Experimental evolution of UV resistance in a phage

Model 1. Faster evolutionary progress is achieved with greater killing—once resistance mutations are present

An idealized survival function of a non-growing viral population exposed to UV may be assumed to follow an exponential decay with time: S = e^−wt being the survival probability after t min of exposure (w > 0). Smaller values of w have higher survival rates, with w = 0 experiencing no death. Letting w represent the survival rate of the wild-type, μ the survival rate of a beneficial resistant mutant (hence μ < w), the mutant has a relative survival advantage of (1) $${\text{Ω}}_t=\frac{{\text{e}}^{-\mu t}}{{\text{e}}^{-wt}}={\text{e}}^{(w-\mu )t},$$ increasing without bound over time. The longer the duration of exposure, t, the greater the relative survival advantage of the mutant. The expression in (1) is a ratio of the two (positive) fitnesses, and with the constraint μ < w, the ratio is bounded to lie between 1 and +∞, a value of 1 indicating equivalent survival of the two types. This expression is for deterministic changes in abundance, as if both wild-type and mutant are so numerous that stochastic effects can be ignored.

If at the outset, the ratio of mutant abundance to wild-type abundance is $\frac{n_{\mu }}{n_w}$, the ratio of abundance after one exposure of duration T will be (2) $$\frac{n_{\mu }}{n_w}{\text{e}}^{(w-\mu )T}.$$

Thus longer exposures will lead to greater increases in mutant frequency per cycle, so fewer cycles of longer exposure will be required to raise the mutant frequency to a desired level.

For our design of a 4-log wild-type kill over each of 30 cycles and with no adaptation to better survival, the cumulative killing would be 10⁻¹²⁰. (As each cycle of 10⁻⁴ kill was followed by amplification, the cumulative kill is the overall measure from 30 cycles and is not a measure of kill applied in a single episode.) For a mutant whose survival after exposure is double that of wild-type [Ω_T = 2], its cumulative kill would be 10⁻¹²⁰ × 2³⁰. From (2), and given an initial frequency of 10⁻⁵, the mutant would reach a frequency (proportion of the population) of 0.9999 if originating at cycle 1, reach a frequency of 0.91 if first arising immediately before cycle 11, and reach a frequency of 0.01 if first arising immediately before cycle 21. A mere doubling of survival would be difficult to detect in many assays, but the cumulative effect of several such mutations would be easier to demonstrate. If needed, a longer exposure could be used to assay viability than is used in the selection, increasing the quantitative impact of the survival difference in the assay.

Model 2. Greater killing risks extinguishing pre-existing mutants

The foregoing results assume large populations of both mutant and wild-type. Mutant abundance will often be low initially, so a long, lethal exposure risks killing all pre-existing beneficial mutants. If N_μ is the initial number of mutants before exposure (in the relevant volume), a lethal exposure of length T will leave an average of (3) $$N_{\mu }{\text{e}}^{-\mu T}$$ surviving mutants, independently of other genotypes in the culture. If the value of (3) is less than 1, there will be an average of less than one mutant remaining after exposure. For example, a mutant with fitness equivalent to wild-type (w), would survive the lethal phase (on average) only if it existed in at least 10,000 copies before exposure. With a 10-fold advantage over wild-type, it would need to be present in 1,000 copies. If no individuals with a particular mutation survive exposure, then that mutation will need to re-generate before it can possibly evolve to high frequency, and there will be less time for its ascent after it is re-introduced.

Any beneficial mutant that persists through the exposure bottleneck—or happens to be present at the end of the exposure phase because that is when it was generated—will then be amplified during the growth phase so that its numbers increase at least enough (on average) to survive the next cycle of killing. (This argument neglects any possible disadvantage during the growth phase.) So once a beneficial mutation survives the first exposure phase, it should progressively tend to escape extinction in subsequent cycles. The problem is achieving a sufficient initial abundance of the mutant so that it survives its first lethal exposure bottleneck.

