Effects of NP Fertilizer Placement Depth by Year Interaction on the Number of Maize ( Zea mays L.) Plants after Emergence Using the Additive Main Effects and Multiplicative Interaction Model

: Field experiments were carried out at the Department of Agronomy of the Pozna´n University of Life Sciences to determine the effect of the depth of NP fertilization placement in maize cultivation on the number of plants after emergence. The adopted assumptions were veriﬁed based on a six-year ﬁeld experiment involving four depths of NP fertilizer application (A1—0 cm (broadcast), A2—5 cm (in rows), A3—10 cm (in rows), A4—15 cm (in rows)). The objective of this study was to assess NP fertilizer placement depth, in conjunction with the year, on the number of maize ( Zea mays L.) plants after emergence using the additive main effects and multiplicative interaction model. The number of plants after emergence decreased with the depth of NP fertilization in the soil proﬁle, conﬁrming the high dependence of maize on phosphorus and nitrogen availability, as well as greater subsoil loosening during placement. The number of plants after emergence for the experimental NP fertilizer placement depths varied from 7.237 to 8.201 plant m − 2 during six years, with an average of 7.687 plant m − 2 . The 61.51% of variation in the total number of plants after emergence was explained by years differences, 23.21% by differences between NP fertilizer placement depths and 4.68% by NP fertilizer placement depths by years interaction. NP fertilizer placement depth 10 cm (A3) was the most stable (ASV = 1.361) in terms of the number of plants after emergence among the studied NP fertilizer placement depths. Assuming that the maize kernels are placed in the soil at a depth of approx. 5 cm, the fertilizer during starter fertilization should be placed 5 cm to the side and below the kernel. Deeper NP fertilizer application in maize cultivation is not recommended. The condition for the use of agriculture progress, represented by localized fertilization, is the simultaneous recognition of the aspects of yielding physiology of new maize varieties and the assessment of their reaction to deeper seed placement during sowing. ◦ 16 ◦ 45 in years The experiments were carried out for six years as single-factor experiments in four ﬁeld replications. The following variable was tested: A—NP fertilizer placement depth (A1—0 cm (broadcast), A2—5 cm (in rows), A3— 10 cm (in rows), A4—15 cm (in rows)). The same level of mineral fertilization (100 kg N ha − 1 , 70 kg P 2 O 5 ha − 1 and 130 kg K 2 O ha − 1 was applied in all experimental objects. Fertilization 46% P 2 5 (46% (60%). Fertilizer coulters starter fertilization) set 5 aside from seeds. depth of NP fertilization application regulated on the seeder frame The maize variety P7905 was used in the experiment. Is this a commercial hybrid. Two-way analysis of variance was applied to determine the magnitude of the main effects of NP fertilizer placement depth and years as well as NP fertilizer placement depth by years interaction on the number of plants after emergence. The main effects

enabling a single analysis of DY interaction. For this reason, AMMI is also known as interaction PCA (IPCA) [24,25]. The advantages of the AMMI model are that they use overall fitting, impose no restrictions on the multiplicative terms, and result in a least squares fit; within limits, any model may also be expected to fit data from which it was derived. The AMMI method is used for three main purposes. The first is that the model diagnoses other models; secondly, AMMI clarifies treatment × environment interaction and summarizes patterns and relationships of treatment and environment [23,26], and the third use is the accuracy of trait estimates [23,26]. The AMMI method is widely used in stability and adaptability analyses because it (i) provides an initial diagnosis of the model and is well-suited for data analysis with many environmental influences, (ii) allows greater unfolding of the treatment × environment interaction and summarizes the patterns and relationships between treatments [27][28][29][30][31][32][33].
Field studies at the Department of Agronomy of the Poznań University of Life Sciences were carried out to determine the effect of the depth of NP fertilization placement in maize cultivation on the number of plants after emergence. The objective of this study was to assess NP fertilizer placement depths by years interaction on the number of maize (Zea mays L.) plants after emergence using the additive main effects and multiplicative interaction model.

