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• The nitrification inhibitors DCD and DMPP were effective in mitigating N 2 O emissions from urea applied to potato cultivated on sandy soil. • The biostimulant containing N-fixing microorganisms increased nitrate leaching one growing season and N 2 O emissions over both seasons. • Nitrification inhibitors and biostimulants had modest agronomic benefits due to adequate available N for potato production. • Further studies should assess biostimulants performance and investigate their effects on biological processes in other agro-ecosystems. Urea is the dominant form of nitrogen (N) fertilizer used globally. Various additives have been designed for co-application with urea to improve performance of N-intensive crops including potato (Solanum tuberosum L.). Few if any studies have compared 'inhibitor' additives with 'biostimulants' designed to enhance plant growth or microbial activity. Over two potato growing seasons (2015–2016) in an irrigated loamy sand in Minnesota, we quantified agronomic performance and N losses as both nitrate (NO 3 −) and nitrous oxide (N 2 O) in treatments receiving urea, with and without additives including: nitrification inhibitors dicyandiamide (DCD) or 3,4-dimethylpyrazole phosphate (DMPP), alone or combined with the urease inhibitor N-(n-butyl) thiophosphoric triamide (NBPT), or a biostimulant containing N-fixing microbes (NFM) by itself or combined with an amino acid blend (AAB). The biostimulants produced modest (˜10%) improvements in tuber yield, under limited conditions, compared to urea alone. However, NFM increased N 2 O emissions by 32–56%, in contrast to the inhibitors, which decreased N 2 O emissions by 42–75%. Compared to urea alone, the inhibitors tended to increase soil ammonium and decrease soil NO 3 − concentrations; however, no differences in soil inorganic N in the upper 0.3 m of the profile were observed with the biostimulants. During the growing season with greater rates of soil water flux (2015), none of the inhibitors decreased NO 3 − leaching, while NFM increased NO 3 − leaching by 23%. When AAB was combined with NFM, reactive N losses did not differ from the urea-only treatment. Biostimulants can have unintended impacts on reactive N losses and should be used with caution pending additional study to better understand their effects on biological processes, and to quantify their performance in other agro-ecosystems. [ABSTRACT FROM AUTHOR]

• Nitrogen use efficiency [NUE] is best understood in terms of its constituent parts. • Interpreting N utilization efficiency depends on both N nutrition index and biomass. • A critical N utilization efficiency curve can be defined based on previous theory. • Increasing N uptake efficiency [NUpE] will reduce N losses to the environment. • Maximizing NUE does not necessarily improve agronomic or environmental outcomes. Maximizing nitrogen (N) use efficiency [NUE] is commonly identified as a key strategy to improve both agronomic and environmental outcomes; however, interpretation of NUE requires explicit consideration of crop N status. In this study, we derived a set of novel theoretical relationships between the nitrogen nutrition index [NNI] and NUE used to better interpret values for nitrogen uptake efficiency [NUpE] and nitrogen utilization efficiency [NUtE]. A small-plot trial for potato [ Solanum tuberosum (L.) 'Russet Burbank'] was conducted in 2016 and 2017 in Central Minnesota, USA, on a Hubbard loamy sand with six N rate, source, and timing treatments and two irrigation rate treatments. Impacts of treatments on NNI, NUpE, NUtE, NUE, biomass, harvest index, and potential N losses were interpreted within the context of a theoretical quantitative relationship between NUE and NNI. We found that for a constant NNI value, NUtE values increased non-linearly as biomass increased; at an NNI value of 1.0, this relationship defines the critical N utilization efficiency curve. As N rate increased from 40 to 270 kg N ha−1, NUtE significantly decreased from 109.8–69.7 g g−1 N, corresponding with a significant increase in both biomass (from 12.0–17.8 Mg ha−1) and in NNI (from 0.520 to 0.973), respectively. Additionally, we found that potential N losses (e.g., leaching) decreased as NUpE increased, or as total N inputs decreased. Potential N loss was lower in 2016 than 2017 (135 and 187 kg N ha−1, respectively) due to both greater NUpE and lower total N input from all sources in 2016 (0.602 g N g-1 N and 339 kg N ha-1, respectively) than in 2017 (0.526 g N g-1 N and 395 kg N ha-1, respectively). Interpreting NUE to evaluate agronomic and environmental outcomes requires separate consideration of its constituent factors (e.g., NUpE, NUtE, and HI) and explicit consideration of both NNI and biomass. [ABSTRACT FROM AUTHOR]