One simple solution to the mutant extinction problem is merely to increase the pre-exposure population size. If mutant frequency remains unaltered with increasing population size and the same kill (duration of exposure) is maintained, then a larger initial population will allow more mutant individuals to survive the killing. The same effect is achieved by transferring a larger volume of the exposed pool (e.g. as if we had transferred 1 mL instead of 0.1 mL). This approach will work up to the point that protocol constraints allow the entire surviving population to be carried forward into the next cycle; if the surviving population is so large that it must be thinned to accommodate the limitations of equipment, the benefit of increasing pre-exposure population size may disappear.

Model 3. Mutations generated by the lethal agent

The preceding models have assumed mutations are pre-existing. UV is mutagenic and so may generate mutations that improve resistance to UV. As UV also has lethal effects, longer exposures mean fewer total survivors but more beneficial mutations per survivor. Letting β be the beneficial mutation rate coefficient during exposure, the number of surviving individuals in a starting population of size N that acquire a beneficial mutation approximately follows (4) $$N{\text{e}}^{-wt}\text{β}t$$ (for small βt; this approximation assumes that the new mutation does not convey a survival advantage in the generation in which it arises and that the lethal effects of exposure are independent of beneficial mutations). This formula reflects both an increased appearance of beneficial mutations with longer exposures (βt) as well as a decreased survival rate from longer exposures (e^−wt). This quantity is maximized over t at wt = 1, hence an exposure that kills 63% of the population, or a survival of 0.37—a low level of killing (Mundry & Gierer, 1958; Gierer & Mundry, 1958; Bull, 2008). Thus, independently of the beneficial mutation rate, the highest success rate in acquiring a surviving beneficial mutation is with a relatively low kill rate.

In many protocols, a practical problem stemming from such mild killing is that it generates weak selection: e^{(w − μ)t} in (1) is very near 1.0. For example, the per cycle level of killing used here (10⁻⁴) was more than three orders of magnitude higher than 0.37 (10^−0.434). Thirty cycles of a 10⁻⁴ survival is a kill equivalent to 276 cycles of a 0.37 survival per cycle. Although a survival fraction of 10⁻⁴ may be harsh on pre-existing mutants, conducting the equivalent total selection for a survival rate of 0.37 becomes tedious without automation. A more relevant question is then whether the number of surviving beneficial mutants generated by UV in (4) is expected to exceed 1 after exposure. If even a few beneficial mutants persist, then a high killing reaps the benefits of rapid evolution without extinguishing the mutational input needed for evolution.

Expression (4) may be interpreted as a product: the number of survivors times the genomic beneficial mutation rate. In our study, the first factor approached 10⁴ in each cycle, so if the genomic beneficial mutation rate was 10⁻⁵ or higher, then the first 10 cycles of exposure would be expected to generate at least a few such mutations in the survivors. We do not know the beneficial mutation rate for any length of exposure, but there are indicators of the T7 genomic mutation rate under some mutagenic conditions. For T7 grown in a high concentration of the mutagen nitrosoguanidine (not lethal to the free phage), approximately four viable mutations are produced per genome per cell infection (Springman et al., 2010). For the mutagen hydroxylamine used to kill down to a survival between 10⁻³–10⁻⁴, the genomic mutation rate is up to eight mutations per genome (Bull et al., 2013). The T7 genome has 4 × 10⁴ nucleotide sites, so if a mutation at even one site was beneficial, a rate of four mutations per genome would generate a genome with a beneficial mutation at least once in 10⁴ genomes (this calculation neglects mutational biases and it further combines different types of mutations at a single nucleotide site). The fitness effects of individual random mutations have been estimated in phages, with 13 of 45 randomized point mutations being measured as beneficial in the DNA phage ϕX174 (although the effects of most of the 13 were not significantly different from 0 (Domingo-Calap, Cuevas & Sanjuán, 2009)). How closely these calculations apply to UV mutagenesis is unknown, but they suggest that the protocol may well have introduced enough mutations to allow adaptive evolution—if mutations with a benefit exist.

