We construct a data-constrained mechanistic inverse model of the ocean’s coupled phosphorus and iron cycles. The nutrient cycling is embedded in a data-assimilated steady global circulation. Biological nutrient uptake is parameterized in terms of nutrient, light, and temperature limitations on growth for two classes of phytoplankton that are not transported explicitly. A matrix formulation of the discretized nutrient tracer equations allows for efficient numerical solutions, which facilitates the objective optimization of the key biogeochemical parameters. The optimization minimizes the misfit between the modelled and observed nutrient fields of the current climate. We systematically assess the nonlinear response of the biological pump to changes in the aeolian iron supply for a variety of scenarios. Specifically, Green-function techniques are employed to quantify in detail the pathways and timescales with which those perturbations are propagated throughout the world oceans, determining the global teleconnections that mediate the response of the global ocean ecosystem. We confirm previous findings from idealized studies that increased iron fertilization decreases biological production in the subtropical gyres and we quantify the counterintuitive and asymmetric response of global productivity to increases and decreases in the aeolian iron supply.