Quantifying the relationship between intra- and interspecific transmission rates and host density in a snail symbiont system
Temporal and spatial variation in host population densities can cause variation in intra- and interspecific host contact rates. Variation in contact rates can, in turn, affect the rates at which both detrimental and beneficial symbionts are transmitted within and among host species. The two classic mechanistic epidemiological models limit our description of the relationship between contact rates and host density to just two ends of a continuum: contact rates do not change with host density (frequency-dependent transmission) or contact rates increase linearly with host density (density-dependent transmission). However, nonlinear relationships between contact rates and density may be more appropriate for many host-symbiont systems. In a system where symbiotic oligochaetes (Chaetogaster limnaei) are typically directly transmitted among aquatic snail hosts, we quantified (1) biweekly host densities and infestation prevalences in two host snail species in a single pond and (2) the corresponding rates at which susceptible sentinel snails (Helisoma trivolvis) maintained in field enclosures in the pond became infested by symbionts. We then used model selection approaches to determine whether density-dependent, frequency-dependent, or nonlinear transmission functions in single or two-host epidemiological models best described the observed forces of infestation.
The densities of the two resident snail host species (Physa gyrina and H. trivolvis) showed distinctly different temporal patterns, with Physa densities peaking earlier in the summer. Surprisingly, when the densities of infested Physa were the highest, the observed forces of infestation in sentinel Helisoma snails were very low. Correspondingly, even though both species were infested with symbionts in the field and Chaetogaster is thought to be a host generalist, the best-fitting models always included little to no role for transmission from Physa to Helisoma. This suggests that there may be barriers to interspecific transmission. After restricting the analysis to single host models with transmission limited from resident Helisoma snails to sentinel Helisoma snails, both the density-dependent and nonlinear transmission functions provided substantially better fits than the frequency-dependent transmission function. The nonlinear transmission function also provided a better fit than the density-dependent transmission function, suggesting that Helisoma-Helisoma contact rates may saturate with density. Incorporating the nonlinear transmission function into epidemiological models is straightforward, and competing it with the classic mechanistic functions may provide valuable insight into transmission dynamics in many symbiont systems.