The experiment was conducted in western Jutland, Denmark (55°36’13.4”N, 8°57’09.0”E) on a field where P deficiency had previously been observed in potatoes. Soil samples from the top 25 cm were randomly collected, air dried and sieved through a 2 mm mesh. The soil samples were analyzed by standard procedures and included: texture, pH, Olsen-P and ammonium extractable Mg and K at a commercial laboratory (Agrolab, Germany) ( Table 1 ). Furthermore, P availability was determined by the C_DGT technique as presented by Tandy et al. (2011) and Christel et al. (2016) ( Table 1 ). Seed potatoes Solanum tuberosum L., cv. Kuras were planted with a row distance of 0.75 m and a distance between tubers of 0.2 m. The experimental site was irrigated when there was no precipitation. Fertilizer was placed between the rows (10 cm from the tubers and 5 cm below tuber level) while planting. The following fertilization rate was used: 136.5 kg N ha^-1, 250 kg K ha^-1, 60 kg Mg ha^-1, 170 kg S ha^-1 and it was provided as diammonium phosphate, N-S (27-4) and patentkali (25% K, 6% Mg, 17.5% S). Two soil P fertilizer treatments were used: P+ and P-. P+ was supplied with 30 kg P ha^-1, while P- did not receive P fertilizer.

Soil moisture (0-20 cm below the soil surface) and soil temperatures (6 cm below the surface, at the soil surface and 15 cm above ground) were monitored using two Standard TMS dataloggers (Tomst, Czech Republic) throughout the entire growing season. On the days when tissue sampling and chlorophyll a fluorescence measurements were made, the photosynthetically active radiation (PAR) was recorded for a period of at least 3 hours using a universal light meter (ULM-500, Heinz Walz GmbH, Germany).

All leaf positions were harvested from 4 field grown potato plants at each sampling date, giving a total of 4 independent replicates of each leaf position. Sampling occurred twice in June at 51 and 58 days after planting (DAP) during the tuber initiation stage, and twice in August at 99 and 113 DAP, during the tuber bulking stage. The leaves were dried at 50°C on the day of harvesting. Ultra-wave digestion of plant tissue was performed in a mixture of 500 µL ultra-pure acid (70% HNO₃) and 250 µL 15% H₂O₂ under an inert gas (N₂) at a pressure of 45 bars and 240°C for 15 min (Ultrawave, Milestone Inc., USA). When leaf tissue dry weight exceeded 150 mg, the leaves were pulverized and homogenized before taking a sub-sample. All samples were analyzed on a 5100 DW ICP-OES (Agilent Technologies, USA) with multi-element detection. Data were validated with the analysis of seven replicates of certified reference material (Apple leaves, NIST 1515, National Institute of Standards and Technology, USA). Only elemental data with accuracies and precision better than 95% were included (Chen et al., 2020).

Chlorophyll a fluorescence analysis was performed on all leaf positions (n = 4) before harvesting at 51, 58, 99 and 113 DAP, using a HandyPEA chlorophyll fluorometer (Hansatech instruments, UK). Prior to measuring, leaves were dark adapted for 25 minutes using Hansatech leaf clips (Hansatech instruments, UK). Leaves were exposed to continuous saturating actinic light (3000 µmol m^-2 s^-1) for 10 seconds. The resulting fluorescence emission was recorded by a PIN photodiode to construct a fluorescence transient (Kautsky and Hirsch, 1931). The transients were created by double normalizing the data between F0 and Fm to get the relative fluorescence, V(t), using the formula:

F0 and Fm correspond to the minimal fluorescence at time 0 and the maximum fluorescence, respectively, and F(t) is the measured fluorescence at time t. Furthermore, the fluorescence transients were used to evaluate the plant P status, by preprocessing and analysis using a Python 3.9 script based on a partial least square (PLS) model to quantify the level of P deficiency (Frydenvang et al., 2015) (Patent EP3049792B1). P-predict values can provide an indication of plant P status and identify P deficiency. Plants are considered P deficient at P-predict<0.40 and P sufficient at P-predict >0.65 while P-predict values in the range 0.40-0.65 indicate intermediate P status (Frydenvang et al., 2015; Carstensen et al., 2018a).