Soil and Climate Information
Maize placement was performed using a precision seeder, with a built-in granular fertilizer applicator (Monosem). Gross plot size was 24.5 m 2 (length-8.75 m, width-2.8 m), while the plot size used to observe the number of plants after emergence was 12.25 m 2 . In the 3-leaf stage (BBCH 13), the plants in each row of the plot were carefully counted, and subsequently their sum was divided by its size, thus establishing the number of plants after emergence. The structure of the experimental field morphology was characteristic of the bottom moraine of the North Polish (Baltic) glaciation, the Poznań stadium. Sandy-loam formations constituted parental materials of the soil. Terrain configuration was slightly diversified, and the dominant area was flat and slightly undulating. Typologically, the soils in the test field were of the black-earth type, the cambic black-earth subtype that belonged to the black-earth order. These soils should be classified as Phaeozemes according to the international WRB classification [34], and as Mollisols according to the US Soil Taxonomy [35]. Humic horizon was homogeneous on the entire experimental field. The percentage content of the sand fraction of the Ap level showed little differentiation and ranged from 77-79%, while the average values for individual fertilization objects were almost identical for the depths of 0-0.15 m and 0.15-0.30 m. Dust content in these levels was also not very diverse and was within 17-18% for both depths. Clay content, relatively low, fluctuated in the top and deeper soil layers in a narrow range of 4-5%. Granulometric composition of the soils from the experimental field in the arable-humic horizons (Ap) was even in all the tested fertilization objects in this experimental field. All analyzed samples from the experimental objects belonged to one grain size group, i.e., loamy sands [36]. The experimental field was valuated as class IIIb. The black earth type are soils with direct impact of groundwater or heavy rainfall on the lower and partly central portions of the soil profile. Precipitation and water management dominate in the surface horizons and it can be somewhat modified through changes of water properties in the deeper parts of the soil profile (0-0.30 m, genetic horizon Ap). Soil abundance in nutrients and soil pH before establishing the experiment in maize growing seasons are presented in Table 1. Air temperature and rainfall in the maize growing seasons are presented in Table 2. Definitely the warmest and driest growing season was recorded in 2018. In turn, the largest sum of precipitation in the initial period of maize growth was recorded in 2016. The lowest average daily temperature at the level of 12.8 • C was recorded in 2017. Generally, it should be said that thermal and rainfall in the initial maize vegetation varied considerably in individual growing seasons. The effect of temperature and humidity factors is best described in a comprehensive manner by the hydrothermal water supply index [K] according to Szulc et al. [37]. K = 10 · monthly precipitation total [mm] Number of days · mean daily air temperature in a given month [ • C] Interpretation of the hydrothermal index according to Sielianinow: K > 1.5-excessive moisture for most plants, 1 < K < 1.5-sufficient moisture for most plants, 0.5 < K < 1.0insufficient moisture for most plants, K < 0.5-drought.

Field Experiment
Field trial was carried out at the Department of Agronomy of the Poznań University of Life Sciences on the fields of the Gorzyń Experimental and Educational Unit, branch in Złotniki (52 • 26 N; 16 • 45 E), in the years 2015-2020. The experiments were carried out for six years as single-factor experiments in four field replications. The following variable was tested: A-NP fertilizer placement depth (A1-0 cm (broadcast), A2-5 cm (in rows), A3-10 cm (in rows), A4-15 cm (in rows)). The same level of mineral fertilization (100 kg N ha −1 , 70 kg P 2 O 5 ha −1 and 130 kg K 2 O ha −1 ) was applied in all experimental objects. Fertilization was balanced against phosphorus, which was applied at the whole required concentration in the form of ammonium phosphate (18% N, 46% P 2 O 5 ). N and K fertilization was performed before maize placement using urea (46% N) and potassium salt (60%). Fertilizer coulters (on objects with starter fertilization) were set 5 cm aside from the seeds. The depth of NP fertilization application was regulated on the seeder frame ( Figure 1). The maize variety P7905 was used in the experiment. Is this a commercial hybrid.
Agronomy 2021, 11, x Field trial was carried out at the Department of Agronomy of the Poznań U of Life Sciences on the fields of the Gorzyń Experimental and Educational Unit, b Złotniki (52°26′ N; 16°45′ E), in the years 2015-2020. The experiments were carrie six years as single-factor experiments in four field replications. The following var tested: A-NP fertilizer placement depth (A1-0 cm (broadcast), A2-5 cm ( A3-10 cm (in rows), A4-15 cm (in rows)). The same level of mineral fertilizatio N ha −1 , 70 kg P2O5 ha −1 and 130 kg K2O ha −1 ) was applied in all experimental obje lization was balanced against phosphorus, which was applied at the whole requ centration in the form of ammonium phosphate (18% N, 46% P2O5). N and K fer was performed before maize placement using urea (46% N) and potassium sa Fertilizer coulters (on objects with starter fertilization) were set 5 cm aside from t The depth of NP fertilization application was regulated on the seeder frame (F The maize variety P7905 was used in the experiment. Is this a commercial hybri

