Wiki site of the practical exercise of the VI Southern-Summer School on Mathematical Biology.

Here you will find the exercise assignment and the group's products.

If you are a group member login to edit this page, create new pages from it, and upload files.

Zoochlorella are microscopic algae that form endosymbiotic relationships with several protists, including the Paramecium bursaria. As with most endosymbiotic relations of this kind, the Paramecium gains a (relatively) stable nutrient source, while the algae gain motility and protection. In particular, the Paramecium protects the zoochlorellae inside it from infection by chloroviruses, large DNA viruses that infect a range of green algae. Unable to penetrate the protist's membrane, the chloroviruses must resign themselves to adhering to the outer membrane and waiting for toe Paramecium's rupture.

A possible undertaker of this task is the ciliate Didinium nasutum, which predates on protists like the P. bursaria. As it feeds, it may attemp to envelop the entire Paramecium and, if that fails (if, for instance, the Didinium is too small), it ruptures the protist's membrane and consumes part of it in a process called messy feeding. This method releases the zoochlorellae passengers into the water, where they are exposed to infection by chloroviruses. Thus, the prevalence of chlorovirus infection among zoochlorellae comes to depend on two other species sharing their own predator-prey interactions.

Didinium (left) attempting to phagocyte a Paramecium (right). Image taken from https://images.fineartamerica.com/images-medium-large/1-didinium-nasutum-ingesting-paramecium-eric-v-grave.jpg

Develop and analyse an ODE model describing the interactions in this system. Add whatever components you see fit in order to capture the system's essential mechanisms.

• Are the dynamics different from a system where messy feeding releases spores rather than hosts? (You don't have to create a new model for this second system; see Cáceres, Knight and Hall (2009) for a lead)
• What happens if the predator is a specialist?

• DeLong J. P., Al-Ammedi Z., Lyon S., Van Etten J. L. and Dunigan D. D. Size-dependent catalysis of Chlorovirus population growth by a messy feeding predator. Microbial Ecology, November 2017.
• Cáceres C. E., Knight C. J. and Hall S. R. Predator-spreaders: predation can enhance parasite success in a planktonic host-parasite system. Ecology, 2009.