Integrating the models

The three models apply to different aspects of the protocol. ‘Model 1’ describes the magnitude of selection as a function of exposure. The model applies once mutants have risen to an abundance allowing them to escape stochastic loss and also applies to protocols in which several different phage types are grown to high numbers and mixed before exposure/selection. ‘Model 2’ is merely a deterministic description of the number of individuals expected to survive an exposure, given an initial abundance and fitness. Since the initial number of mutations will often be unknown, its purpose is primarily qualitative—a caution against the overuse of selection and to highlight the possibility than a highly lethal exposure may kill all rare mutants. Model 3 provides insight to the relationship between kill and the introduction of beneficial mutations, specifically when the lethal agent is also the source of new mutations. The optimal exposure has the general property of being independent of the actual beneficial mutation rate. If the optimal exposure is applied successively to each cycle, then Model 3 accrues to the generation of mutations within each cycle, whereas Models 1 and 2 accrue to the selection and survival of mutants generated in previous cycles.

The calculations in these models were developed after the experimental selection was completed. The design had been chosen to impose strong selection, and the original intent was to limit the study to 10 cycles—for which any detectable progress would require strong selection. However, upon analysis at 11 cycles, it was decided to extend the study ∼20 additional cycles. A 30 cycle experiment would have afforded a less intense selection and greater propensity for beneficial mutation accumulation. Nonetheless, UV resistance was obtained under the current design, indicating that at least some beneficial mutations survived the UV-induced bottlenecks.

Strains

IJ1133 [Escherichia coli K-12, F⁻ ΔlacX74 thi Δ(mcrC- mrr)102::Tn10] was the host used for phage growth and non-selective plating. IJ512K [K-12 ΔlacX74 supE44 galK2 galT22 mcrA rfbD1 mcrB1 hsdS3/F′ lac Kan-R] was the F-bearing host used to selectively plate phage carrying T3 gene 1.2. IJ1126 [K-12 recB21 recC22 sbcA5 endA gal thi Su⁺ Δ(mcrC- mrr)102::Tn10] was the host used for transfection of T7 DNA (Heineman, Bull & Molineux, 2009). Phage Δ16 and complementing plasmids were reported elsewhere (Chang, Kemp & Molineux, 2010).

An isolate of presumed wild-type T7 (T7⁺) was used to initiate the study. This phage was later found to carry two mutations differing from the ‘standard’ wild-type (Genbank V01146.1): 15094 G→T and 29258 A→G. A variant of T7⁺ (JB14-37) was created by recombination over plasmid pMK-RQ-T7trxAdspB to insert T3 gene 1.2 into and largely replacing T7 non-essential gene 3.8 (Schmerer et al., 2014). In contrast to T7⁺, JB14-37 is able to plate on IJ512K.

Recombinant genomes were created by restriction digestion of genomes with BstEII, which cuts T7 at wild-type base 20066. Other enzymes whose sites were limited to either the left or right fragment were used in conjunction with BstEII, so that only one of the two halves remained intact. Digests were precipitated and, without gel purification, cognate fragments were ligated and transfected into IJ1126 and plated.

Selection protocol

A single phage line was subjected to 30 cycles of exposure, each cycle followed by non-selective amplification. Host IJ1133 was used for amplification and most platings; for amplification, it was grown at 37 °C in minimal M9 glucose (0.2%) to approximately 10⁸ cells/mL, phage were added and the culture grown to lysis. The phage concentration in the lysate was typically 10⁸–10⁹ per mL. About 5 mL of lysate were then added to a polystyrene Petri dish and exposed to 302 nm UV for 120 s on the surface of a UVP® transilluminator (bulbs UVP 34-0042-01). For the initial phage, this exposure led to an approximately 4-log decline in viable phage, but the exposure was fixed to 120 s throughout regardless of possible evolutionary increases in survival. 0.1 mL of the survivors were added to a new culture of IJ1133, and the process repeated.