Statistical Analysis
Two-way analysis of variance was applied to determine the magnitude of effects of NP fertilizer placement depth and years as well as NP fertilizer placeme by years interaction on the number of plants after emergence. The main effects o tilizer placement depths and years were fixed; however, the effect of NP fertiliz ment depth by year interaction was random. In parallel, least-squares means we lated for the AMMI model. The model first fitted the additive main effects of NP placement depths (D) and years (Y), followed by the multiplicative effects of DY tion by PCA. The AMMI model [24,38] was defined by the following equation:

Statistical Analysis
Two-way analysis of variance was applied to determine the magnitude of the main effects of NP fertilizer placement depth and years as well as NP fertilizer placement depth by years interaction on the number of plants after emergence. The main effects of NP fertilizer placement depths and years were fixed; however, the effect of NP fertilizer placement depth by year interaction was random. In parallel, least-squares means were calculated for the AMMI model. The model first fitted the additive main effects of NP fertilizer placement depths (D) and years (Y), followed by the multiplicative effects of DY interaction by PCA. The AMMI model [24,38] was defined by the following equation: where y de is the mean of NP fertilizer placement depth d in the year e, µ is the grand mean of the number of plants after emergence, α d is the mean deviation of NP fertilizer placement depth, β e is the year mean deviation, N is the number of PCA axes retained in the adjusted model, λ n is the eigenvalue of the PCA axis n, γ dn is NP fertilizer placement depth score for the PCA axis n, δ en is the eigenvector score for the PCA axis n, and Q de is the residual, which includes AMMI noise and pooled experimental error. The expected distribution of Q de was found to be normal. The AMMI stability values (ASVs) were used to compare the stability of NP fertilizer placement depths as described by [39]: where SS is the sum of squares, IPCA 1 and IPCA 2 are the first and the second interaction principal component axes, respectively; and the IPCA 1 and IPCA 2 scores were the NP fertilizer placement depth scores in the AMMI model. ASV is the distance from zero in a two-dimensional scatterplot of IPCA 1 scores against IPCA 2 scores. Since the IPCA 1 score contributes more to the NP fertilizer placement depth by year sum of squares, it has to be weighted by the proportional difference between IPCA 1 and IPCA 2 scores to compensate for the difference in contribution. The distance from zero is then determined using Pythagoras's theorem. The greater the IPCA score, either negative or positive, the more specifically adapted the NP fertilizer placement depth is to certain years. The higher the IPCA score (which can be negative or positive), the more accurately selected NP fertilizer placement depth in an individual year. Lower ASV score indicates more stable NP fertilizer placement depth across the year [29,31,33,38,40]. The level of significance in PCA analysis was tested with the F test.
The level of significance of PCA analysis was tested using the F test according to Gollob [41]. In the biplot, which is an efficient representation of the AMMI model, DY interactions are plotted on the vertical axis (IPCA 1), while means of NP fertilizer placement depth and year are plotted on the horizontal axis. The applied analytical procedures and result interpretation were based on the protocol of Gauch and Zobel [24]. All statistical analyses were conducted using the GenStat software package (v. 18) [42].

