Modeling the Performance Parameters of Pollen Grains of Male Date Palms Using an Artificial Neural Network Based on the Mineral Composition and Morphological Properties of Their Leaves

Abstract

One of the key factors for sustainability in agricultural systems, particularly, for cultivation of date palms, is the identification of the performance parameters of the pollen grains of male date palms (Phoenix dactylifera L.). This study was carried out to predict the performance parameters of pollen grains using an artificial neural network (ANN) model. The morphological features of spathe length, spathe weight, number of pinnae per leaf, leaf length, leaf width, length of the pinna part, pinna length, pinna width, length of the spathe stem, and spathe width, as well as the concentrations of minerals such as Mg, N, K, P, and Ca in their leaves were used as inputs to the ANN model. For this purpose, we collected the required data from nine male date palms grown in Saudi Arabia. The ANN model utilized in this work included an input layer with 15 parameters, a hidden layer of 30 neurons, and an output layer with 8 neurons. The ANN model was trained with 27 patterns. Seven patterns were utilized for testing purposes. The coefficient of determination (R²) obtained between the observed and predicted performance parameters’ values using the testing dataset was 0.902 for the number of strands per spathe, 0.967 for strand length, 0.963 for the number of flowers per strand, 0.941 for the number of flowers per spathe, 0.985 for the weight of pollen grains per spathe, 0.810 for the pollen grains’ viability, 0.936 for the pollen grains’ length, and 0.992 for the pollen grains’ width. The length of the spathe stem had the most critical effect on how the ANN model predicted the values of the dependent variables, i.e., the number of strands per spathe, with a percentage of contribution of 17.66%; the weight of pollen grains per spathe, with 17.85%; the pollen grains’ length, with 19.78%, and the pollen grains’ width, with a percentage of contribution of 30.59%. Spathe weight had the most critical influence on strand length and pollen grains’ viability, with percentages of 26.29% and 14.92%, respectively. Leaf width had the most critical effect on the number of flowers per spathe, with a percentage of 12.55%. The elemental concentration of K in the male date palm leaves had the most critical effect on the number of flowers per strand, with a percentage of 13.98%. It was therefore concluded that using a modeling process with the ANN technique can help estimate the performance parameters of male date palms’ pollen grains for different purposes, such as providing a starting point for mathematical analyses associated with the physiological mechanisms of male date palm. Moreover, the outcomes of this research work can be supportive as a practical tool in this field of study.

1. Introduction

The date palm, Phoenix dactylifera L. is considered to be the primary fruit crop in the Kingdom of Saudi Arabia, which occupies around 72% of the land used for permanent crops [1]. Moreover, 75% of all fruit production is generated as dates [2]. Furthermore, the Kingdom of Saudi Arabia is home to almost 30 million palm trees, which yield more than 1.5 million tons of date fruits [3]. In the Saudi community, palm trees are highly valued not only for their potential to support food security but also for their compatibility with the local environment and societal values. According to the results, there were 31,234,155 palm trees in the kingdom overall, and 1,539,755 tons of palm trees were produced in total in the season of 2018 [4]. The region of Riyadh possessed the greatest quantity of palm trees, totaling 7,924,947, or 24% of production. The Qassim region came next, with 7,542,914 trees (25%); the Madinah region came next, with 4,751,040 trees (15%) [4]. The date palm is a multipurpose tree that provides food, shelter, and wood products. Date fruit has anti-mutagenic and anti-carcinogenic properties, in addition to being high in fiber, carbohydrates, minerals, and vitamins [5,6]. Saudi Arabia’s Ministry of Environment, Water, and Agriculture has attempted to improve date production by conducting related research [7]. One of the key factors for sustainability in agricultural systems, particularly, for date palm plantations, is identification of the performance parameters of pollen grains of male date palms (Phoenix dactylifera L.). However, no works have tackled this subject, producing empirical mathematical models to predict the performance parameters of date palms’ pollen grains. Because date palms (Phoenix dactylifera L.) are important economically, numerous studies have been conducted to quantify and evaluate the female varieties [8]. However, considering that pollen grains quality greatly influences the quality and quantity fruit, male genotypes have seldom been described regardless of their essential part in both the pollination and the yield of date crops. Pollen grain is a fine, like dust present in flower anthers, which act as the transmission unit and source for male gametes [9].

According to Hachef et al. [8], the quality of the pollen grains produced by male date palm genotypes is a crucial agronomic characteristic that guarantees production. As a result, pollen grains from date palms are essential for the fruit to display particular traits. Consequently, research on pollen grains’ performance is required to investigate potential variabilities in the pollen grains’ quality and to identify a male genotype provider of pollen grains with high reproductive quality from the current collection. Wide morphological variation has been shown among the male date genotypes in terms of their flowering behavior [8]; however, such morphological markers can be used in the assessment of male date palms’ variability. Furthermore, there are concerns about the sustainability of date palm cultivation, and thus there is a need to develop technologies and practices related to producing good pollen grains from the males. The performance of pollen grains is the key factor for sustainability in agricultural systems, particularly for date palm cultivation. Pollen grains’ performance, however, is essential for the production and breeding of flowering plants, as well as for the development of fruit in agricultural systems. Moreover, successful fruit set depends in part on pollen grains’ germination and the pollen grains’ properties [10].

