Complex Daphnia interactions with parasites and competitors

Abstract

Species interactions can strongly influence the size and dynamics of epidemics in populations of focal hosts. The "dilution effect" provides a particularly interesting type of interaction from a biological standpoint. Diluters - other host species which resist infection but remove environmentally-distributed propagules of parasites (spores) - should reduce disease prevalence in focal hosts. However, diluters and focal hosts may compete for shared resources. This combination of positive (dilution) and negative (competition) effects could greatly complicate, even undermine, the benefits of dilution and diluter species from the perspective of the focal host. Motivated by an example from the plankton (i.e., zooplankton hosts, a fungal parasite, and algal resources), we study a model of dilution and competition. Our model reveals a suite of five results: • A diluter that is a superior competitor wipes out the host, regardless of parasitism. Although expected, this outcome is an ever-present danger in strategies that might use diluters to control disease. • If the diluter is an inferior competitor, it can reduce disease prevalence, despite the competition, as parameterized in our model. However, competition may also reduce density of susceptible hosts to levels below that seen in focal host-parasite systems alone. • As they decrease disease prevalence, diluters destabilize dynamics of the focal host and their resources. Thus, diluters undermine the stabilizing effects of disease. • The four species combination can generate very complex dynamics, including period-doubling bifurcations and torus (Neimark-Sacker) bifurcations. • At lower resource carrying capacity, the diluter’s dilution of spores is 'helpful' to the focal host, i.e., dilution can elevate host density by reducing disease. But, as the resource carrying capacity increases further, the equilibrium density of the diluter increases while the density of the focal host decreases, despite competition. Namely, the negative effects of competition start to outweigh the positive effects of dilution from the perspective of equilibrium density of the focal host.

Keywords: Bifurcation theory; Daphnia; Endemic equilibria; Epidemic model; Holling model; Resource competition.