Dependence on Genome Length

Population Structure and Genome Lengths

The structure of an RNA virus population depends also on the length of the viral genome. For example, the relative abundance of the E=0 class (the wildtype sequence) in the population is:

For any given µ>0, (1-µ) is less than 1, so that as the genome length, L, increases, the relative abundance of the wildtype sequence decreases; i.e., synthesis of a full-length, unmutated copy of the genome becomes less likely as the genome length increases:

Figure 1. The abundance of the E=0 class for different genome lengths

The graph shows the number of E=0 progeny genomes for L = 3 x 10³ to 3x 10⁴ nt,
and a population size of 10⁴.

Correspondingly, the total number of mutants will increase with increasing L. For example, when the mutation rate is 10^-5, the number of E=1 mutants increases from ca. 290 to 2,200, as the genome length increases from 3,000 to 30,000:

Figure 2. The abundance of mutants for different genome lengths

The graphs show the number of E=1 and E=2 progeny genomes for L = 3 x 10³ to 3 x 10⁴ nt,
and a population size of 10⁴.

E=1 mutants E=2 mutants

As genome size increases, the graph for an error class shifts to the left. The graph is otherwise unaffected. Thus, a population of a virus with a long genome and relatively low mutation rates is similar to a population of a virus with a shorter genome but with higher mutation rates.
Sampling of the error classes is much less than 1 in these examples, thus the sequence diversity in each error class is essentially equal to the abundance of the class.