Human exploitation of marine resources is profoundly altering marine ecosystems, while climate change is expected to further impact commercially-harvested fish and other species. Although the global fishery is a highly complex system with many unpredictable aspects, the bioenergetic limits on fish production and the response of fishing effort to profit are both relatively tractable, and are sure to play important roles. Here we describe a generalized, coupled biological-economic model of the global marine fishery that represents both of these aspects in a unified framework, the BiOeconomic mArine Trophic Size-spectrum (BOATS) model. BOATS predicts fish production according to size spectra as a function of net primary production and temperature, and dynamically determines harvest spectra from the biomass density and interactive, prognostic fishing effort. Within this framework, the equilibrium fish biomass is determined by the economic forcings of catchability, ex-vessel price and cost per unit effort, while the peak harvest depends on the ecosystem parameters. Comparison of a large ensemble of idealized simulations with observational databases, focusing on historical biomass and peak harvests, allows us to narrow the range of several uncertain ecosystem parameters, rule out most parameter combinations, and select an optimal ensemble of model variants. Compared to the prior distributions, model variants with lower values of the mortality rate, trophic efficiency, and allometric constant agree better with observations. For most acceptable parameter combinations, natural mortality rates are more strongly affected by temperature than growth rates, suggesting different sensitivities of these processes to climate change. These results highlight the utility of adopting large-scale, aggregated data constraints to reduce model parameter uncertainties and to better predict the response of fisheries to human behaviour and climate change.