Simultaneous increases of filter-feeding fish and bivalves are key for controlling cyanobacterial blooms in a shallow eutrophic lake

•Biomass-dependent synergy effects of filter-feeding fish and bivalves were detected.•Filter-feeding fish biomass underpins the synergistic effects in eutrophic lakes.•High fish biomass decreased algal sizes, increasing bivalves’ feeding efficiency.•Fish biomass in lake Taihu is too low to drive synergistic algal controls with bivalves.