To assess the potential of the male date palms planted in Tunisia, Hachef et al. [8] designed an experiment based on several agro-morphological parameters, including flowering characteristics, pollen grains quality, and the shape of inflorescences. Substantial variation was seen for the majority of the qualities investigated, such as length to the branching region, the maximum breadth of the spathe, and the spathe’s total length, with a highly significant variance in the quantitative parameters of the tree. Pollen grains’ viability fluctuated from 51.10% to 98.75%, while the germination rate varied from 0.90% to 70.50%. Furthermore, Hachef et al. [8] specified that there was an association between the inflorescence’s morphological indicators and the pollen grains’ performance. These outcomes highlight the significance of the agro-morphological variables used for evaluating date palms’ inherent agrobiodiversity. Any male palm’s pollen may generally be used to pollinate any female cultivar. Nonetheless, there are significant differences in the quality of their pollen because the majority of male palms originate from seedlings. Different sources of date palm pollen may cause a variety of variations in color, size, fruit set, ripening time, the fruits’ weight and shape, seed weight, etc. [11]. Thus, finding superior male palms to fertile female plants requires us first to characterize and assess the very potent males available [12]. Similar to all other characteristics, the morphology of pollen is an expression of the genome; therefore, it is important to comprehend how genotypes differ from one another [10]. Developing predictive mathematical models that help agronomists and farmers organize their operations in date palm orchards is one of the primary goals of research. Since the precision of a prediction is crucial to the success of a lengthy agri-food chain, advanced and accurate forecasting of activities such as crop yields continues to be a pressing issue for any government. Nonetheless, predictive models of different crops can be created using soft computing approaches. Crop predictive models and decision tools have become essential parts of precision agriculture globally due to the quick development of technology [13]. These tools and the predictive models can be created by different procedures, such as using artificial neural network (ANN) techniques. Moreover, one objective of agricultural production is to maximize date palm yields at the lowest possible cost. Date palm’s yield indicators can be used to identify and address issues early on, which can boost production and, ultimately, profit [14]. Crop managers could utilize predictions to reduce losses when unfavorable conditions might arise. When favorable growing conditions are possible, these forecasts may also be utilized to optimize predictions of the crop [14]. Because of this, the performance parameters of male date palms (Phoenix dactylifera L.) pollen grains can be modeled using an ANN based on their leaves’ morphological traits and mineral compositions. This makes it possible to investigate the pollen grains in terms of the unanticipated features of hybridization and breeding systems in addition to comparative morphological data [10].

The high predictive accuracy of ANN models is a benefit [15]. Functions that establish how features and predictors depend on the output data are the foundation of the algorithms used to construct and train ANN models. ANNs are clearly superior to traditional models in a few key areas. Consequently, they are able to replicate nonlinear correlations among various data sources [16]; as a result, studies on the creation of an ANN model for predicting an agricultural activity are pertinent [15]. Furthermore, the feed-forward ANN backpropagation model is the most commonly used method of creating ANN models [14]. As such, ANN models have been used to model and forecast cultivars’ agricultural activities on the basis of a range of predictive factors [13,14,15].

Since the female palm is the one that produces the fruits, when establishing a new date plantation, a producer usually plants mostly female palms and a few male palms. In a contemporary plantation, the pollen grain output of a single healthy adult male palm can fertilize up to 50 females [17,18]. The source of the male pollinator affects the germination and vitality of the pollen grains [19]. However, in order for them to produce large yields, compatibility with female cultivars is being sought after. However, the male palms differ morphologically in terms of growth, vigor, date of flowering, features of the spathe, and the quality of the pollen grains [20,21,22,23,24]. Because the sustainability of date palms’ output depends on pollen grains increasing under the right circumstances, it is vital to evaluate male date palms in terms of their vegetative and blooming traits. However, selecting high-quality pollen grains is essential for increasing yields and improving the quality of the product, since obtaining notable harvests is dependent on successful pollination and astute selection of the pollinators [25].

The conventional procedures for evaluateing the germination and viability of pollen grains produced from male date palms (Phoenix dactylifera L.) are time-consuming [19]. However, ANN modeling is becoming more widely recognized as a promising method for predicting an agricultural activity and real-time monitoring. By emulating the human brain’s procedures, ANN models are a collection of computational algorithms that can solve complex issues or construct intricate associations between variables [26]. According to Basheer and Hajmeer [27], ANNs are significant due to their special information-processing capabilities, which include tolerance of faults and noises, nonlinearity, learning, and generality. Therefore, the goal of this research was to use an ANN model to simulate the performance parameters related to pollen grains of male date palms (Phoenix dactylifera L.) on the basis of the morphological traits and mineral compositions of their leaves. Farmers can enhance the morphological traits of male date palms and the mineral content of their leaves in a season by using modeling to the extent necessary to obtain high-quality pollen grains and subsequently boost the output of fruit. Researchers can make a significant contribution to sustainable agriculture. Thus, the contribution of this study is to use features such as the morphological traits of male date palms and the mineral content of their leaves as a numerical experiment on the ANN model’s ability to predict the performance parameters related to pollen grains of male date palms under a range of variation in such features. We used nine males. Additionally, short-range predictions of the performance parameters provided valuable insights for agricultural resource management and the likely economic impacts associated with low date palm yield.

