Energetically relevant predator-prey body mass ratios and their relationship with predator body size

Food web structure and dynamics depend on relationships between body sizes of predators and their prey. Species-based and community-wide estimates of preferred and realized predator-prey mass ratios (PPMR) are required inputs to size-based size spectrum models of marine communities, food webs, and ecosystems. Here, we clarify differences between PPMR definitions in different size spectrum models, in particular differences between PPMR measurements weighting prey abundance in individual predators by biomass (r ^bio) and numbers (r ^num). We argue that the former weighting generates PPMR as usually conceptualized in equilibrium (static) size spectrum models while the latter usually applies to dynamic models. We use diet information from 170,689 individuals of 34 species of fish in Alaskan marine ecosystems to calculate both PPMR metrics. Using hierarchical models, we examine how explained variance in these metrics changed with predator body size, predator taxonomic resolution, and spatial resolution. In the hierarchical analysis, variance in both metrics emerged primarily at the species level and substantially less variance was associated with other (higher) taxonomic levels or with spatial resolution. This suggests that changes in species composition are the main drivers of community-wide mean PPMR. At all levels of analysis, relationships between weighted mean r ^bio or weighted mean r ^num and predator mass tended to be dome-shaped. Weighted mean r ^num values, for species and community-wide, were approximately an order of magnitude higher than weighted mean r ^bio, reflecting the consistent numeric dominance of small prey in predator diets. As well as increasing understanding of the drivers of variation in PPMR and providing estimates of PPMR in the north Pacific Ocean, our results demonstrate that that r ^bio or r ^num, as well as their corresponding weighted means for any defined group of predators, are not directly substitutable. When developing equilibrium size-based models based on bulk energy flux or comparing PPMR estimates derived from the relationship between body mass and trophic level with those based on diet analysis, weighted mean r ^bio is a more appropriate measure of PPMR. When calibrating preference PPMR in dynamic size spectrum models then weighted mean r ^num will be a more appropriate measure of PPMR.