are genetically and structurally homogeneous. According to the survival of the flattest effect, CSVd should outcompete CChMVd at low mutation rates, whereas CChMVd should be superior at high mutation rates.

Results/Discussion Increasing the Mutation Rate Affects the Outcome of the Competition between CSVd and CChMVd
To directly test the survival-of-the-flattest phenomenon, chrysanthemum plants (Dendranthema grandiflora Tzvelev. cv ''Bonnie Jean'') were grafted with scions taken from donor plants singly infected with CChMVd or CSVd. Then, 2 wk after grafting, the presence of both viroids was confirmed by Northern blot analysis. Forty-two cuttings from a coinfected plant were planted into individual pots. After rooting, half of the plants were moved into a growth chamber (24 8C and a 16-h light period) and the other half were moved into a second chamber (same growth conditions) in which they were irradiated 10 min/d with an ultraviolet C light (UVC) germicidal lamp (Phillips G36T8; maximal output at 253.7 nm; dose 2 J/cm 2 ). The negative impact of UVC radiation on the in vivo replication and accumulation of RNA viruses (e.g., [21][22][23]) and viroids [24] has been known for several decades. UVC irradiation of RNA results in a variety of products, including uridine photohydrates and pyrimidine photodimers [25,26]. Uridine photohydrates may block translation but also miscode for cytidine during the synthesis of progeny RNA [27]. Molecules carrying pyrimidine cyclobutane photodimers between adjacent residues or cross-linked nonadjacent residues produce abortive RNA synthesis when used as templates. In addition, UVC radiation generates reactive oxygen species that may produce more than 35 different base modifications [28]. The UVC daily dose used in this experiment was in the same order of magnitude as that required for inducing in vitro and in vivo intramolecular cross-linking in viroids from both families [29,30], while still minimizing its effect on the growth of the host plants.
The first set of plants represents the control for competition under normal (low mutation rate) environmental conditions, whereas the second represents the competition under environment-induced mutagenic conditions. Two (n ¼ 3), four (n ¼ 6), and six (n ¼ 12) weeks after initiation of the experiment, n plants from each treatment regime were taken and the proportion of both viroids in each sample was estimated by quantitative Northern blot using 32 P-labeledspecific riboprobes. Figure 1 shows that a UVC-induced increase in mutation rate affects the outcome of the competition between CChMVd and CSVd (t-test, p ¼ 0.002). Under unmanipulated (i.e., low mutation rate) conditions, the median ratio CChMVd:CSVd significantly decreased as CSVd outcompeted CChMVd (t-test, p ¼ 0.011). The negative slope of the log regression on the median values, À0.086 6 0.019, represents a measure of the selective disadvantage of CChMVd relative to CSVd. This ;9% per week selective disadvantage can easily be explained as a consequence of CChMVd's slower growth rate, and is in excellent agreement with the Darwinian survival-of-the-fittest paradigm. In contrast, when the mutation rate was artificially increased by UVC, the competition was completely different, and the faster replicator CSVd was no longer able to outcompete the more robust replicator CChMVd, as predicted by the survival-

Synopsis
Darwin's ''survival of the fittest'' suggests that faster replicators are able to outcompete slower ones. However, when mutation, unavoidably associated with genome replication, is incorporated into the picture, the situation becomes a bit more complicated. At a high mutation rate, being the faster replicator may not always be the best option; in fact, being the more robust against the pernicious effect of mutation may be a better option. If a tradeoff exists between mutational robustness and replication rate-for example, because faster polymerases are more prone to mistakes than slower ones-then selection may favor an organism to replicate faster or to be more robust, but not both at the same time. At a low mutation rate, a faster replicator would displace a robust one. However, beyond a critical mutation rate, the slower replicator should outcompete the faster replicator. This phenomenon is known as the ''survival of the flattest''. Here, the authors have confirmed this prediction using a pair of subviral plant pathogens (viroids) competing under normal and mutagenic conditions. of-the-flattest effect. The slope of the log regression (0.017 6 0.033) was slightly, although non-significantly (t-test, p ¼ 0.622), positive, suggesting that the competitive advantage of CSVd vanished as a consequence of the 2-fold larger mutational neutral neighborhood surrounding CChMVd's optimum genotype.