Fitness estimation

The value of Ω in (1) gives a relative survival benefit of one phage over another. (We omit time notation, assuming that all exposures are for the same length of time—2 m in this study.) We want to know its value; here Ω was estimated in two ways. Motivated by the definition $\text{Ω}=\frac{S_{\text{μ}}}{S_{wt}}$ (where S is survival, subscripted according to wild-type or mutant), one method simply calculated a ratio of observed survivals of each phage exposed separately of the other. The estimator of Ω replaces the true values with the estimated values (all estimated values are indicated with ^): $$\widehat{\text{Ω}}=\frac{{\widehat{S}}_{\mu }}{{\widehat{S}}_{wt}}.$$ Ŝ for a phage type is merely the ratio of phage density observed after exposure to phage density observed before exposure.

The second estimator relied on relative survival in a mixed stock of phage. To use this estimator, proportions of each type of phage are determined before and after UV exposure. Letting N be the initial density of the phage mix (with wild-type phage at a frequency of 1 − p in the mix) and K be the post-exposure density of the phage mix (with wild-type at a frequency of 1 − p′), the ratio (5) $$\frac{Kp\prime /K(\text{1}-p\prime )}{Np/N(\text{1}-p)}$$ is simply the ratio of numbers of each type of phage in the mix before and after exposure. Except for sampling error, (6) $$\frac{Kp\prime }{Np}={\text{e}}^{-\text{μ}T},$$ (7) $$\frac{K(\text{1}-p\prime )}{N(\text{1}-p)}={\text{e}}^{-wT},$$ so that the ratio in (5) is the empirical manifestation of (8) $$\frac{{\text{e}}^{-\text{μ}}}{{\text{e}}^{-w}}=\text{Ω\hspace{0.17em}\hspace{0.17em}}.$$

As (5) reduces to (9) $$\frac{p\prime /(\text{1}-p\prime )}{p/(\text{1}-p)},$$ Ω may be estimated without knowing N or K, merely from the proportions of each type of phage in the post-exposure sample and the proportions of each type of phage in the pre-exposure sample. In contrast to the first method of Ω estimation, here there is no need to know the absolute phage densities in either sample, only the proportions of each type. This method can be used to measure fitness of a single mutant genome compared to wild-type in the same sample but can also be extended to compare two genomes in different mixes, each compared to the same standard; in the latter case, the ratio of the two Ω values gives the Ω between the two genomes.

Statistics

Two tests of statistical significance were employed. One simply measured the phage titre for each of two types (X, Y) before and after UV exposure, (subscripts a and b indicating after and before, respectively). The ratios X_a/X_b and Y_a/Y_b are the respective survivals of each phage type, and if the survival rate of type X is the same as of type Y, the ratio (10) $$\frac{X_a/X_b}{Y_a/Y_b}=1,$$ hence (11) $$\text{log}(X_a)-\text{log}(X_b)+\text{log}(Y_b)-\text{log}(Y_a)=0.$$ With multiple, independent measures of the different survivals the logged values will be approximately normally distributed, and the left side of (11) provides a statistic that will follow a t-distribution with degrees of freedom equal to 4 less than the number of survival measures.

The preceding t-statistics require multiple, independent samples. An alternative approach to testing sampling distributions is to do so empirically, essentially by ‘bootstrapping.’ Thus, the distribution of phage type X in a sample of size N in which the observed number of type X is O_X may be simulated by drawing N independent, uniform random variables each with probability O_X/N. Any statistic that uses O_X may be reconstituted with the simulated numbers to obtain its distribution.

Genome sequences

Population sequences from cycles 11 and 30 were generated by MiSeq at the University of Texas GSAF. Average read depth was ∼4500X at cycle 11, ∼3000X at cycle 30. Fastq sequence files were analysed with breseq (Deatherage & Barrick, 2014); some statistics were obtained from a C program written to sort breseq output. Mutations whose frequencies were less that 0.001 were excluded from analysis, to reduce possible attribution of sequence error to mutation. Sequence of the initial T7 was considered to be wild-type (GenBank V01146.1) except possibly for the four high-frequency changes observed at cycle 11. The status of those mutations in the initial T7 was evaluated by Sanger sequences (or size) of PCR products over the relevant regions; two of the four were observed in the ancestor, as given in Table 1 below. Fastq files are deposited in the NCBI Sequence Read Archive (SRP142350).