2. Materials and Methods

2.1. The Experimental Location

A 15-hectare date palm orchard located in the Dirab area (24°25′ N, 46°34′ E; elevation, 400 m) within the Research and Agriculture Experimental Station was the study’s site during the 2021 growing season. Because we did not conduct any treatments on male date palm trees, our study focused on significant variations in the morphometric characteristics of different genotypes in only one growing season. The College of Food and Agriculture Sciences at King Saud University in Riyadh region, Saudi Arabia, owns the station and its experiment facilities. The date palms are spaced 8 × 8 meters apart. Sandy soil is the category given to the soil. A drip irrigation system was used for irrigation. In addition to receiving mineral fertilizer appropriate for date palm trees, the orchard is fertilized using organic fertilizers. Every agricultural practice that took place here was carried out in accordance with the regular timetable for date palm plantations. For the investigation, the required data were extracted from nine male date palms. The males were labeled DPM1, DPM2, DPM3, DPM4, DPM5, DPM6, DPM7, DPM8, and DPM9. The trees were male seedlings of date palms. The chosen palm trees were robust, evenly sized, and in good health.

2.2. Morphological Features of Male Date Palm Leaves

In mid-October, four completely developed leaves were randomly selected from each male side. An average of six pinnae, three on each side, collected from the central section of the rachis were used to calculate the pinnae’s length and width. Measurements of morphological features such as, number of pinnae per leaf, leaf length, leaf width, pinnae length of the pinna part, pinna length, pinna width, length of the spathe stem, and spathe width were determined. Leaflets (pinnae) were defined as described by Zaid and Arias-Jimenez [18]. The leaf’s length was measured from the base of the lowest spine to the tip of the most proximal pinnae [28]. In addition, four fully grown spathes (Figure 1) were taken at random from every male tree. Recorded were spathe length, spathe weight, number of strands per spathe, strand length, number of flowers per strand, and the total number of flowers per spathe were recorded. Additionally, pollen grains samples were taken from the spathe of male date palms’ blooms. The weight of pollen grains per spathe, the pollen grain length, and the pollen grain width were determined.

2.3. Pollen Grains’ Viability

In order to avoid contamination from other pollen sources, three strands from distinct areas of each tree (three for each male) were separated using paper bags prior to anthesis. The threads of each spathe were snipped and then left to air-dry at a specific temperature of 25 ± 1 °C. Subsequently, the pollen grains and flowers were separated using fine sieves featuring a 40-mesh size [29]. This was followed by determining the weight of pollen grains per male. Pollen was gathered in small vials and stored at the temperature determined by Javady and Arzani [30] before being used. The length and width of pollen grains were measured at 20 KV using a Scanning Electron Microscope (SEM) of Stereoscan (360 SEM-FEI/Inspect S50 model), Manufacturer FEI, Model INSPECT S50, CAE Company, Menlo Park, CA, USA. According to Pearson and Harey [31], the pollen grains’ viability was evaluated using the germination method in Albert media, and the pollen tubes’ length was measured after a specific amount of time in a drop-hanging solution. The proportion of germinated grains was then calculated using the following equation

$$\mathrm{P}\mathrm{P}\mathrm{G}=\frac{\mathrm{G}\mathrm{P}\mathrm{G}\mathrm{N}}{\mathrm{T}\mathrm{N}\mathrm{G}\mathrm{P}\mathrm{G}}\times 100$$

(1)

where GPGN is the number of germinated pollen grains (-), TNGPG is the total number of germinated pollen grains (-), and PPG is the percentage of pollen grains that germinated (%).

2.4. Determination of Nutritional Status of the Male Trees’ Leaves

In mid-October, 20 pinnae (samples) from each of the four sides were harvested from the middle section of five successive leaves that were less than a year old, situated slightly above the fruiting zone, as per Rizk’s description [32]. For the determination of the mineral content in the leaves, leaf samples were cleaned using distilled water after first being treated with tap water, as per the methodology described by Evenhunis and De Waard [33]. After that, they were dried in an air-electric universal drying oven LDO-030E, Labtech, Korea. The oven was adjusted to 70 °C for 72 h, and the drying process was completed when a constant weight of the samples was achieved. After the drying process, the dry material samples were ground, and a 0.3 g of the ground dry material from each sample was digested with the help of sulfuric acid and hydrogen peroxide according to Evenhuis and De Waard [33]. A precision balance with a capacity of 2500 g/0.01 g (model KERN EMB precisions balance, Kern & Sohn Company, Waagen, Mikroskope, Germany) was used to determine each sample’s weight.

The Kjeldahl technique as described by Chapman and Pratt [34] was utilized to determine the nitrogen (N) content. Murphy and Riley [35] reported that the ascorbic acid method was used to quantify phosphorus (P). Total N and P were calorimetrically determined with a spectrophotometer (9100UV-VIS, PerkinElmer, Woodbridge, ON, Canada) according to the methods described by Evenhuis [36] and Murphy and Riley [35], respectively. For potassium (K), a flame photometer (model PFP7 PFP 7/C, Cole-Parmer Ltd., Staffordshire, UK) was used. Utilizing a Model 305 atomic absorption spectrophotometer (Perkin-Elmer Corp., Norwalk, CT 06586, USA), the amounts of calcium (Ca) and magnesium (Mg) were determined. On a dry weight basis, the concentrations of N, P, K, Ca, and Mg are shown as percentages. These measurements were taken at King Saud University’s Fruit Laboratory, which is housed in the College of Food and Agriculture Sciences in Riyadh, Saudi Arabia.

