Size structure of organisms at logarithmic scale (i.e. size spectrum) can often be described by a linear function with a negative slope; however, substantial deviations from linearity have often been found in natural systems. Theoretical studies suggest that greater nonlinearity in community size spectrum is associated with high predator-prey size ratios but low predator-prey abundance ratios; however, empirical evaluation of the effects of predator-prey interactions on nonlinear structures remains scarce. Here, we aim to empirically explore the pattern of the size-specific residuals (i.e. deviations from the linear regression between the logarithmic fish abundance and the logarithmic mean fish size) by using size spectra of fish communities in 74 German lakes. We found that nonlinearity was strong in lakes with high predator-prey abundance ratios but at low predator-prey size ratios. More specifically, our results suggest that only large predators, even if occurring in low abundances, can control the density of prey fishes in a broad range of size classes in a community and thus promote linearity in the size spectrum. In turn, the lack of large predator fishes may cause high abundances of fish in intermediate size classes, resulting in nonlinear size spectra in these lakes. Moreover, these lakes were characterized by a more intense human use including high fishing pressure and high total phosphorus concentrations, which have negative impacts on the abundance of large, predatory fish. Our findings indicate that nonlinear size spectra may reflect dynamical processes potentially caused by predator-prey interactions. This opens a new perspective in the research on size spectrum, and can be relevant to further quantify the efficiency of energy transfer in aquatic food webs.