The experimental field site was chosen due to a historical yield response to P fertilization, which was confirmed by a pot trial that showed an increased barley biomass following P fertilization (data not shown). The soil has a high percentage of coarse sand ( Table 1 ), which is suitable for potato cultivation. The soil type has a low water holding capacity often resulting in low P availability and drought stress in absence of irrigation, and for this reason irrigation was implemented. The volumetric soil moisture was maintained above 25% for the duration of the experiment ( Supplementary Figure S1 ), thus exceeding the field capacity for the sandy soil (Zotarelli et al., 2019). Soil tests for P status showed that the soil was near deficiency according to C_DGT, which is the most reliable indicator of plant available soil P (Mundus et al., 2017), while it had sufficient P levels according to the Olsen-P value (Rubæk, 2015) ( Table 1 ). The field experiment was fertilized according to standard practices and recommendations based on the soil tests, and the plants presented no visible symptoms of any nutrient deficiencies ( Figure 1 ).

The elemental composition was measured in all leaves from four randomly selected plants at each sampling date and showed striking patterns of nutrient concentrations depending on leaf position and sampling date ( Figure 2 ). P fertilization had a significant effect on the P concentration at the individual leaf positions during tuber initiation on the first sampling date 51 DAP (P<0.001), but no significant differences were found 7 days later, nor at the tuber bulking stage 99 and 113 DAP. During tuber initiation, halfway through the growing period at 51 DAP, P concentrations were very high in the youngest leaves (0.85-0.94% in leaf 1) and decreased markedly with increasing leaf age. Leaf 5 had P concentrations of 0.40-0.44%, while leaf 11 had P concentrations of 0.20-0.26%, which is within 1 standard deviation of the reported critical P concentration of 0.22% ( Figure 2A ). One week later, at 58 DAP, P concentrations in leaves 3-7 had decreased by a remarkable 19-40% compared to the previous week, with concentrations in older leaves (leaf 7-13) near the critical P concentration. During tuber bulking in the later part of the growing season (99 and 113 DAP), P concentrations in all leaves had stabilized at or below the critical P concentration ( Figure 2B ). Furthermore, no differences were found in tuber P concentration between P fertilization treatments ( Supplementary Table S1 ).

The distribution patterns observed for Mg and K concentrations were opposite to the ones observed for P during tuber initiation ( Figure 2 ). Mg and K did, however, resemble those of phloem immobile nutrients such as Ca, Mn and B, while the nutrients S, Fe, Zn and Cu all differed in distribution patterns with seemingly no relation to their phloem mobility ( Supplementary Figures S2 and S3 ). While the younger leaves had the highest P concentrations, they had the lowest Mg and K concentrations, ( Figures 2C, E ). The youngest leaves had Mg concentrations slightly above the critical Mg concentration of 0.25%, while Mg concentrations in leaf 11-13 were four times higher, peaking at around 1%. Similar to Ca and Mn, Mg concentrations did not decrease between 51 and 58 DAP. During tuber bulking, Mg concentrations in leaf 7 had fallen to 0.51%, while both older and younger leaves contained high levels of Mg (up to 0.81-1.0%) ( Figure 2D ). The K concentration decreased systematically over time. In the span of one week during tuber initiation, K concentrations were significantly reduced in all leaves ( Figure 2E ), similar to the P concentrations. The K concentrations had fallen by 50% at the time of tuber bulking 113 DAP ( Figure 2F ). In the time between tuber initiation and tuber bulking, the K concentration decreased from 4% to 1.7% in the youngest leaves and from 7% to 4% in the oldest.

These data indicate that the results of leaf nutrient analyses are highly dependent on leaf position and time of sampling, more so than on the availability of nutrients in the soil.

Prior to the elemental analysis shown in Figure 2 , chlorophyll a fluorescence was measured to generate P-predicts for all leaf positions. P-predict values are used to estimate the P status in plants, where values below 0.4 indicate a P concentration below the critical P concentration. Correlating P-predicts with leaf P concentrations during tuber initiation (51 DAP) shows that according to both P concentrations and P-predict values, 72% of the leaves were not P deficient ( Figures 2A , 3A ). Only 8% of the leaves were classified as being P deficient according to both P-predict and leaf concentration, while 19.5% of the leaves were misclassified by P-predicts. Strikingly, the rate of P-predict misclassification increased to 43% at 58 DAP. Most of the misclassifications on both days came from P-predicts indicating P deficiency, although leaf concentrations were above the critical P concentration. At 51 DAP, most of the leaves misclassified as deficient by P-predict had relatively low P concentrations between 0.22% and 0.4%. At 58 DAP, leaves 1-11 were frequently misclassified as P deficient by P-predict, irrespective of their P concentration ( Figure 3B ). At 51 DAP, the P-predicts were highest in the YFELs at position 4-5, while the youngest, not fully expanded, leaf positions 1-3 showed decreasing P-predict values despite having the highest P concentrations. Two replicates of leaf 1 had P concentrations of nearly 1% but were classified as deficient by their P-predicts.

