We quantify the response of the global nutrient cycles and phytoplankton community structure to Southern Ocean iron fertilization using an inverse model of the coupled Fe-P-Si cycles that contains a mechanistic representation of phytoplankton abundance and nutrient colimitation. We find that different parameterizations of the iron dependence of the Si:P uptake ratio allow equally good fits to the observational nutrient climatology but produce very different responses to iron fertilization. The different Si:P parameterizations considered are also consistent with the available observational data of diatom physiology but the steady-state response to iron fertilization depends sensitively on the rate with which the Si:P uptake ratio decreases with increasing dissolved-iron concentration (DFe).  For a sufficiently rapid decrease of Si:P, iron fertilization leads to silicic acid becoming partially untrapped from the Southern Ocean and leaking to low latitudes with an accompanying shift in floral composition.  If Si:P decreases more slowly with increasing DFe, iron fertilization leads to strengthened Southern Ocean silicon trapping.  For all cases, the global response of the biological phosphorus and silicon pumps, and its implications for carbon uptake, are dominated by the Southern Ocean.  The Si-isotope signature of the opal flux to the sediments distinguishes between different forms of the Si:P uptake ratio, with leakage producing isotopically lighter sediments similar to the observational record for the last glacial maximum.