The Observations Cannot Be Explained by UVC-Induced Differences in Plant Physiology
It was necessary to exclude the possibility that the above observations were driven primarily by UVC-induced differences in plant responses to viroid infection (e.g., UVC light induction of SOS-like functions that disproportionately affected CSVd replication) rather than, as we hypothesized, determined by the competition dynamics between both viroids. To this end, we analyzed plants singly infected with each viroid that had been treated in exactly the same manner as the coinfected plants. On average, no compelling differences were found between samples taken after 4 wk and 6 wk (test of covariable: F 1,35 ¼ 0.418, p ¼ 0.522), indicating that viroid concentrations were in steady state density after 4 wk, and, as expected, different for each viroid (test of viroid species factor: F 1,35 ¼ 600.571, p , 0.001). The UVC treatment negatively impacted the accumulation of both viroids. Indeed, treated plants carried, on average, 23.81% fewer viroid RNA molecules than the control plants (test of treatment factor: F 1,35 ¼ 12.869, p ¼ 0.001). However, this negative effect of UVC light on viroid accumulation during single infections was the same for both viroids (test of the interaction term: F 1,35 ¼ 2.245, p ¼ 0.143). Nevertheless, this is a negative result, and the objection can be raised that our experiment lacked sufficient power to reject the null hypothesis of no differential effect of UVC radiation on each viroid's accumulation. Statistical power reflects several factors, including sample size and the ratio of signal to noise. Computation of variance components [31] indicates that the error variance due to imprecision in measuring viroid concentration (s 2 ¼ 0.141) only represents 5.98% of total variance. Thus, the negative result cannot be entirely due to noisy measurements. A second and more direct approach to the statistical power of the test of the interaction term is to compute the confidence interval for the F ratio test statistic and then estimate the significance level for its upper 95% limit (the worst-case value). According to Tukey's jackknife method [31], the 95% confidence interval for the test statistic was À3.693 F 1,35 4.124. Hence, in the worst case, the probability of accepting the null hypothesis of equal effects of UVC radiation on the accumulation of CSVd and CChMVd as actually being false is only p ¼ 0.050. All in all, any change in plant physiology associated with the mutagenic treatment did not differentially impact the accumulation of each viroid. Therefore, we conclude that the outcome of the competition experiments run under mutagenic conditions is most likely due to the survival-of-the-flattest effect rather than to viroidspecific interactions with plant factors influenced by UVC irradiation. However, competition experiments in some cases may magnify differences in viral fitness that were undetectable when replication rate was the only measurable parameter (e.g., by one-step growth curves). As such, it may be possible that UVC induced changes in plant physiology that had a minor effect on CSVd replication and were undetectable with the power of our experiments; however, these changes became important only during competition against CChMVd. Although certainly possible, the above power analyses leave little room for this possibility.

Characterization of Genetic Variability
To better understand the effect of the mutagenic and control treatments on the genetic composition of CChMVd and CSVd quasispecies, we randomly picked three plants from each treatment after 6 wk and cloned and sequenced 20 molecules from each viroid per plant. First, we confirmed the mutagenic effect of UVC radiation. If UVC radiation increases genetic variability, then it is expected that the number of new haplotypes (i.e., those that were not detected in the coinfected plants prior to the mutagenic treatment) in the irradiated plants would be larger than in the nonirradiated plants. When this calculation was done for CSVd, the average frequency of new haplotypes across nonirradiated plants (Dataset S5) was 66.87% (i.e., approximately 1/3 of the haplotypes were already detected in the ancestral population), but increased to 92.32% in irradiated plants (Dataset S6) (i.e., only 7.68% of identified haplotypes were detected in the ancestral population). Therefore, there are 38.6% more new haplotypes in the irradiated plants than in the control ones, the difference being statistically significant (t 4 ¼ 3.872, p ¼ 0.018). The picture for CChMVd is slightly different. None of the haplotypes present in the ancestral population was detected in the evolved ones; thus, both UVCtreated (Dataset S3) and non-treated (Dataset S2) CChMVd populations were constituted by newly created haplotypes. This is not surprising given the already high level of diversity in CChMVd prior to the competition experiment. Second, we analyzed the genetic diversity present in each plant. To do so, the haplotype diversity and the average number of nucleotide differences were computed. Diversity data from each viroid were compared using model II nested analysis of variance in which the ''plant'' factor was nested within ''treatment''. Both factors were treated as random factors. Figure 2 shows the averages of these two measures across plants. On the one hand, the survival-of-the-flattest effect predicts that a robust organism replicating under mutagenic conditions would increase its genetic variability without noticeably affecting its fitness. In other words, a larger genetic variability is expected for CChMVd under UVC than under control conditions. Although the differences were not statistically significant, the change in the data goes in the expected direction ( Figure 2). CChMVd quasispecies replicating under UVC contained, on average, 0.8% more haplotypes and 30.3% more nucleotide differences than CChMVd quasispecies replicating under non-mutagenic conditions. On the other hand, the hypothesis predicts the opposite effect for a non-robust organism, such that the extrinsic increase in mutation rate would produce very low-quality genotypes (including lethal ones) that compete poorly against robust organisms and therefore would be quickly eliminated from the population. Only those molecules preserving a sequence close to the wild-type, which rapidly becomes a minority, will be capable of surviving. Hence, a reduction in the amount of viable (and therefore detectable) genetic variation within CSVd quasispecies is expected under UVC conditions. Indeed, this is the pattern observed for CSVd ( Figure 2). On average, CSVd quasispecies that evolved at a high mutation rate contained 24.9% fewer haplotypes than control populations (test of the UVC effect; p ¼ 0.009) and with 30.3% fewer nucleotide differences (p , 0.001).

Simulation Analysis and Results
To support the above interpretation, we simulated two populations of digital viroids (bit strings) replicating, mutating, and competing on a given landscape at given mutation rates. The fitness of each competing population was modeled by a multiplicative decaying function f(k) of the number of mutations k. The sharpness or flatness of the landscape was controlled by a single parameter s (small for flat peaks and large for sharp peaks). The previously mentioned nonviability for highly mutated CSVd genomes was incorporated by the cutoff condition f(k) ¼ 0 if k . k c . Because little is known about the exact parameters that might fit the experimental results, we performed a search of parameter combinations such that they were consistent with the experimental observations. The algorithm systematically searched the parameter space defined by fs CSVd , s CChMVd , l, l UVC , k c g, where l and l UVC are the mutation rates under control and UVC conditions, respectively. The target is defined in terms of minimizing the distance between the number of nucleotide differences found in the in planta experiments and those generated by the in silico model runs. The size m of the bit strings was fixed to m ¼ 64 and initial populations of N ¼ 2,000 bit strings of each class were used. After 40 generations, 20 bit strings of each class were randomly sampled and the average number of differences (the Hamming distance, D H ) calculated over five independent runs. If the survival-of-the-flattest effect is at work, the average fitness of the digital-CSVd population should be smaller than the average fitness of the digital-CChMVd  population after some critical mutation rate, l crit , is exceeded. Figure 3 summarizes the results of these simulations. The outcome of the in silico competition experiments is shown in Figure 3A for the best-fitting combination of parameters (see the Figure 3 legend for estimated values). Results perfectly match those observed in planta for a 4-fold increase in mutation rate and a mutational load cutoff for CSVd of three mutations (regression of observed to simulated data: R 2 ¼ 0.995, p ¼ 0.003). Figure 3B illustrates the changes in genetic diversity induced by this 4-fold increase in mutation rate for both digital viroids. In silico results are consistent with the in planta observations: digital-CChMVd populations were 38.5% more diverse after the mutation rate increase. The situation for digital-CSVd populations replicating at a high mutation rate is a bit more complex and depends on whether or not lethal genotypes are taken into consideration when computing the average D H between digital genomes. Indeed, the lethality fraction (i.e., the number of genomes carrying more than three substitutions) was as large as 66.5%. When lethal genotypes were incorporated into the computation, digital-CSVd population diversity also increased to 45.4%. However, if lethals were not considered for calculating the average D H , digital-CSVd populations were 51.4% less variable than nonmutagenized digital-CSVd populations, which is in agreement with the in planta observations. Thus, we conclude that the apparent reduction in genetic diversity experimentally observed for CSVd populations competing at a high mutation rate is entirely explained by the existence of a large fraction of lethal genotypes that bring about the reversal of fortune in the survival-of-the-flattest effect. In turn, these lethal genotypes cannot be detected by cloning and sequencing methods in the in vivo experiments.