Given the increasing number of misclassifications, it is clear that the reliability of the P-predict as a diagnostic tool was affected prior to day 58. This indicates a disturbance in the photosynthetic machinery, as chlorophyll a fluorescence is tightly correlated with the linear electron flow from PSII to PSI. Besides nutrient deficiencies, fluorescence emissions can also be affected by stressors such as light or temperature. The irradiance was significantly higher on day 58 compared to day 51, which was likely contributing to the higher rate of misclassified P-predicts ( Supplementary Figure S4 ). During fluorescence measurements on day 51, the irradiance fluctuated around 600 PAR, with single spikes at 1600, while the irradiance was significantly higher at 1400-1500 PAR on day 58, with short dips when clouds passed. Similarly, the air temperature was 26°C on day 50 and 51, but 32°C on day 57 and 58 ( Supplementary Figure S5 ).

The fluorescence transients serving as input to the P-predict calculations were severely distorted on day 58, especially in the young and mid-level leaves (positions 1-7). These leaves represent the most sun-exposed parts of the plant, and their fluorescence transients lost their J- and I-steps and instead developed D-dips where the I-step is usually located. The transients of the older leaves, deep in the shaded canopy looked normal ( Figure 4A ).

To avoid light stress and potential photoinhibition, some plants were shaded from day 51, which resulted in normal transients and reliable P-predict values on day 58. The transients of shaded leaves showed distinct OJIP steps on day 58 and were markedly different from the distorted transients in the same leaf positions in unshaded plants ( Figure 4B ). The shading decreased the irradiance from 1400 to 600 PAR, while the temperature inside and outside the shaded areas were nearly identical. P-predict values ranged from –2 to 2 (average –0.07 ± 0.65) in the unshaded leaf 4, while shading of leaf 4 improved P-predict values to 0.62 ± 0.03. Shading thus enabled a correct P-predict diagnosis ( Figure 4B ).

In this study, we observed a steep gradient of leaf P concentrations through the canopy. The youngest leaves had a high P concentration during tuber initiation, while the older leaves had concentrations around or just above 0.22% ( Figure 2A ). When the nutrient supply becomes limiting, it is often observed that young leaves retain high nutrient levels at the expense of older leaves due to remobilization (Smith and Loneragan, 1997). In the current experiment, the observed P depletion of the older leaves was caused by a substantial remobilization of P from source to sink tissue, i.e. to the young leaves and the developing tubers of the potato plant. During tuber initiation, the P concentration in the YFEL fell by 25-33% in the span of just one week, indicating a large remobilization from shoot to tuber. Later in the growing season, during the tuber bulking period, all leaves ended up near or just below the critical P concentration of 0.22% which indicated that the shoot P was remobilized to the tubers and settling at the critical P concentration. The timing and leaf sampling prior to measurements is therefore incredibly important for a meaningful interpretation of leaf analysis data.

Interestingly, K and Mg distribution presented opposite patterns compared to P. The concentration of K and Mg were highest in the older leaves and did not exhibit deficiency levels in the late season. This indicates a sufficient K and Mg availability, even though the concentration of K fell significantly between 51 and 58 DAP and was close to the critical K concentration in the youngest leaves 113 DAP.

It is remarkable that the distribution patterns of K and Mg resemble those of the phloem immobile nutrients Ca and Mn during tuber bulking, despite Mg and K presumably having a high phloem mobility similar to that of P ( Supplementary Figures S2 , S3 ). P concentration in tubers at harvest was 0.15% ( Supplementary Table S1 ), and from Figure 2B it is clear that P was remobilized fully until it reached the critical P concentration of the shoot. This did not occur to the same extent for Mg and K and indicates that the tubers were a stronger sink for P than for Mg and K ( Figures 2D, F ). This is likely because the primary involvement of K and Mg in starch synthesis occurs through phloem loading of photosynthates in the shoots. P is also engaged in phloem loading but is remobilized to the tubers due to a key-functionality in activating enzymes of the starch synthesis pathway in the amyloplasts (MacNeill et al., 2017).