UV resistance evolves

A single phage line was subjected to 30 cycles of UV exposure; survival improved significantly. The improved survival of the evolved phage (cycle 30) over the starting phage (Ω) was estimated in two ways, one comparing separate measures of absolute survivals between the initial and evolved phages, the other a relative measure using the change in proportion of the two phages in a mixed stock (see Methods; as all exposures were 2 m, the time subscript on Ω is omitted). Comparing absolute survivals, the evolved population exhibited a Ω = 45.1-fold improvement in survival (Fig. 1; this test was based on five independently exposed samples of wild-type and five of evolved virus, t(8) = 10.5, P < 0.001; survival data were converted to log₁₀ to estimate means and to conduct the statistical test; the mean log₁₀ difference was 1.65 ± 0.11).

Absolute survival calculations were based on platings of each stock, both before and after exposure. The plaque forming units are affected by several sources of error—intrinsic Poisson variation in phage per volume, variation in pipette volume, and chance effects in plaque initiation per phage that affects plating efficiency. A relative measure of change in survival was therefore also used to independently estimate the survival difference. This assay used a mix of the evolved phage and a derivative of a wild-type phage carrying a selectable marker (JB14-37; see Methods). The mixed sample was exposed to UV for a single cycle. Exposed and unexposed samples were separately plated on a permissive host and individual plaques then stabbed onto the restrictive host, yielding proportions of the evolved phage before and after irradiation. The change in proportion of the evolved phage gives its survival relative to the other phage in the mix. By this method, the relative advantage of the evolved line over wild-type was Ω = 57.4 (Fig. 1), significantly larger than 1 but compatible with the absolute fitness superiority estimate of 45.1: using the bootstrap test, the sample yielding Ω = 57.4 was found to generate a value of Ω = 45.1 or less in 25% of trials but a value of 1.0 or less in none of 2 × 10⁵ trials. (This assay was based on a single stock irradiated once for the treatment and not irradiated for the control, with a total of over 450 plaques assayed from each of the irradiated and non-irradiated populations.)

Population sequences reveal a few candidate resistance mutations

The population of T7 was sequenced after 11 and 30 cycles (Table 1). Two differences from the ancestor were at high frequency by cycle 11: a 2.1 kb deletion of the early region, as is typical in other adaptations of T7 (Studier et al., 1979; Cunningham et al., 1997), and a point mutation in gene 17 (35,095 A→G, N→D in codon 158). By cycle 30, those two mutations plus two additional high frequency changes were found, the latter both affecting gene 16. The deletion was an in-frame fusion of the first 53 codons of gene 0.3 with gene 1, encoding the RNA polymerase gene, but the RNA polymerase gene was truncated for its first 14 codons. T7 RNA polymerase is essential for phage growth, so transcription and other functions must have been retained in this fusion.

At cycle 11, many uncommon mutations were observed (mutations whose population frequencies were <5%). These mutations were found at nearly 11,000 sites in the ∼40 kb genome, and although individually rare, they were collectively so abundant—occurred at so many sites—that the average individual genome carried approximately 49. The dominant mutations were GC→TA transversions (80%), in contrast to expectation from repair of cyclobutane pyrimidine dimers or pyrimidine:pyrimidone 6,4, photoproducts (Karran & Brem, 2016; Schuch et al., 2017), or the domination by GC→AT mutations observed following nitrosoguanidine or hydroxylamine mutagenesis of T7 (Springman et al., 2010; Bull et al., 2013). Sequences from cycle 30 revealed a much lower level of uncommon mutations per genome (approximately 11), and the mutation spectrum was no longer dominated by GC→TA.

