Nitrogen (N) and potassium (K) are key elements for crop growth, yet studies on the impact of N–K interactions on plant N and K status and yield are lacking.  This study aimed to develop effective indicators for diagnosing N and K nutrition and predicting the yield of wheat under N–K interactions based on the theoretical framework of a critical nutrient dilution curve.  A 4-year N–K interaction experiment involving three wheat cultivars was employed for building and validating nutrient indices (NIs) based on the critical N dilution curve (CNDC) and the critical K dilution curve (CKDC).  In addition, relevant data from the literature were collected for supplementary validation.  The results revealed that changes in parameter A1 of the critical K dilution curves (CKDCs) can reflect the impact of nitrogen application on K absorption and utilization.  However, the difference in K nutrition index (KNI) values calculated by CKDC under different N levels was not significant.  Based on the aboveground biomass (AGB), a universal CKDC was established and defined as K_c=3.63AGB^–0.37 under N–K interactions.  The results showed that the direct effects of N or K deficiency on crops could be quantified by the N–K interaction index (NKI) calculated by integrating CNDC and CKDC, and the changes in crop growth in response to proportional N and K concentrations could be determined by NKI as well.  In addition, topdressing N fertilizer at the jointing stage significantly improved the N–K interaction effect on the N nutrition index (NNI) and NKI at the booting stage (P<0.05), but it had no significant N–K interaction effect on the KNI.  All indicators at the heading stage demonstrated the best predictive capability for relative yield (RY) compared to other stages.  Compared with NNI and KNI, the prediction accuracy of yield with NKI improved by 11.63 and 17.44%, respectively.  The NKI has better performance in diagnosing N and K nutrition and predicting yield under N–K interactions than either NNI or KNI.  This result enhances our understanding of the effects of N–K interactions on wheat growth and has important applications for improving the accuracy of N and K nutrition diagnosis and yield prediction.

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