However, although we observed remobilization of P from old to younger tissue, it is not clear whether P availability was actually limited in this experiment. In fact, no differences could be observed between fertilized and unfertilized plots, neither in P-predicts, P concentrations nor in the final yields. Across both treatments, we only observed P concentrations below 0.22% in the older leaves on the later sampling dates. The missing response to P fertilization could indicate that the availability of P from residual pools in the soil made the applied fertilizer P redundant. This has previously been observed during optimal water conditions, and is therefore a likely observation in the current study (Potarzycki and Grzebisz, 2019). It is also possible that the buffering capacity of the soil was sufficient to supply the plants with enough P to satisfy the functional requirement, although it would be unexpected, as the field was chosen due to a history of P fertilization responses.

The lack of fertilizer effect could also imply that the applied P was immobilized and not available for uptake by the roots. It is therefore unclear if the low P concentrations measured in the older leaves in the early growing season, and in all leaves in the late growing season, should be classified as a nutrient deficiency or a normal physiological consequence of massive P remobilization to the tubers. Once the shoot has become a P source for tuber development, any further P uptake is not likely to be reflected in leaf concentrations as it will be directed towards the tubers. The P response, which was not achieved under field conditions, could certainly have been obtained under controlled conditions (climate chamber or greenhouse). However, this would clearly have omitted all interactions with the environment that are so essential for an appropriate and “real-life” assessment of the P-predict method.

The nutrient concentrations are highly dynamic and observed to change drastically within a few days, which essentially prevents meaningful data interpretation based on single leaf analysis. Furthermore, the nutrient demand of plants fluctuates during a growth cycle, and a tissue analysis cannot foresee if deficiencies will arise later in the season. The tissue concentration would therefore need to be regularly monitored, which is both labor and cost intensive. The critical P concentration of 0.22% in the YFEL is widely used as a threshold for diagnosing P deficiency (Rosen et al., 2014). This critical P concentration is set for mid- to late season potatoes, but the critical concentration is higher in the early growth stages (Walworth and Muniz, 1993; Huett et al., 1997). The critical concentration of 0.22% corresponds well with the concentration at which most leaves are classified as deficient by P-predict. The P concentration in the YFEL of P sufficient potato plants decreases from 0.6% in early season to 0.4% in mid-season and 0.2% in late season (Walworth and Muniz, 1993). A concentration of 0.3% might therefore be indicative of P deficiency in the early growth phases, but not in the late growing season. In this study, the YFEL (leaf 4) had a P concentration around 0.4% in the mid-season (51 and 58 DAP), which would also be deemed sufficient by these standards.

When chlorophyll a fluorescence is measured, thresholds are also used to evaluate the P status of plants. The fluorescence parameter P-predict is used to indicate when P deficiency physiologically affects the functionality of the photosynthetic processes in the plants (Frydenvang et al., 2015; Carstensen et al., 2018a). In this study, the different leaf positions presented a wide range of P status, from severely deficient in the older leaves late in the season to very high concentrations in the youngest leaves early in the season. A positive correlation between leaf P concentration and P-predict was observed for leaf positions 4-13 ( Figure 3A ). However, the three youngest leaves had lower P-predicts despite having higher P-concentrations. These leaves are not yet fully evolved and have thus not yet transitioned from being sink to source tissue which is reflected in the fluorescence signal. Measuring a fully expanded leaf is therefore necessary for correct classification of P status.

The advantages of chlorophyll-based diagnosis in field settings, as an alternative to measuring the nutrient concentration in leaves, include the cheap cost and rapid on-site classification compared to plant tissue analysis by external laboratories, where it can take up to several weeks to receive the result of tissue sampling. Obtaining data about the crop nutrient status in real time will allow immediate fertilization efforts to alleviate P deficiencies, before the deficiency can affect yield outcomes.

