The prevalence of asymmetrical indirect effects in two-host-one-parasitoid systems

Empirical studies of indirect effects mediated by shared enemies have been characterized by several puzzling features: (a) there exist far fewer documented cases than for interactions via shared resources; (b) the majority of empirical studies have measured indirect effects where one of the two reciprocal effects could not be distinguished from zero; (c) there is a lack of documented positive effects mediated by a shared enemy, in spite of several mechanisms that could produce such effects. One potential explanation is that these are statistical expectations over the range of potential species characteristics. We systematically examine the indirect interactions between two hosts with a shared parasitoid across all potential parameter values, using a family of simple models. By including a detection limit for nonzero interspecific effects, we demonstrate that (-,0) indirect interactions between hosts are the most common type for many variants of the model. However, the absence of positive indirect effects in empirical studies constitutes a puzzling inconsistency between the empirical and theoretical literatures.