2.5. Structure of the Artificial Neural Network Model

In this research work, an artificial neural network (ANN) model was used as an alternative method to predict the performance parameters of pollen grains of male date palms, i.e., strand length, number of flowers per spathe, number of strands per spathe, weight of pollen grains per spathe, pollen grains’ width, number of flowers per strand, the pollen grains’ viability, and pollen grains’ length. The required data were collected during the growing season of 2021, based on field measurements of 15 properties, namely length of the pinna part, leaf length, leaf width, pinna width, pinna length, spathe length, number of pinnae per leaf, spathe width, length of spathe stem, strands per spathe, spathe weight, strand length, total number of flowers per spathe, and number of flowers per strand. Additionally, data were acquired from nine different males. Data from the measurement of the 15 attributes were acquired by the input layer in the ANN model. The data were processed by the hidden layer, and the continuous predicted values of the goal performance parameters were produced by the output layer. The values from the input layer connected to a hidden node were multiplied by their weights, a set of predetermined values, and the outcomes were used to create a new value. Ultimately, the generated value was supplied as an input to both an activation function and a mathematical function in order to forecast the desired specific values. As shown in Figure 2, the weighted value of a neuron was transformed into its sigmoid, an output activation function, by adding the weighted inputs that entered Node j and the output activation function of the neural network.

Equations (2) and (3), as described by Mohammed et al. [7], can be used to express the activation functions and the summation.

$${\mathrm{X}}_{\mathrm{o}\mathrm{j}}={\sum }_{\mathrm{i}=1}^{\mathrm{n}}{\mathrm{X}}_{\mathrm{i}}{\mathrm{W}}_{\mathrm{i}\mathrm{j}}+\mathrm{b}\mathrm{j}$$

(2)

$${\mathrm{O}}_{\mathrm{j}}=\frac{1}{1+{\mathrm{e}}^{{-\mathrm{X}}_{\mathrm{o}\mathrm{j}}}}$$

(3)

where X is the input value, with i being the number of inputs; O_j is the neuron’s output; W is the weight of the input; and X_oj is the result of the summation.

The weight values that determine the error function must be changed to reduce this inaccuracy. For a training set (X₁, t₁), (X₂, t₂), … (X_n, t_n) with k ordered pairings of n inputs and m outputs (the input and output patterns) [7], the error for the neurons’ output and the error function of minimizing the network’s error can be represented, for instance, by Equations (4) and (5).

$${\mathrm{E}}_{\mathrm{j}}=\frac{1}{2}{\left[{\mathrm{O}}_{\mathrm{j}}-{\mathrm{t}}_{\mathrm{j}}\right]}^2$$

(4)

$${\mathrm{E}}_{\mathrm{j}}=\frac{1}{2}\sum _{\mathrm{j}=1}^{\mathrm{k}}{\left[{\mathrm{O}}_{\mathrm{j}}-{\mathrm{t}}_{\mathrm{j}}\right]}^2$$

(5)

When the target value is t_j (Equation (4)), the input pattern from the training set produces the output O_j (Equation (4)), and E_j represents the errors. On the other hand, bias (represented by b_j in Figure 2) either increases or decreases the activation function’s net input [7]. An ANN model’s convergence toward the ideal solution is accelerated by increasing its learning rate until it is no longer possible to continue [7]. The ANN model can automatically forecast the linked outputs using a different dataset with unknown output values once a set of acceptable weights has been determined.

The multilayer perceptron (MLP) module designed by Vesta Services Company, which uses commercial software (Qnet v2000 for Windows), as reported in Silva et al. [37], made it simple to determine the best ANN model for this investigation. The typical backpropagation learning algorithm was used to train the MLP module of the neural networks, updating the weights in the direction of minimizing the error function. In order to prevent an algorithmic hidden bias with regard to the dataset’s higher values, normalization was applied to both the dataset’s input and outputs [38]. The software (Qnet v2000) was directed to achieve this normalization between 0.15 to 0.85. Once the predictions had finished, the software reversed the scaling data to be normal. The steps for building and testing the ANN model using the Qnet v2000 were illustrated by Al-Sager et al. [39]. Random choice by the Qnet v2000 software, which is now the most commonly used unsupervised splitting technique, guided the use of automatic random selection to prevent displaying bias in the choice of datasets [40]. Following the example of numerous other research results, the existing observations were assigned to training and testing datasets for the ANN model [41,42]. In this study, the software was directed to select nine patterns for the testing phase of all the data, and the rest (27 patterns) were for training purposes. The testing dataset were used to identify the faults in the training mode, while the training dataset was utilized to establish the weights and biases and build the ANN model. Generally, if the dataset was small, it was used as one dataset for both testing and validation purposes [43].

In order to use the ANN model, Qnet v2000 was used to create the model, and certain important parameters had to be established in order to obtain good results in the training data. Initially, by varying the weight during the training phase, the nodes’ size was determined via the learning rate coefficient. A quicker learning rate could be made possible by having a greater learning rate coefficient. However, this brought in instability and disarray. A smaller value for this coefficient’s can enhance the numerical convergence. A good procedure for the training data was provided without the possibility of divergence when the coefficient was within the range of 0.001 to 0.1 [44]. Subsequently, 0.8 was chosen as the momentum factor for Qnet’s training algorithm. There was no set method for choosing the number of iterations, and the problem’s complexity determined how many were needed. Finally, the Qnet v2000 defaults were applied after the remaining selections. Figure 3 displays the block diagram of the ANN (15-30-8) prediction model used. The definition and training controls of the network as acquired from Qnet v2000 software are displayed in Figure 4. In Figure 4, the learning rate was 0.077811, the momentum factor was 0.8, the training speed (CPS) was 31,942 K, the number of connections in the network (connected arcs between the input and hidden nodes, and between the hidden and the output nodes) was 690, the transfer function between the hidden and output nodes was a sigmoid function, the number of training iterations was 100,000, the training error was 0.000709, and the testing error was 0.052855. The training mode used by the Qnet v2000 software was a standard backpropagation method.

