Dinitrogen fixation (DNF) provides a large fraction of the 'new' nitrogen supporting upper ocean productivity, and is associated with environmental conditions likely to show substantial change under anthropogenic warming. For example, surface warming induces stronger stratification, weaker nutrient supply and more rapid nutrient depletion. Using six Earth System Models, we have examined spatial patterns and trends of DNF in the CMIP5 historical and RCP 8.5 experiments. Four models (CanESM2, CESM1-BGC, IPSL-CM5R-LR, and UVicESCM) show high DNF rates in warm, stratified waters mostly associated with the western parts of the ocean basins, while GFDL-ESM2M and MPI-ESM-LR show elevated rates near the eastern boundaries because of coupling of DNF and denitrification. Despite a growing body of data, the spatial pattern of DNF is still insufficiently resolved by available observations, and none of the models agrees well with the observations. Modelled and observed rates are mostly in the same general range except for UVicESCM, and frequency distributions are similar, but spatial pattern correlations are weak and in most cases not statistically significant. Only a few models show strong trends in DNF and primary production in a warming climate, and the signs of the trends are inconsistent. Observations of primary production at the benchmark subtropical station ALOHA (22.75°N, 158°W) and proxies for historical DNF from the same region appear to corroborate trends in CanESM2 that are not present in other models. However, the CanESM DNF parameterization does not include any limitation by P or Fe, so modelled future trends may not materialize due to nutrient limitation. Analysis of available models and observations suggests that our understanding of environmental controls on ocean DNF remains limited and future trends are highly uncertain. Long-term global simulations of DNF will only be meaningful if we maintain long-term observations and extend coverage to undersampled regions.Keywords: ocean dinitrogen fixation; Earth system modelling; anthropogenic climate change Riche and Christian: Ocean dinitrogen fixation and its potential effects on ocean primary production in Earth system model simulations of anthropogenic warming Art. 16, page 2 of 18 of phosphorus or iron are available, with opposing effects on primary production (Karl et al., 1995(Karl et al., , 1997Karl, 1999). As diazotrophic phytoplankton thrive in warm, stratified waters (Sohm et al., 2011), investigating the potentially enhanced role of diazotrophs in tropical and subtropical ocean ecosystems in a warming climate is important. Proxy δ
15N measurements of the DNF contribution to the N inventory in the subtropical Pacific suggest that the recent apparent enhancement discussed by Karl (1999) is a long-term trend throughout the 20 th century, possibly associated with anthropogenic warming (Sherwood et al., 2014).We have examined trends in DNF in a variety of Earth System Models associated with the CMIP5 project (Taylor et al., 2012) to determine which if any sh...