Results
Three sources of variation (NP fertilizer placement depth, year and DY interaction), were found to be significant for the number of plants after emergence. In ANOVA, the sum of squares for the main effect of the year represented 61.51% of the total variation in the number of plants after emergence, and this factor had the highest effect on the number of plants after emergence. The differences between NP fertilizer placement depths explained 23.21% of the total variation in the number of plants after emergence, while the effects of the DY interaction explained 4.68% of the variation ( Table 3). The values of the two principal components were also statistically significant and jointly accounted for 91.87% of the whole effect on the variation in the number of plants after emergence. The first principal component (IPCA 1) explained 80.21% of the variation caused by interaction, while the second component (IPCA 2) accounted for 11.66% of the variation in the number of plants after emergence ( Figure 2). Among the tested NP fertilizer placement depths, the A4 had the highest IPCA 1 value of 0.882, while the lowest value of IPCA 1 was −0.251 for A1. The values of IPCA 2 ranged from −0.147 (for A1) to 0.153 (for A3) (Figure 2, Table 4).  Table 4).   Table 4). Variation of the number of plants after emergence, measured coefficient of variation-CV, was equal to 3.28%, across all four NP fertilizer placement depth and six years of study ( Table 3). The highest variation of the number of plants after emergence was observed for A1 (CV = 3.17%), while the lowest for A3 (2.78%) ( Table 4). Values of coefficient of variation for particular years of study varied from 1.34% (in 2018) to 3.03 (in 2016) ( Table 4).
Stability of the analyzed NP fertilizer placement depths during six years with respect to the number of plants after emergence was visualized as a biplot (Figure 3). NP fertilizer placement depth A1 interacted positively with the year 2015, but negatively with the years    Table 4). Variation of the number of plants after emergence, measured coefficient of variation-CV, was equal to 3.28%, across all four NP fertilizer placement depth and six years of study ( Table 3). The highest variation of the number of plants after emergence was observed for A1 (CV = 3.17%), while the lowest for A3 (2.78%) ( Table 4). Values of coefficient of variation for particular years of study varied from 1.34% (in 2018) to 3.03 (in 2016) ( Table 4).
Stability of the analyzed NP fertilizer placement depths during six years with respect to the number of plants after emergence was visualized as a biplot (  Figure 2). The analysis indicated that some NP fertilizer placement depths exhibited a high level of adaptation; however, most of them showed a specific adaptation. The ASVs varied in the number of plants after emergence between four NP fertilizer placement depths tested (Table 4). NP fertilizer placement depths A3 and A2 with the ASV of 1.361 and 1.615, respectively, were the most stable, while NP fertilizer placement depths A4 and A1 with the ASV amounting to 1.999 and 1.745, respectively, were the least stable (Table 4).
aptation. The ASVs varied in the number of plants after emergence between four NP fertilizer placement depths tested (Table 4). NP fertilizer placement depths A3 and A2 with the ASV of 1.361 and 1.615, respectively, were the most stable, while NP fertilizer placement depths A4 and A1 with the ASV amounting to 1.999 and 1.745, respectively, were the least stable (Table 4).

Discussion
The number of plants after emergence per unit area is one of the most important agriculture factors in the cultivation of this plant for grain [43]. According to current recommendations, the number of plants after emergence in grain cultivation ranges from 8 to 10 pcs. m −2 . In the present study, the number of plants after emergence decreased along with the increase of NP fertilizer placement depth in each of the six years of research. In turn, Szulc and Kruczek [44] showed no significant effect of the method of placement phosphorus and phosphorus-nitrogen fertilizers on plant emergence. Nevertheless, many authors have indicated that too high a concentration of the component in the immediate vicinity of seeds can cause disturbances in germinating seeds [10,12,45,46]. However, the latter authors have not provided the maximum nutrient concentration that can be used in the immediate vicinity of germinating seeds. The confirmation obtained in these studies [45] that even the maximum concentration of 130 kg P2O5 ha −1 , applied in the immediate vicinity of the seeds, did not affect maize emergence, seemed to be a positive result. Consistent reproducibility of the lack of influence of fertilization of the on maize emergence in the following days of observation indicated that relationship [45]. To obtain more general conclusions, these authors standardized the intermediate values of subsequent emergence

