INTEGRATING DIRECT EFFECTS AND TRAIT-MEDIATED INDIRECT EFFECTS USING A PROJECTION MATRIX MODEL

Abstract

In systems where indirect effects are mediated by traits (e.g., behavior) rather than density, direct and indirect effects may be measured in different biological currencies, making it difficult to quantify their relative contributions to a net interaction. For instance, the hydroid Hydractinia symbiolongicarpus, which colonizes shells occupied by the hermit crab Pagurus longicarpus, affects its host directly by reducing its fecundity and indirectly by modifying the behavior of its predators. In this study, I construct population projection matrices for P. longicarpus, which were housed with different assemblages of hydroids and predators. By defining direct and indirect effects as combinations of log-transformed λ's from these matrices, I translate direct effects on fecundity and indirect effects on survival into a common currency (population growth rate), allowing me to assess the relative strength of these effects. In the presence of a fish predator, strong positive indirect effects countered negative direct effects, producing a net mutualism. In the presence of a crab predator, indirect effects were equivalent in size and magnitude to direct effects, resulting in a net parasitism. These results provide insight into the mechanisms underlying context-dependency and help to explain the geographical and temporal variation observed in outcomes of symbiotic interactions.