2.6. Evaluation of the ANN Model

The values of the root mean square error (RMSE), the coefficient of determination (R²), and mean absolute error (MAE) indices were used to evaluate the performance of the predictive ANN model. The indices of MAE and RMSE can be expressed as follows [45,46]

$$\mathrm{M}\mathrm{A}\mathrm{E}=\frac{1}{\mathrm{N}}{\sum }_{\mathrm{i}=1}^{\mathrm{N}}\left|\left(\mathrm{Y}\mathrm{i}-\widehat{\mathrm{Y}}\right)\right|$$

(6)

$$\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{E}=\sqrt{\frac{1}{\mathrm{N}}{\sum }_{\mathrm{i}=1}^{\mathrm{N}}{\left(\mathrm{Y}\mathrm{i}-\widehat{\mathrm{Y}}\right)}^2}$$

(7)

where Ŷ signifies the predicted value, Yi denotes the observed value, and N is the total number of data points in the testing and training sets.

2.7. Sensitivity Analysis

Sensitivity analysis is a useful technique for defining the influencing factor of the subordinate relationships in the existing practice from an evaluation of the main operator [43]. It is applied in a feed-forward ANN that has been trained to automatically detect all input parameters that affect the output. This approach is the best way to find the input’s percentage of contribution to the model’s outputs [47]. Furthermore, the sensitivity analysis method in the ANN approach may ascertain the percentage contributed by each input based on the output of the input node interrogator option in the Qnet v2000 program. By iteratively repeating the training patterns process with every input and computing the network’s output, this option can be utilized to calculate the sensitivity. Furthermore, it is important to keep in mind that the interpretation of the findings on sensitivity was predicated on the idea that the input value was independent. Therefore, the sensitivity method in neural networks determines the outcome of the influencing components of the subordinate relationships.

3. Results and Discussion

3.1. Statistical Analysis of the Features Used as Input Parameters in the Newly Developed ANN Model

The data on the leaves’ morphological traits, the pinnae’s morphological traits, the spathes’ morphological traits, and the nutritional status of the leaves were subjected to statistical analysis using Excel spreadsheets to evaluate their variation among the investigated male date palms. The average values ± standard deviation are shown in

Table 1. Average ± standard deviation of the experimental results of the input parameters (morphological features) in the newly developed ANN model.

Male Date Palms	Leaf Length	Leaf Width	Length of Pinna Part	Number of Pinnae per Leaf	Pinna Length	Pinna Width	Spathe Length	Spathe Width	Length of Spathe Stem	Spathe Weight
	(m)	(m)	(m)	(-)	(cm)	(cm)	(cm)	(cm)	(cm)	(kg)
DPM1	4.37 ± 0.04	0.35 ± 0.01	3.08 ± 0.02	204 ± 2.65	48.00 ± 3.65	3.43 ± 0.06	153.75 ± 0.96	18.13 ± 0.32	76.50 ± 1.29	4.10 ± 0.14
DPM2	3.68 ± 0.05	0.72 ± 0.02	2.78 ± 0.02	176 ± 1.83	43.98 ± 0.21	3.45 ± 0.02	123.56 ± 0.66	15.63 ± 0.32	51.25 ± 0.96	2.95 ± 0.13
DPM3	3.97 ± 0.10	0.49 ± 0.01	3.07 ± 0.02	178 ± 1.26	58.50 ± 0.74	4.17 ± 0.02	73.00 ± 2.16	14.75 ± 0.46	26.00 ± 0.82	2.04 ± 0.08
DPM4	4.14 ± 0.05	0.60 ± 0.01	3.04 ± 0.03	206 ± 3.65	44.25 ± 1.71	3.51 ± 0.06	94.00 ± 1.83	20.41 ± 0.17	52.50 ± 1.29	3.09 ± 0.10
DPM5	3.86 ± 0.03	0.59 ± 0.01	3.13 ± 0.02	188 ± 0.96	52.33 ± 0.06	3.52 ± 0.07	70.50 ± 1.29	17.64 ± 0.11	21.50 ± 0.54	2.23 ± 0.06
DPM6	3.57 ± 0.02	0.59 ± 0.01	2.62 ± 0.07	196 ± 0.82	47.44 ± 0.13	3.74 ± 0.05	117.89 ± 1.16	18.69 ± 0.13	47.45 ± 0.09	3.70 ± 0.04
DPM7	3.67 ± 0.04	0.47 ± 0.01	2.87 ± 0.02	210 ± 2.75	50.60 ± 0.29	3.86 ± 0.04	60.50 ± 1.29	17.68 ± 0.06	23.50 ± 0.58	1.65 ± 0.02
DPM8	3.84 ± 0.02	0.87 ± 0.02	2.75 ± 0.03	204 ± 1.29	47.95 ± 0.14	3.93 ± 0.03	72.00 ± 0.82	18.00 ± 0.09	16.66 ± 0.09	0.78 ± 0.02
DPM9	4.45 ± 0.03	0.49 ± 0.01	2.61 ± 0.03	202 ± 2.94	49.72 ± 0.30	3.77 ± 0.02	97.28 ± 0.55	13.02 ± 0.07	38.28 ± 0.22	1.58 ± 0.05

of the experimental results of the input parameters (morphological features) of the developed ANN model.

