First of all, an extremely broad continuum is defined as an infinite pan-genome, with a low core/pan-genome ratio.
One of the implications of early pan-genome estimates is that some bacterial species might have an "infinite" pan-genome [ 2, 6].
The infinite pan-genome was first proposed by Tettelin et al. for S. agalactiae based on the use of 9 S. agalactiae genomes.
Our modeling using the 67 S. mutans genomes by applying the model described above without any restrictions pointed to an infinite pan-genome of S. mutans.
Thus, without considering the "gene loss events", it's quite understandable to have a "growing" or "infinite" pan-genome as gene acquirement occurs no matter how slow it might be.
Both the fitting results of using y = a + bx c and y = a − b ln(x + c) indicated an infinite pan-genome, while the fitting result of using y = a × e− x / b + c resulted in a negative value of the parameter a, suggesting a finite pan-genome However, the last fitting shows obvious deviations to many of the data points.
Hogg et al. [ 14], reported a finite pan-genome for Haemophilus influenzae, extrapolating from 12 whole genome sequences, while results for Streptococcus agalactiae indicate an infinite asymptotic pan-genome [ 21].
Another study suggests that the bacterial pan-genome is infinite [ 9].
The curve for the pan-genome size can be represented by the following mathematical function of Y = 2735.2287 X0.5 + 544.4458 (R = 0.99) where, Y represents pan-genome size, while X represents number of sequenced genomes (Pan-genome size = infinite when X → ∞).
In contrast, the lineage III (currently with only 4 available complete genomes) showed a closed pan-genome, reflecting that this lineage might have a conserved genome structure compared to the other lineages (Table 3 and Fig. 4a).> -wrap-foot> Y represents the pan-genome size while X represents the number of sequenced genomes (Pan-genome size = infinite when X → ∞).
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