Table 1.
Mathematical models of CRISPR-Cas virus coevolution
| Type | Features | Major results | Ref. |
|---|---|---|---|
| SDE | Single type of virus/plasmid, 5 types of hosts | Strong defence against viruses, weak defence against plasmids | 67 |
| SDE | 3 Types of hosts, 3 types of viruses | Importance of multiple spacer–protospacer matches | 65 |
| SDE | 6 Types of hosts with and without plasmids | CRISPR-Cas loci might be selected to be labile | 82 |
| ABS | Lattice population model, CRISPR arrays in host, protospacer arrays in virus | Long-term virus–host and virus strain coexistence in spatially structured population | 69, 70 |
| ABS, SDE | Strain-level host and virus representation; CRISPR arrays in host, protospacer arrays in virus | Diversification of host and virus, incomplete selective sweeps | 72, 73 |
| ABS, SDE | Strain-level host and virus representation; CRISPR arrays in host, protospacer arrays in virus | Rapid fluctuations of host population distributed immunity (PDI), limiting effect of high PDI on virus diversity | 74 |
| ABS | Strain-level host and virus representation; CRISPR arrays in host, protospacer arrays in virus | Rapid selection sweeps, distal end conservation of CRISPR arrays | 76 |
| ABS | Strain-level host and virus representation; CRISPR arrays in host, protospacer arrays in virus | Virus diversity threshold for CRISPR-Cas maintenance | 54 |
| ABS | Individual-level host and virus representation; CRISPR arrays in host, protospacer arrays in virus | Direct correlation of virus diversity with population size, importance of multiple spacer–protospacer matches | 71 |
| SDE | 2 Types of hosts, single type of virus | Quasi-chaotic oscillations at high virus reproduction rates | 66 |
| ABS, SDE | Strain-level host and virus representation; virus mutation and recombination, CRISPR arrays in host, protospacer arrays in virus | Proximal end heterogeneity with distal end conservation of CRISPR arrays, effects of virus mutation and recombination depend on multiplicity of spacer–protospacer matches | 78, 79 |
| ABS | Evolution of CRISPR arrays via acquisition and deletion | Clock-like divergence of arrays, estimation of host phylogeny and divergence times by CRISPR array comparison | 77 |
| SDE | Levels of processed and unprocessed CRISPR locus transcripts under expression and degradation | Rapid upregulation of processed transcript abundance, phase transition-like behavior | 80, 81 |