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Cestodes are parasitic flatworms (phylum Plathelminthes) that typically live in the digestive tract of adult vertebrates (definitive hosts) and frequently parasitize other animals in the early stages of their development (intermediate hosts). Several species of helminthes parasitize ungulates in North America in their early development. They are the main resource in wolves' diet in this region and, upon predation, the juvenile parasites infect the wolves, their definitive hosts, completing the parasites' cycle.

However, wolves can also predate alternative prey, like beavers, which are not intermediate hosts to many wolf parasites. A recent study (Friesen and Roth, 2016) has shown that alternative resources use is correlated with reduced incidence of parasites in wolves. This suggests that alternative resources use by wolves influence the parasite prevalence in the community, what can benefit both wolves and ungulates.

Propose and explore a simple mathematical model to study the prevalence of parasites in the system composed by wolves and two prey species (e.g. ungulates and beavers).

Here are some questions you may explore, but further well-grounded insights are also welcome.

• You might start with wolves and ungulates only and study the infection dynamics, and only then introduce an alternative prey to see how this balance is altered. Can you find a biologically plausible set of parameters that leads to coexistence of all populations in your system?

• Feeding only on alternative prey (that do not host parasites) would probably lead to the exclusion of the parasites from the system, but could severely impair the population of this alternative prey. What would happen to the dynamics of the system if the prey choice depended on the population sizes of the available prey?

• Changing sides in this arms race, what would be the set of parameters that could lead to the maximum prevalence of the parasites in this system? Would this lead to the collapse of the system? Can anything be said about how coevolution might have shaped the interactions between these species?

• Friesen, O.C. and Roth, J.D., 2016. Alternative prey use affects helminth parasite infections in grey wolves. Journal of Animal Ecology.

• Group presentation