We used the distribution of mutants across bursts to investigate whether the bacteriophage

6 replicated by a stamping machine or geometric growth model. We found that our observed distribution had a variance-to-mean ratio of 1.37. With a pure stamping machine model, the distribution is expected to be Poisson, with a variance-to-mean ratio of 1 (

27). By replicating with a computer model the data structure of our experiment, we determined that our observed ratio was best explained by a stamping machine model of replication in which newly synthesized progeny templates have a probability (

*m*) of 10

^{−4} per replication round of becoming replicative templates themselves. Thus, replication in

6 is not a pure stamping machine model. Because progeny templates can replicate, there is an element of geometric growth. However, because the burst size of

6 is about 100 (see above) (

30), the proportion of bursts in which progeny templates become replicative is on the order of 100 × 10

^{−4}, or 10

^{−2}. Thus, replication in

6 is effectively by a stamping machine model because approximately 99% of infections are pure stamping machine.

The value we estimated for

*m* was much lower than expected because indirect evidence had suggested that progeny

6 genomes could replicate at a much higher rate. If reoviruses provide an example by analogy, the incorporation pattern of labeled uridine has shown that progeny genomes replicate (

21,

23). Reoviruses are ds RNA viruses that replicate by a conservative plus-strand displacement mode that is otherwise similar to

6. In

6, procapsids synthesized from cloned cDNA are capable in vitro of taking up plus-strand RNA, completing minus-strand synthesis to form a ds progeny, and producing new plus strands (

18). The fact we find very little replication by the progeny genomes argues that some of the steps observed in vitro are delayed by regulation in vivo.

The demonstration that a virus such as

6 replicates primarily by a stamping machine is useful for the purpose of estimating mutation rates. Because the distribution will be much more Poisson than Luria-Delbruck, mutation rates can be estimated without much error as the frequency of mutants in one large pool of pseudo-single bursts, instead of applying equation

3 to a very large collection of many pools. For example, by using a collection of many pools (

*N* = 1,648 plates), we obtained our best estimate of

*u* of 2.7 × 10

^{−6} (equation

4) in the final analysis. However, had we pooled all of our pseudo-single bursts and then selected for mutants on one plate, we would have obtained a single plate with 444 mutants (Table ). These mutants would have been among the progeny phage produced by

*T* number of bursts or among

*T* × (

*B* − 1), or 98,133,750, phage. Thus, the frequency of mutants in the hypothetical single pool would have been 444/98,133,750, or 4.5 × 10

^{−6}. This estimate of

*u* differs less than twofold from our more accurate estimate of 2.7 × 10

^{−6}. Thus,

*u* in

6 or any other virus that replicates by an equivalent stamping machine could be estimated within a factor of two by simply screening for mutants in a single pool of pseudo-single bursts. Note also that much of the twofold error is due to the inclusion of the plates with 69 and 79 mutants, which were removed from our estimate of

*u* of 2.7 × 10

^{−6} (see Results). If

*T* is reduced so that the probability of having a revertant in the original

*sus*297 population is also reduced, the accuracy of an estimate of

*u* based on a single pool is increased greatly.

Because RNA viruses are thought to have generally a high mutation rate, our estimate of

*u* of 2.7 × 10

^{−6} for

6 was lower than expected. Drake and Holland (

12) estimated the genomic mutation rate (

*U*) to be between 1 and 0.1 for most RNA viruses, where

*U* is

*G* ×

*u*,

*G* is the genome size in nucleotides, and

*u* is the per-nucleotide mutation rate. For

6,

*G* is approximately 10

^{4} (

18), in which case we had anticipated that

*u* is approximately 10

^{−4} to 10

^{−5}. If the amber mutation in

*sus*297 can be reverted by only one nucleotide change, then our

*u* value of 2.7 × 10

^{−6} is a per-nucleotide estimate. If there is more than one way to revert, then our value is an overestimate of the per-nucleotide rate. In either case, our estimate was over 1 order of magnitude lower than expected from Drake and Holland's estimates. Perhaps

6 is an exception and RNA viruses are more variable than previously suspected. However, because our estimate was obtained for a single amber mutation, it is not appropriate to generalize. Additionally, there may be a simpler explanation. The

*sus*297 mutant of

6 was originally chosen for its stability as a marker for genetic crosses, in which case we could have selected for an amber mutation that naturally reverted at a low rate.

The existence of different modes of replication in viruses raises the question of whether one or another provides an adaptive advantage. Geometric growth clearly provides the power of replication speed. If

*B* is 100, a stamping machine requires 100 − 1, or 99, rounds of replication. Because 99 ≈ 2

^{6.6}, geometric growth requires only 6.6 rounds of replication to achieve an equivalent burst size. However, a stamping machine could be advantageous if the rate of deleterious mutations is high. As indicated previously, viruses have become commonly used to measure the rate of deleterious mutations, and high values have generally been reported for RNA viruses. To illustrate the effect of a high rate of deleterious mutations, let

*g*(0) be the proportion of genomes synthesized without any mutations during the course of one infection and burst. If replication is by a stamping machine, the proportion is given by the Poisson null class, or

However, if replication is by geometric growth,

*g*(0) will depend on the number of doublings that occur during one infection and burst cycle. After the first doubling, the proportion of mutation-free genomes is given by equation

6. However, after the second doubling, the proportion is reduced by a factor of

*e*^{−U}. Following the argument,

after

*n* doublings.

Depending on the values of

*n* and

*U* and assuming that most mutations are deleterious, the difference between equations

6 and

7 can be large. For example,

*U* is 0.002 for most DNA viruses, whereas

*U* is 1 for most RNA viruses. Thus, if DNA viruses replicate by a stamping machine,

*g*(0) is

*e*^{−0.002}, or 0.998. By geometric growth, using DNA phages as an example,

*B* is 100 and

*n* is 6.6 (see above). Thus,

*g*(0) is 0.998

^{6.6}, or 0.987, and the gain of replicating by a stamping machine over geometric growth for avoiding deleterious mutations is on the order of only 1%. However, for an RNA virus with the same value of

*n*, the difference is significant. By a stamping machine,

*g*(0) is

*e*^{−1}, or 0.37. By geometric growth,

*g*(0) is 0.37

^{6.6}, or 0.0014, and the relative advantage of a stamping machine is over 26,000%.

The above analysis suggests that RNA viruses have much more to gain by evolving a stamping machine mode of replication. The fact that we find support for a stamping machine in

6 supports such a viewpoint. DNA viruses, on the other hand, have little to gain by evolving a stamping machine. Thus, they would have more to gain by evolving a geometric growth mode of replication and capitalizing on the resulting speed. However, the data for DNA phages are not supportive. As indicated previously, whereas the DNA phage T2 replicates by geometric growth, the DNA phage

X174 follows a stamping machine. Both T2 and

X174 have approximately the same genomic mutation rate (

*U*), 0.003 (

9,

13).

Determining whether the replication mode of viruses is itself an adaptive trait or whether it is simply a by-product of other constraints in the viral developmental system will require information on many more viruses. Additional information would help by providing larger sample sizes to determine whether any patterns or correlations are robust. For example, is

X174 the example that rejects the hypothesis that DNA viruses should replicate by a geometric growth, or is it the exception that proves the rule? We hope that our study encourages the collection of similar data sets and also demonstrates the utility of distributional data from pseudo-single-burst experiments. The value of pseudo-single-burst data is more than just complementing alternative approaches, such as using label incorporation during replication. Because pseudo-single-burst data track replication by mutated progeny genomes, the sensitivity of the analysis is increased and it is much easier to estimate

*m*.