Discussion
The number of plants after emergence per unit area is one of the most important agriculture factors in the cultivation of this plant for grain [43]. According to current recommendations, the number of plants after emergence in grain cultivation ranges from 8 to 10 pcs. m −2 . In the present study, the number of plants after emergence decreased along with the increase of NP fertilizer placement depth in each of the six years of research. In turn, Szulc and Kruczek [44] showed no significant effect of the method of placement phosphorus and phosphorus-nitrogen fertilizers on plant emergence. Nevertheless, many authors have indicated that too high a concentration of the component in the immediate vicinity of seeds can cause disturbances in germinating seeds [10,12,45,46]. However, the latter authors have not provided the maximum nutrient concentration that can be used in the immediate vicinity of germinating seeds. The confirmation obtained in these studies [45] that even the maximum concentration of 130 kg P 2 O 5 ha −1 , applied in the immediate vicinity of the seeds, did not affect maize emergence, seemed to be a positive result. Consistent reproducibility of the lack of influence of fertilization of the on maize emergence in the following days of observation indicated that relationship [45]. To obtain more general conclusions, these authors standardized the intermediate values of subsequent emergence days to the average period of emergence, uniform for individual years. Logarithmic function most optimally reflected the emergence of maize, and its course for the tested fertilization methods was almost identical. Hence, the result obtained in these studies confirmed that the fertilization method did not differentiate maize by the number of plants after emergence. One can ask why the application of a lower phosphorus concentration of 70 kg P 2 O 5 ha −1 (30.8 kg P ha −1 ) in the immediate vicinity of the seeds in the current study resulted in a reduction in plants' quantity after emergence and before maize harvest along with an increase in depth fertilizer application. The increase in fertilizer placement depth using a fertilizer coulter most likely worked in the same manner as the use of a subsoiler (Figures 4 and 5). Most probably, the subsoil was too loosened and water penetration was interrupted. Therefore, placing the seeds in such soil did not occur at the planned depth (4-5 cm), but deeper. This was confirmed by maize plant losses during the vegetation period that were in fact the lowest in objects with deep (15 cm) fertilizer placement during seed placement.
days to the average period of emergence, uniform for individual years. Logarithmic function most optimally reflected the emergence of maize, and its course for the tested fertilization methods was almost identical. Hence, the result obtained in these studies confirmed that the fertilization method did not differentiate maize by the number of plants after emergence. One can ask why the application of a lower phosphorus concentration of 70 kg P2O5 ha −1 (30.8 kg P ha −1 ) in the immediate vicinity of the seeds in the current study resulted in a reduction in plants' quantity after emergence and before maize harvest along with an increase in depth fertilizer application. The increase in fertilizer placement depth using a fertilizer coulter most likely worked in the same manner as the use of a subsoiler (Figures 4 and 5). Most probably, the subsoil was too loosened and water penetration was interrupted. Therefore, placing the seeds in such soil did not occur at the planned depth (4-5 cm), but deeper. This was confirmed by maize plant losses during the vegetation period that were in fact the lowest in objects with deep (15 cm) fertilizer placement during seed placement.  Other authors argued [47] that deeper sowing should be a common practice in the development of sustainable agriculture in arid and semi-arid areas of our globe. Nevertheless, most commercial maize varieties are not adapted to deeper sowing (>5 cm), which results in a disturbance of emergence dynamics [47] and reduction of the planned plant density. Therefore, scientists determined a recommended sowing depth, which is dependent on the type of soil, texture, pH and moisture conditions that vary for each crop species. However, arable fields are not uniform, therefore deeper sowing becomes a difficult task Other authors argued [47] that deeper sowing should be a common practice in the development of sustainable agriculture in arid and semi-arid areas of our globe. Nevertheless, most commercial maize varieties are not adapted to deeper sowing (>5 cm), which results in a disturbance of emergence dynamics [47] and reduction of the planned plant density. Therefore, scientists determined a recommended sowing depth, which is dependent on the type of soil, texture, pH and moisture conditions that vary for each crop species. However, arable fields are not uniform, therefore deeper sowing