Because of the discrepancy between cycles 11 and 30, the rare mutations were characterized more fully. The modest difference in read depth between cycles 11 and 30 was one possible concern, so these new analyses forced a read depth of at least 1,500 per site. When requiring each mutation to have a minimum frequency of 0.001, the average mutation load per genome was 40.9 vs 6.0 (for cycle 11 and 30, respectively). Using a minimum mutation frequency of 0.005 (or 0.01), the corresponding numbers were 16.8 vs 1.1 (1.3 vs 0.8). Thus the overall load of mutations was from the low-frequency spectrum, chiefly frequencies less than 0.01, and the large difference between cycles 11 and 30 was not due to differences in the coverage.

The improved survival of the adapted populations is plausibly attributed to the high-frequency mutations, but the effect sizes may differ greatly. Recombinant genomes between the initial and evolved (cycle 30) populations were generated by reciprocal exchanges of BstEII fragments (which cuts the genome at 20066), separating the left-end deletion from the right end substitutions in 16 and 17; mutational status of the recombinants was verified by sequences of PCR fragments. UV sensitivity of recombinant isolates exhibited a significant Ω = 2.4 benefit of the ‘left end’ of the evolved genome, carrying the deletion, and a significant Ω = 21.2 benefit of the right side, carrying the gene 16 and 17 mutations (Fig. 1; for both tests, P < 10⁻⁴ that Ω ≤ 1 by bootstrap using the combined data). The product of benefit from both halves is approximately as expected for the total. As noted under Model 1, above, a mutant with a relative survival benefit of even two would be expected to rise to high frequency by cycle 30 but be barely detectable by cycle 11. As the deletion was virtually fixed by cycle 11, its advantage in UV protection is either higher than 2 in the presence of the 17 mutation (i.e. epistasis), or it has an advantage in the growth phase (as seen with an early-region deletion in another study using M9 media Springman et al., 2012).

We note that recombinants are clonal (isolated as plaques) and may thus carry some low-frequency mutations from the evolved population at cycle 30 (mutation status was confirmed for the high-frequency mutations by size or sequence of PCR products from the relevant regions but those methods would not have detected mutations in other parts of the genome). Any deleterious fitness effects of uncommon mutations were likely minor, as the phage population was subjected to several generations of liquid growth to generate a phage stock for DNA preparation; this growth phase would have purged strongly deleterious mutations.

Does the mechanism of genome entry explain the benefit?

At first glance, none of the changes makes sense for UV protection. For gp17 (tail fibre) it is not obvious how the mutation could improve survival—unless UV specifically destroyed the wild-type protein and thereby ravaged adsorption capacity. Indeed, UV (300–400 nm) fluxes have actually been shown to inactivate T7 by causing an adsorption defect (Hartman & Einsenstark, 1982). Alternatively, our experimental regime may have allowed adaptation of a tail fibre that then binds a UV-shielding agent such as cellular debris, but as the observed substitution lies within or near the tail-binding, rather than the cell-binding, domain this possibility seems unlikely.

One of the changes in gene 16 is plausibly protective, but only indirectly. The internal virion protein (gp16) has multiple functions, a critical one being in catalysing genome internalization (García & Molineux, 1996; Kemp, Gupta & Molineux, 2004; Chang, Kemp & Molineux, 2010). The wild-type phage genome enters the cell in three phases. The initial ∼1 kb enters by a proton motive force-dependent mechanism that involves both T7 gp16 and gp15 present in the mature virion (Chang, Kemp & Molineux, 2010); this process internalizes the three early major promoters for E. coli RNAP. Host-mediated transcription from these promoters then pulls the following ∼6 kb into the cell. T7 RNAP is encoded on this 6 kb and when synthesized internalizes the remainder of the genome via transcription from T7-specific promoters.

It is well established that cis–syn cyclobutane pyrimidine dimers, pyrimidine:pyrimidone 6,4, photoproducts, and other UV-induced DNA damage block transcription by E. coli and T7 RNAP when the lesions are present on the transcribed strand (Sonohara, Iwai & Kuraoka, 2015). However, the lesions have little to no effect when present on the non-template strand. Thus half of UV-induced DNA damage would be expected to interfere with or completely inhibit T7 genome internalization.

