Handling times and saturating transmission functions in a snail-worm symbiosis.

All dynamic species interaction models contain an assumption that describes how contact rates scale with population density. Choosing an appropriate contact-density function is important, because different functions have different implications for population dynamics and stability. However, this choice can be challenging, because there are many possible functions, and most are phenomenological and thus difficult to relate to underlying ecological processes. Using one such phenomenological function, we described a nonlinear relationship between field transmission rates and host density in a common snail-oligochaete symbiosis. We then used a well-known contact function from predator-prey models, the Holling Type II functional response, to describe and predict host snail contact rates in the laboratory. The Holling Type II functional response accurately described both the nonlinear contact-density relationship and the average contact duration that we observed. Therefore, we suggest that contact rates saturate with host density in this system because each snail contact requires a non-instantaneous handling time, and additional possible contacts do not occur during that handling time. Handling times and nonlinear contact rates might also explain the nonlinear relationship between symbiont transmission and snail density that we observed in the field, which could be confirmed by future work that controls for other potential sources of seasonal variation in transmission rates. Because most animal contacts are not instantaneous, the Holling Type II functional response might be broadly relevant to diverse host-symbiont systems.