Table 2. Average ± standard deviation of the experimental results of input parameters (mineral composition of the leaves) in the newly developed ANN model.

Male Date Palms	N	P	K	Ca	Mg
	(%)	(%)	(%)	(%)	(%)
DPM1	0.98 ± 0.02	0.04 ± 0.001	1.01 ± 0.02	0.54 ± 0.01	0.15 ± 0.01
DPM2	0.94 ± 0.02	0.04 ± 0.001	0.81 ± 0.02	0.55 ± 0.01	0.14 ± 0.01
DPM3	0.86 ± 0.02	0.04 ± 0.002	1.25 ± 0.01	0.54 ± 0.01	0.15 ± 0.01
DPM4	0.96 ± 0.01	0.04 ± 0.0012	1.27 ± 0.02	0.46 ± 0.01	0.16 ± 0.01
DPM5	1.03 ± 0.04	0.04 ± 0.001	1.21 ± 0.01	0.47 ± 0.02	0.12 ± 0.01
DPM6	1.12 ± 0.04	0.06 ± 0.002	1.09 ± 0.03	0.43 ± 0.01	0.16 ± 0.01
DPM7	0.91 ± 0.03	0.05 ± 0.001	1.20 ± 0.02	0.49 ± 0.02	0.18 ± 0.01
DPM8	0.94 ± 0.02	0.05 ± 0.001	1.34 ± 0.01	0.35 ± 0.01	0.11 ± 0.01
DPM9	0.85 ± 0.01	0.05 ± 0.002	1.00 ± 0.02	0.52 ± 0.01	0.16 ± 0.01

shows the average ± standard deviation of the experimental results of the input parameters (mineral composition of the leaves) in the newly developed ANN model. According to the analysis of the morphological characters, the investigated male date palms revealed large variations in all characteristics. Twenty female date palm cultivars (Phoenix dactylifera L.) from Morocco were found to have significant morphological variability by Elhoumaizi et al. [48]. This provided an indicator for the identification of cultivars prior to ripening. These differences may have an impact on the males’ capacity to produce quality pollen grains [12]. Furthermore, one of the common methods used to identify date palm varieties and the degree of diversity is the use of morphological features [49]. Furthermore, Kassem [50] and Ibrahim et al. [51] revealed that the male date palms’ leaves had different concentrations of nutrients (N, P, K, Ca, and Mg).

3.2. Distribution of the Investigated Performance Parameters of Pollen Grains

Information on the variability in the investigated performance parameters of pollen grains among the examined male date palms was estimated by the average ± standard deviation based on eight attributes (

Table 3. Average ± standard deviation of the experimental results of the output parameters in the newly developed ANN model.

Male Date Palms	Number of Strands per Spathe	Strand Length	Number of Flowers per Strand	Number of Flowers per Spathe	Weight of Pollen Grains per Spathe	Pollen Grains’ Viability	Pollen Grains’ Length	Pollen Grains’ Width
	(-)	(cm)	(-)	(-)	(g)	(%)	(μm)	(μm)
DPM1	234 ± 2.63	35.31 ± 0.90	57 ± 1.29	13,205 ± 195.31	27.19 ± 0.69	84.25 ± 1.71	21.50 ± 0.54	10.23 ± 0.10
DPM2	286 ± 2.38	31.50 ± 1.29	62 ± 1.29	17,556 ± 227.90	18.78 ± 0.51	94.25 ± 1.26	19.51 ± 0.12	7.70 ± 0.12
DPM3	294 ± 1.29	30.50 ± 1.29	65 ± 0.96	19,152 ± 343.61	17.43 ± 0.06	85.50 ± 1.29	19.63 ± 0.10	8.45 ± 0.05
DPM4	246 ± 3.50	28.64 ± 0.11	50 ± 1.29	12,188 ± 309.93	19.45 ± 0.07	80.00 ± 1.83	19.38 ± 0.19	9.58 ± 0.10
DPM5	222 ± 2.89	26.78 ± 0.10	60 ± 1.29	13,178 ± 276.05	15.14 ± 0.05	88.25 ± 0.96	17.20 ± 0.08	6.94 ± 0.06
DPM6	284 ± 1.71	32.20 ± 0.37	51 ± 1.29	14,353 ± 298.46	15.65 ± 0.05	92.50 ± 1.29	19.34 ± 0.06	9.25 ± 0.02
DPM7	243 ± 2.65	21.50 ± 0.58	90 ± 2.16	21,823 ± 476.13	17.44 ± 0.02	83.50 ± 1.29	18.44 ± 0.09	7.21 ± 0.02
DPM8	201 ± 3.51	15.94 ± 0.02	59 ± 0.82	11,830 ± 276.74	14.75 ± 0.04	92.50 ± 1.29	18.49 ± 0.06	7.64 ± 0.02
DPM9	151 ± 3.16	27.62 ± 0.15	57 ± 0.96	8643 ± 88.29	29.01 ± 0.17	79.75 ± 0.96	20.27 ± 0.04	8.08 ± 0.10

). The data in Table 3 show that the greatest values of the number of strands per spathe were found for DPM2, DPM3, and DPM6, whereas DPM1, DPM4, DPM5, and DPM7 were characterized by medium values, and DPM8 and DPM9 were categorized as having the smallest values. For the number of flowers per strand, Table 3 shows that the greatest value of the number of flowers per strand was found for DPM7, whereas DPM1, DPM2, DPM3, DPM5, DPM8, and DPM9 were characterized by medium values, and DPM4 and DPM6 were categorized as having the smallest values. For the number of flowers per spathe, Table 3 shows that the greatest number of flowers per spathe was found for DPM3 and DPM7, whereas DPM1, DPM2, DPM4, DPM5, DPM6, and DPM8 were characterized by medium values, and DPM9 had the smallest value.