becomes a difficult task to solve. Deeper sowing is an alternative agricultural practice that has a strong influence on maize germination rate and consequently the final yield [48]. Hence, research should be focused on the selection of tolerant maize varieties in terms of increasing depth of their sowing. Strong hydrotropic reactions of new varieties should be the highest for its implementation in sustainable agriculture in times of the impending drought caused by the climate crisis [49]. This feature varies greatly from strong (>40 • ) to weak (<40 • ), which confirms the large genetic diversity among commercial maize varieties [50]. Therefore, the selection should use the genetic diversity of native, local maize varieties, which show a strong hydrotropic response and a greater mesocotyl elongation coefficient in deeper seed placement in soil during sowing [51].
In addition to the most important DY interactions, the AMMI biplot allows to visualize the major effects of NP fertilizer placement depths and individual years of cultivation. The present study found that the largest difference in the number of plants after emergence between A1 and A4 was obtained in 2016, which was characterized by the highest sum of atmospheric precipitation (218.4 mm) in the initial period of maize vegetation. On the other hand, the lowest difference between A1 and A4 in the number of plants after emergence occurred in 2018, which was characterized by the highest average daily air temperature (16.1 • C). The AMMI model has been extensively used in studies on numerous species [52][53][54][55][56][57][58][59][60][61][62][63][64]. The AMMI is more appropriate in the initial statistical analysis of yield trials because it provides an analytical tool to diagnose other models, such as subcases, when these are better for particular data sets and also have a good chance of predicting new depths and years, this is a real advance [65]. To our knowledge, this is the first report about using the additive main effects and multiplicative interaction model to analysis of NP fertilizer placement depth by year interaction on the number of maize (Zea mays L.) plants after emergence. The results obtained from AMMI analyses are very important in terms of the development and recommendation of most optimal NP fertilizer placement depths concerning the productivity in a specific year. The AMMI model is a useful tool for diagnosing DY interaction patterns and improving the accuracy of reaction assessments. It allows to group NP fertilizer placement depths based on the similarity of response features and determine potential trends over the years. The proposed strategy could extract more information from DY interactions, thereby helping researchers to determine specific NP fertilizer placement depths, which would contribute to competitive yields in different years.
The AMMI model does not provide for a quantitative stability measure and such a measure is essential to quantify and rank genotypes in terms of observed trait stability [66,67]. Therefore, the AMMI stability value (ASV) was proposed by Purchase et al. [39] to quantify and rank objects according to their observed trait stability. The AMMI stability value (ASV) identified NP fertilizer placement depth A3 (10 cm in rows) as a more stable depth, which also had high mean performance. Such an outcome could be regularly employed in the future to delineate predictive, more rigorous recommendation strategies, as well as to help define stability concepts for recommendations for maize.

Conclusions
The number of plants after emergence decreased with the depth of NP fertilization in the soil profile. Most probably, the main reason for this relationship was too deep placement, caused by excessive loosening of the subsoil during placement. NP fertilizer placement depths of 10 cm in rows (A3) and 5 cm in rows (A2) were found to be the most stable, while 15 cm in rows (A4) and 0 cm in broadcast (A1) were the least stable in terms of the number of plants after emergence. Based on the experiment, it seems reasonable to place the NP fertilizer granules at a maximum depth of 10 cm. A deeper application of fertilizer >10 cm can only be advisable with thin coulters that do not disturb the soil structure under the seed. Maize varieties for deeper application of mineral fertilizer in the soil profile >10 cm (row fertilization) should be more tolerant to deeper seed placement during sowing. AMMI analysis proved to be effective for determining DY interactions with respect to the number of plants after emergence. In order to most efficiently utilize the biological progress, represented by new maize varieties, it is very important to assess the correct depth of mineral fertilizer application and develop plant nutrition on this basis.

Data Availability Statement:
The data presented in this study are available on request from the corresponding authors.

Conflicts of Interest:
The authors declare no conflict of interest.