As predicted from the survival-of-the-flattest hypothesis, a crossing between average fitnesses takes place with increasing  Figure 3C depicts the optimal solution found with the parameter search algorithm. Finally, the qualitative interpretation of our results is displayed in Figure 3D. Below the critical mutation rate, the two populations appear close to their corresponding peaks. At high mutation rates, whereas the flattest population spreads farther across its fitness landscape, the fittest population only spreads until it reaches the mutational cutoff (dashed line) and surviving strings are scattered around it (upper row). Those mutant sequences having a larger number of mutations than the cutoff are unviable (small white balls).

Concluding Remarks
We have shown that under high mutation rate conditions, a slowly replicating organism can easily displace a faster replicating one, provided that the former is supported by a neutral neighborhood capable of buffering the increasing mutational load; in demonstrating this we have thus provided empirical evidence for the survival of the flattest effect in a biological system [6][7][8]. In this case, a 20-fold difference in replication efficiency was overcome by only a 2-fold increase in the neutral neighborhood. This observation also supports the existence of a tradeoff between replication rate and mutational robustness [4,6]. Finally, these findings also clarify the importance of the mutational swarm, as described by the quasispecies model [1][2][3][4], for the evolution of RNA replicons. In recent years doubts have been expressed about the applicability of the quasispecies model to viral evolution [32,33]. Detractors have argued that evidence supporting the quasispecies model was weak and that clear evidence for the action of selection on mutational robustness or for a faster replicator being outcompeted by a slower one was missing. Here, we have provided such evidence for subviral plant pathogens.

Materials and Methods
RNA purification, quantification, and sequencing. Tissue from viroid-infected chrysanthemums was homogenized, and viroid RNA preparations were obtained by chromatography on nonionic cellulose [34]. RNA preparations were separated by denaturing PAGE in 5% gels containing 8 M urea in TBE buffer [35], electroblotted to nylon membranes, and hybridized with viroid-specific 32 P-labeled riboprobes at 70 8C in the presence of 50% formamide [36]. Hybridization signals were quantified using a Fuji BAS1500 bioimage analyzer (http://www.fujifilm.com). For viroid cloning and sequencing, viroid RNAs were RT-PCR-amplified with SuperScript III reverse transcriptase (Invitrogen, http://www.invitrogen.com) and Pfu DNA polymerase (Stratagene, http://www.stratagene.com) by using CChMVd-specific (complementary: 59-GACCTCTTGGGGGTTT-CAAACCC-39 and homologous: 59-GGCACCTGATGTCGGTGTCCT-G A T G -3 9) a n d C S V d -s p e c i fi c ( c o m p l e m e n t a r y : 5 9-GGGGATCCCTGAAGGACTTCT-39 and homologous: 59-GGGGAAACCTGGAGGAAG-39) primers. The amplified cDNAs were ligated into a SmaI-opened pUC18 plasmid and used to transform Escherichia coli DH5a. The cDNAs from the resulting recombinant plasmids were sequenced with an ABI Prism 3100 Genetic Analyzer (Applied Biosystems, http://www.appliedbiosystems.com). All sequences data are provided in MSF format in Datasets S1-S6. Dataset S1 contains the ancestral sequences for CChMVd, whereas Datasets S2 and S3 contain CChMVd sequences from control plants and UVCirradiated plants, respectively. Dataset S4 contains the ancestral sequences for CSVd, and Datasets S5 and S6 the CSVd sequences from control and UVC-irradiated plants, respectively.