The biochemical mechanism of T7 gp15/gp16-dependent genome internalization is incompletely understood, although there is no evidence that it is strand or DNA sequence-dependent. However, the gp16-I754T mutation found in UV-resistant T7 has been shown to allow internalization of the entire genome in the absence of any transcription (García & Molineux, 1996; Struthers-Schlinke et al., 2000; Kemp, Gupta & Molineux, 2004). Thus the potential exists for a phage harboring gp16-I754T to completely internalize a UV-damaged genome where cellular processes might repair damage. The possible magnitude of any such benefit in the evolved phage is limited, of course, as the evolved phage survives over wild-type only by approximately 50 genomes in every 10,000 that die from UV (and over half of this effect is attributable to a deletion in the early region).

To test whether I754T might convey a large benefit, we took advantage of a T7 gene 16 deletion mutant (Δ16), which can be grown on hosts containing complementing plasmids (Chang, Kemp & Molineux, 2010). By growing Δ16 on a host that provides wild-type 16, or alternatively, on a host that provides the gp-I754T substitution, it is possible to generate T7 Δ16 phage differing only in the structural gp16. Each stock was mixed with a wild-type competitor carrying a T3 1.2 insert, the same wild-type competitor used in the experiments described above (JB14-37).

The relative changes in Δ16 frequency within each stock before and after UV exposure gives a survival measure of Δ16 relative to the competitor, and a comparison between the Δ16 grown on wild-type vs I754T gives the benefit of I754T. The data reveal a benefit of the Δ16 genome grown on either plasmid, with only a two-fold greater survival of being assembled with gp16-I754T over assembly with wild-type gp16 (Fig. 1; Table 2). Although both $\widehat{\text{Ω}}$ values are significantly greater than 1.0 (P < 10⁻⁴ by bootstrap tests), the difference in $\widehat{\text{Ω}}$ values is not significant (P ∼ 0.5 by the bootstrap test), nor does the two-fold extra benefit of gp16-I754T over gp16-wt begin to approach the 21-fold benefit observed for the right-end portion of the evolved genome. Thus, the gp16-I754T substitution does not appear to explain the survival benefit of the evolved phage.

The unexpected finding from this test is a large benefit—over 10-fold—of the 16 deletion when carrying a wild-type gp16 (Fig. 1; Table 2). By contrast, the early region deletion in the evolved phage was found to confer an approximately two-fold benefit. There is, of course, expected to be some benefit of the 16 deletion because it removes approximately 10% of the genome, and nearly all of the deleted region is essential—so the target size for UV-induced mutation is reduced. From a target-size effect alone, we would expect the survival benefit to be (12) $$\frac{{\text{e}}^{-0.9L}}{{\text{e}}^{-L}}={\text{e}}^{0.\text{1}L}.$$

For a wild-type survival of 10⁻⁴, L = 9.21, and e^0.921 = 2.5 well short of the observed value of Ω = 12.4 (P ∼ 0.0002 by the bootstrap test). Thus, there appears to be an advantage of the 16 deletion beyond merely the reduction of genomic target size for UV, and the additional benefit of a phage carrying gp16 with I754T is not enough to explain the survival benefit of the ‘right’ end of the evolved phage. This test does raise the possibility of some interaction effect of 16, however, as the overall benefit of the 16 deletion and I754T mutation is roughly the same as observed for the right end of the evolved phage. It may also be significant that the I754T mutation was one of two mutations in 16, and it was not even fixed by cycle 30—consistent with it not having the largest effect. It is also noteworthy that the left-end deletion of (non-essential) 2.1 kb is expected to have a benefit of Ω = 1.6 from the reduction in target size alone; this value is significantly lower than that observed, further suggesting that the benefit of deletions stems from more than just a reduced target size (P < 0.03 by the bootstrap test; although statistically significant, such a difference is small relative to the other fitness effects to be accounted for).