Food web structure of free-living species is an important determinant of parasite species richness. Downwardly asymmetric predator-prey interactions (where there are more prey than predator species) have been shown, both theoretically and empirically, to harbour more trophically transmitted parasite species than expected due to chance. Here, we demonstrate that this could be due to the increase in the basic reproductive ratio that the addition of non-host prey species to a system creates. However, we note that the basic reproductive ratio is only increased by those prey that stabilise oscillations in a predator-prey system, and is decreased by those that do not.