It can be valuable to measure tissue P concentration during the growing season to add P fertilizers in response to low P status (Rosen et al., 2014), and P concentration and yields have been found to correlate (Fernandes et al., 2014). Yet, research has also shown that macronutrient concentrations in leaves can be poor indicators of yield, for both P (White et al., 2018) and N (Grzebisz et al., 2020). White et al. (2018) grew 66 potato genotypes and found a positive effect of P fertilization on both yield and leaf P concentration. However, within the tested cultivars there was no correlation between P concentration in the YFEL and tuber yields. In previous studies, P concentration and P-predict could only predict yield effects in the first few weeks of the barley growing season (Carstensen et al., 2018b). Later in the season, the size of the plant had adjusted to the available P levels, and the P status of each leaf was therefore at sufficient levels, despite a significant yield response. In this study, a transient P effect of P fertilization was observed during the early tuber initiation phase ( Figure 2A ) but disappeared at the next sampling time 7 days later. The transient P response indicates that the plant adapts its size to the available P. However, in this case P fertilization would be expected to influence measured yield which was not found.

Despite the high correlation between leaf P concentration and P-predict on day 51, field grown crops are often exposed to environmental stresses which may interfere with chlorophyll a fluorescence. In this study we observed that high solar irradiance (>1400 PAR) on measurement days impaired the reliability of the fluorescence-based diagnosis of P status. The chlorophyll a fluorescence response in the leaves were severely affected, leading to erroneous P-predict estimates of P status. The fluorescence transients showed indications of photoinhibition, including the development of D-dips in the OJIP transients following the I-step at approximately 0.07 seconds ( Figure 4 ). The D-dips that developed at day 58 under high irradiance might be related to degradation of the Mn cluster of the oxygen evolving complex at PSII (Pospíšil and Dau, 2000; Schmidt et al., 2016a). D-dips have also been observed in transients of Mn deficient plants, which are severely affected by photoinhibition (Schmidt et al., 2016b). Photoinhibition is a light-induced inhibition of PSII. It is a mechanism plants employ to protect the photosystems from photodamage caused by excess energy from absorbed light and is part of non-photochemical fluorescence quenching (NPQ). The primary components of NPQ respond to thylakoid lumen acidification and reverse quickly during dark adaptation. Photoinhibition (qI), however, is only induced over prolonged exposure to excess light, and is caused by inactivation or degradation of the D1 subunit of PSII, or from permanent damage to the photosynthetic systems (Ruban, 2016; Guidi et al., 2019). It therefore reverses slowly, over the span of hours or days, as the reversion depends on D1 repair mechanisms. In order to understand the cause of the distorted transients at the mechanistic level, detailed PAM fluorometry would be required to identify the individual NPQ components (qE, qT, qI). Moreover, to further elucidate the correlations between high light intensity and the shape of the distorted transients, it would be necessary to perform experiments with a range of light levels and plant P tissue levels under controlled growth conditions. Such experiments could determine the intensity at which high light causes distortion at a given P status, and how low the intensity should be to subsequently restore the fluorescence transients for diagnosis of nutrient status.

To understand the cause of the distorted transients in the field, some plants were shaded for one week prior to measuring chlorophyll a fluorescence on a day with high light intensity. In this experiment it was observed that shading the plants resulted in fluorescence transients comparable to those obtained at low light, either measured on a cloudy day or on the leaves shaded in the canopy ( Figures 3 , 4 ). Leaves deep in the canopy will always be shaded, and as a result their transients will be unaffected by photoinhibition, which consequently makes them useful for diagnosing P status. However, these older leaves without exposure to high light were P depleted early in the season due to P remobilization, and a diagnosis based on these leaves would therefore indicate P deficiency, even when the plant might be fully supplied with P. In effect, measuring chlorophyll a fluorescence for diagnosis of nutrient status should be avoided on days with extreme light intensity. If this is not possible, it will therefore be necessary to shade the plants for several hours prior to chlorophyll a based diagnosis of P status.

In order to use these techniques for reliable diagnosis of P deficiency and fertilizer planning, P status needs to be monitored throughout the season. Due to the highly dynamic P concentrations, meaningful interpretation is incredibly challenging when using the traditionally established critical P concentrations. Chlorophyll a fluorescence analysis provides a cheaper and immediate diagnosis, but threshold values for P-predict at the different growth stages are not yet established. Furthermore, interpretation of both methods is complicated by the highly dynamic P concentrations and thresholds for P deficiency which vary throughout the growth season.