The infection rate of Daphnia magna by Pasteuria ramosa conforms with the mass-action principle

Abstract

In simple epidemiological models that describe the interaction between hosts with their parasites, the infection process is commonly assumed to be governed by the law of mass action, i.e. it is assumed that the infection rate depends linearly on the densities of the host and the parasite. The mass-action assumption, however, can be problematic if certain aspects of the host–parasite interaction are very pronounced, such as spatial compartmentalization, host immunity which may protect from infection with low doses, or host heterogeneity with regard to susceptibility to infection. As deviations from a mass-action infection rate have consequences for the dynamics of the host–parasite system, it is important to test for the appropriateness of the mass-action assumption in a given host–parasite system. In this paper, we examine the relationship between the infection rate and the parasite inoculum for the water flee Daphnia magna and its bacterial parasite Pasteuria ramosa. We measured the fraction of infected hosts after exposure to 14 different doses of the parasite. We find that the observed relationship between the fraction of infected hosts and the parasite dose is largely consistent with an infection process governed by the mass-action principle. However, we have evidence for a subtle but significant deviation from a simple mass-action infection model, which can be explained either by some antagonistic effects of the parasite spores during the infection process, or by heterogeneity in the hosts' susceptibility with regard to infection.