Multiple different equations have been used to quantify nutrient uptake rates from stable isotope tracer label incorporation experiments. Each of these equations implicitly assumes an underlying model for phytoplankton nutrient uptake behavior within the incubation bottle and/or pelagic environment. However, the applicability of different equations remains in question and uncertainty arising from subjective choices of which equation to use is never reported. In this study, I use two approaches to investigate the conditions under which different nutrient uptake equations should be used. First, I utilized a moderate‐complexity pelagic ecosystem model that explicitly models the δ¹⁵N values of all model compartments (NEMURO + ¹⁵N) to conduct simulated nitrate uptake and ammonium uptake incubations and quantify the accuracy of different nutrient uptake equations. Second, I used results of deckboard diel nutrient uptake experiments to quantify the biases of 24‐h incubations relative to six consecutive 4‐h incubations. Using both approaches, I found that equations that account for nutrient regeneration (i.e., isotope dilution) are more accurate than equations that do not, particularly when nutrient concentrations are low but uptake is relatively high. Furthermore, I find that if the goal is to estimate in situ uptake rates it is appropriate to use an in situ correction to standard equations. I also present complete equations for quantifying uncertainty in nutrient uptake experiments using each nutrient uptake equation and make all of these calculations available as Excel spreadsheets and Matlab scripts.

中文翻译：

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在贫营养条件下测量溶解性无机养分吸收的研究方程式

已使用多个不同的方程式从稳定的同位素示踪剂标记掺入实验中量化养分吸收率。这些方程式中的每一个都隐含地假设了在保温瓶和/或远洋环境中浮游植物养分吸收行为的基础模型。但是，不同方程的适用性仍存在疑问，并且从未报告过因主观选择使用哪个方程而引起的不确定性。在这项研究中，我使用两种方法来研究应使用不同养分吸收方程式的条件。首先，我利用一个中等复杂程度的远洋生态系统的模式，明确车型δ ^15个所有型号的隔间的N个值（根室+  ¹⁵N）进行模拟的硝酸盐吸收和铵盐吸收培养，并量化不同养分吸收方程式的准确性。其次，我使用了甲板diel养分吸收实验的结果来量化24小时培养相对于六次连续4小时培养的偏差。使用这两种方法，我发现，考虑到养分再生（即同位素稀释）的方程比不考虑养分再生的方程更为精确，特别是当养分浓度较低但吸收相对较高时。此外，我发现如果目标是估计原位摄取率，则对标准方程式使用原位校正是适当的。