Climate change can impact the persistence of native and invasive parasites and their effects on hosts. Given the complexity of interactions in natural systems, models based on parasite–host systems can be helpful to explore long-term impacts. We investigate how two intestinal parasitic copepods impact host populations, and how the predicted temperature increase by year may affect the persistence and impacts of the parasites. We study Mytilicola intestinalis (a specialist established in blue mussels, Mytilus edulis) and Mytilicola orientalis (a recent invader infecting mussels and Pacific oysters, Magallana gigas) in the Wadden Sea. The parasites are non-lethal but can influence host maturation and fecundity. Using a mathematical model parametrized with empirical, field and literature data, we explore how temperature increase affects parasite basic reproduction numbers and the long-term population trends of parasites and mussels. Temperature increase reduces mussel populations below the critical community size for M. intestinalis persistence, while allowing M. orientalis to persist without oysters. M. orientalis does not have a negative effect on the host population in additional to that of M. intestinalis when both are present. We show that environmental change can have qualitatively different effects on related parasites by changing the role of the shared host as a maintenance population. |