For the weight of pollen grains per spathe, Table 3 shows that the greatest value was for DPM1 and DPM9, whereas DPM2, DPM3, DPM4, DPM5, DPM6, and DPM7 were characterized by medium values, and DPM8 had the smallest values. For the pollen grains’ viability, Table 3 shows that the greatest value was for DPM2 and DPM6, DPM8, whereas DPM1, DPM3, DPM4, DPM5, and DPM7 were characterized by medium values, and DPM9 had the smallest value. For the pollen grains’ length, Table 3 shows that the greatest value was for DPM1 and DPM9, whereas DPM2, DPM3, DPM4, DPM6, and DPM8 were characterized by medium values, and DPM5 had the smallest value. For the pollen grains’ width, Table 3 shows that the greatest value was for DPM1, whereas DPM2, DPM3, DPM4, DPM6, DPM7, DPM8, and DPM9 were characterized by medium values, and DPM5 had the smallest value. Previous studies have confirmed that several male date palm cultivars have considerable variations in their vegetative characteristics and the characteristics of spathes [20,22]. Hachef et al. [8] confirmed that there are morphological differences among male palms. In the study of Elboghdady et al. [20], the results of the data analysis revealed significant differences among the male date palms’ genotypes in most of the vegetative characteristics of the leaves, leaflets, spines, and spathes. In addition, pollen grains differed in their width and shape, and these findings were observed in [10,11,52]. Moreover, as shown in Table 3, the pollen grains’ viability of the male date palms was different, and this was seen by Nesiem et al. [53], El-Salhy et al. [54], and Islam [55], who reported that the sources of pollen grains had a positive effect on the characteristics of fruits and seed. There were negative correlations among viability, the germination of pollen grains, and bunch weight, while there was a positive correlation between fruit set and fruit retention. Thus, pollinators must be selected individually for each date palm cultivar [55]. Generally, an accurate description of male date palm trees is an approach for the formation of commercial plantations [56]. Moreover, Ibrahim et al. [57] claimed that the gain in the length and width of date palm pollen grains was 19.7 ± 8.6 μm and 8.6 ± 0.9 μm at 4% db moisture content, and they reported that such dimensions could be supportive of the performance of date palm pollination machines.

3.3. Performance of the Newly Developed ANN Model

The ANN procedure in Qnet v2000 software was adopted to set the optimal ANN model to predict the pollen grains’ productivity and the viability of male date palms’ attributes. The number of hidden layers was one. The input layer in the ANN contained 15 nodes for the independent variables (leaf length and leaf width, length of the pinna part, number of pinnae per leaf, pinna length, pinna width, spathe length, spathe width, spathe length, and spathe weight, and N, P, K, Ca, and Mg in the leaves). The optimal hidden layer contained 30 nodes. The output layer contained eight neurons for the dependent variables (number of strands per spathe, strand length, number of flowers per strand, number of flowers per spathe, weight of pollen grains per spathe, the pollen grains’ viability, the pollen grains’ length, and the pollen grains’ width). The activation function applied for the hidden layer was a sigmoid. The statistical criteria after the training and testing phases for the newly developed ANN model using Qnet v2000 software are displayed in

Table 4. Statistical criteria after the training phase for the newly developed ANN model.

Output Nodes	Standard Deviation	Bias	Maximum Error
Number of strands per spathe	0.19	−0.0021	0.55
Strand length (cm)	0.01	−4.09 × 10−5	0.04
Number of flowers per strand	0.02	0.0006	0.06
Number of flowers per spathe	12.33	−0.11	43.85
Weight of pollen grains per spathe (g)	0.03	−7.74 × 10−6	0.07
Pollen grains’ viability (%)	0.006	0.0002	0.015
Pollen grains’ length (μm)	0.006	3.95 × 10−5	0.019
Pollen grains’ width (μm)	0.002	2.80 × 10−5	0.003

and

Table 5. Statistical criteria after the testing phase for the newly developed ANN model.

Output Nodes	Standard Deviation	Bias	Maximum Error
Number of strands per spathe	10.42	−3.92	22.09
Strand length (cm)	1.54	0.08	2.60
Number of flowers per strand	3.14	−1.07	5.57
Number of flowers per spathe	977.61	−360.97	1946.16
Weight of pollen grains per spathe (g)	0.88	0.18	1.74
Pollen grains’ viability (%)	2.10	−0.06	3.52
Pollen grains’ length (μm)	0.40	0.013	1.094
Pollen grains’ width (μm)	0.12	0.04	0.23

, respectively. The values of bias were less than 1 for all output nodes during the training phase, indicating the high accuracy of the investigated ANN model in making predictions (Table 4). Additionally, compared with the training phase, the output nodes’ bias values were somewhat greater during the testing phase (Table 5).

