Adaptive dynamics of temperate phages

Background: Phages are viruses that infect bacteria. Following infection of a bacterial cell, temperate phages may replicate via one of two distinct pathways, known as lysis and lysogeny. Lysis involves the synthesis of a large number of phage particles, which are then released when the host cell is lysed (i.e. burst open). In lysogenic reproduction, the infecting phage genome is inserted into the genome of the host cell (forming a lysogen cell), and is then replicated via normal bacterial cell division. Lysogens may also undergo lysis in a process known as induction. Questions: How does the virulence of temperate phages evolve over time? How do environmental conditions influence this evolution? Mathematical methods: The methods of adaptive dynamics are used to determine the location and nature of evolutionary singularities. These singularities determine the direction in which evolution proceeds. Key assumptions: Over long periods of time, the probability of lysogeny (p) and the induction rate (i) within a population of temperate phages may evolve via small mutations. There is a trade-off relationship between the parameters p and i. Predictions: The evolutionary singularities may be either attractors or repellors, depending on whether the trade-off cost is accelerating or decelerating. Marginally ESS attractors, which are convergent stable and borderline evolutionarily stable, may also occur. Branching point singularities, which are associated with speciation, do not occur in this framework. A decrease in the level of resources in the environment per susceptible bacterium cell results in a shift towards greater phage virulence