Effect of UVC radiation on the accumulation of each viroid. To assess whether the mutagenic treatment differentially affected the accumulation of each viroid species, 20 chrysanthemums were singly inoculated with CSVd and 20 more with CChMVd. Half of the plants were placed at mutagenic conditions and half were kept under control conditions. Then, 4 wk and 6 wk after inoculation, tissue was homogenized and the concentration of each viroid quantified by Northern blot analysis as described above. Upon log transformation, the data were analyzed by means of a model II two-way analysis of variance using time as covariable [31].
In silico mutational robustness analysis. For each viroid, we measured mutational neutrality, which is the fraction of all possible point mutations that do not disturb the folding of the unmutated RNA molecule. A molecule of length l will have 4l one-error mutants (including one-nucleotide deletions). For each one of the 4l mutants, we numerically evaluated its minimum free energy secondary structure and compared it with that of the unmutated genotype. Folding and comparison among structures was done using ViennaR-NA package version 1.4 [20].
Statistical analysis of the competition data. For each plant sample, the ratio between CChMVd and CSVd was estimated by Northern blot hybridization analysis using equal counts of specific 32 P-labeled riboprobes. Then, for each time point shown in Figure 1, we computed the median ratio (R t ) instead of the mean to minimize the effect of outliers. The standard error of the median was obtained by Tukey's jackknife method [31]. Then, medians were fitted to the non-linear model lnR t ¼ lnR 0 þ (a þ d a M)t, where a represents the common slope and d a accounts for differences in the treatment effect on the slope (M ¼ 0 for control treatment and M ¼ 1 for mutagenic treatment). A d a 6 ¼ 0 value indicates a significant treatment effect. In Figure 1, the fit of the model was highly significant (R 2 ¼ 0.9541, p , 0.001). The least squares estimates of the parameters were lnR 0 ¼ À4.958 6 0.077 (t-test, p , 0.001), a ¼À0.086 6 0.019 (t-test, p ¼ 0.011), and d a ¼ 0.104 6 0.014 (t-test, p ¼ 0.002).
In silico competition model. The population of competing viroids was simulated using a binary bit string model [37], where each digital viroid was represented by a binary string S i ¼ (S i1 , . . ., S im ), where S ij 2f0, 1g, m is the genome length, and i ¼ 1, . . ., N, N being the maximum population size. The population started with a small sample of size N 0 , N of each competing viroid. Initial populations were sampled from two independent populations evolved to the stationary state under control conditions. The other N À 2N 0 strings were empty. The fitness of a string S i , indicated as f(S i ), is a decreasing function of the number of mutations with respect to the master sequence, defined as the all-ones string. For a sequence at a Hamming distance of k mutations from the master sequence, fitness was computed using a multiplicative landscape [38]: where k ¼ m À P m l¼1 S il . The parameter s weights the relative decrease of fitness associated with mutations (i.e., the peak steepness). Digital-CSVd populations are expected to have a sharp peak, with a large s CSVd value and thus fitness rapidly decaying until reaching the cutoff k c, beyond which molecules are unable to replicate: if k , k c and zero otherwise. Digital-CChMVd populations inhabit a flat peak with s CChMVd , s CSVd ; thus, mutations have a much smaller effect on fitness. Each digital viroid can be degraded and removed with probability d ¼ 0.01. Each generation involves N independent individual updates in which each digital viroid is chosen to replicate with probability f(S i ) and each bit can mutate with probability l. Specifically, at each round of replication, every bit S ij in the newborn string can mutate to 1 À S ij with probability l. The presence of a survival-of-the-flattest effect can be predicted by looking at the equilibrium distributions of each competing population under varying mutation rates [8,39]. Specifically, for a given parameter combination, the average fitness, hf(s, l)i, of our digital populations will be hf ðs; lÞi ¼ 1 N PðS k Þ ð1 À sÞ k X j ð1 À sÞ j ; where P(S k ) represents the frequency of genotype S k in the population. If there is a fitness change at some given mutation rate, l crit , where the sign of hf(s 1 ,l)i À hf(s 2 ,l)i changes from positive (fittest PLoS Pathogens | www.plospathogens.org December 2006 | Volume 2 | Issue 12 | e136 wins) to negative (flattest wins), then a survival of the flattest scenario should be observed as this critical mutation rate is crossed. This criterion was used in searching for candidate solutions that consistently matched the experimental observations with the theoretical prediction.