A comparison of the error results of the newly constructed ANN model, namely the mean absolute error (MAE), the root mean square error (RMSE), and the coefficient of determination (R²) in the training and testing phases is shown in

Table 6. Comparison of statistical indices for the performance of the ANN model (15-30-8) for the training and testing datasets.

Output Nodes	Training Dataset			Testing Dataset
	RMSE	MAE	R2	RMSE	MAE	R2
Number of strands per spathe	0.19	2.88	1.000	10.42	2.88	0.902
Strand length (cm)	0.01	1.16	0.999	1.549	1.16	0.967
Number of flowers per strand	0.02	1.67	0.999	3.143	1.67	0.963
Number of flowers per spathe	12.33	28.03	0.999	977.61	28.03	0.941
Weight of pollen grains per spathe (g)	0.03	0.80	0.999	0.88	0.80	0.985
Pollen grains’ viability (%)	0.006	1.32	0.999	2.10	1.32	0.810
Pollen grains’ length (μm)	0.006	0.51	0.999	0.40	0.51	0.936
Pollen grains’ width (μm)	0.002	0.32	0.999	0.12	0.32	0.992

. According to these results, the investigated independent variables could successfully predict the dependent variables of the number of strands per spathe, strand length, number of flowers per strand, number of flowers per spathe, weight of pollen grains per spathe, the pollen grains’ viability, pollen grains’ length, and pollen grains’ width.

Figure 5 depicts the scatter graphs of the observed values of the number of strands per spathe and strand length against the values predicted by the ANN model in the testing stage on the basis of the measured independent variables. Moreover, Figure 6 depicts the scatter graphs of the observed values of number flowers per strand and the number of flowers per spathe against the values predicted by the ANN model in the testing stage on the basis of the measured independent variables. Additionally, Figure 7 depicts the scatter graphs of the observed values of the weight of pollen grains per spathe and the pollen grains’ viability against the predicted values by the newly developed ANN model in the testing phase on the basis of the measured independent variables. Furthermore, Figure 8 depicts the scatter graphs of the observed values of the pollen grains’ length and the pollen grains’ width against the values predicted by the newly developed ANN model in the testing phase on the basis of the measured independent variables.

The ANN model’s structure was composed of one hidden layer with 30 nodes, which displayed the highest level of accuracy. The regression line connecting the target performance parameters’ observed and predicted values for the number of strands per spathe (y = 1.0125x − 7.0561, R² = 0.902) and strand length (y = 1.1324x − 3.6178, R² = 0.967), using the testing dataset, had approximately high correlations (Figure 5). The regression line connecting the target performance parameters’ observed and expected values for the number of flowers per strand (y = 0.8882x + 6.0808, R² = 0.963) and the number of flowers per spathe (y = 0.9515x + 417.36, R² = 0.941), using the testing dataset, had approximately high correlations (Figure 6). The regression line between the predicted and the observed values of the target performance parameters for the weight of pollen grains per spathe (1.1523x − 2.7754, R² = 0.985) and pollen grains’ viability (y = 0.988x + 0.9844, R² = 0.810), using the testing dataset, had approximately high correlations (Figure 7). The regression line connecting the target performance parameters’ observed and expected values for the pollen grains’ length (y = 1.2128x − 4.146, R² = 0.936) and pollen grains’ width (y = 1.0277x − 0.1944, R² = 0.992), using the testing dataset (Figure 8), had approximately high correlations.

Growing date palms is regarded as one of the key economic drivers in many nations, Saudi Arabia included. The nutritional and therapeutic value of this tree’s fruits, as well as their potential applications in certain biochemical processes, make them extremely valuable [58]. Furthermore, in order to enhance farmers’ abilities, with the goal of maintaining date palm plantations, several studies pertaining to the influence of agricultural extension services are required. Using some of the new methodologies, another set of studies might be proposed that deal with modeling the interactions between the date palm plantation and the cultivated land [59]. Artificial intelligence and other cutting-edge technology are being used by the date palm industry to meet international requirements for sustainability. However, date palm agriculture is being improved by intelligent systems that use artificial intelligence and machine vision [58,60,61,62,63]. Artificial intelligence has the potential to improve crop management, facilitate predictive analytics, boost productivity, and encourage sustainable date palm farming [64]. As far as we are aware, no research has used feed-forward artificial neural networks (ANNs) in conjunction with a backpropagation training technique to predict the parameters pertaining to the performance of the pollen grains in male date palms (the number of flowers per strand, pollen grains’ viability, number of strands per spathe, pollen grains’ length, strand length, weight of pollen grains per spathe, number of flowers per spathe, and the pollen grains’ width) on the basis of the morphological features of leaf length, the length of the pinna part, leaf width, pinna length, number of pinnae per leaf, pinna width, spathe length, length of the spathe stem, spathe width, and spathe weight, as well as concentrations of minerals such as Ca, N, Mg, P, and K in their leaves.

Several research studies [65,66,67,68,69,70] have discussed the use of the ANN technique for categorizing date fruits. Since it is extremely difficult for the human eye to distinguish similar things, such as date fruit, others have used ANN models to identify varieties of date palm using leaves and fruits [71]. They concentrated on distinguishing the different types of date fruits by utilizing photos of both dates and palm leaves. They had a good accuracy of 99.82% for the fruit model. However, Shoukry [72] proposed an ANN model-based method of detecting change for monitoring palm tree plantations. An ANN model was proposed by Eskandari et al. [73] to estimate the date yield on the basis of soil parameters. Additionally, scientists have claimed that the ANN model is better than previous destructive methods, since it can evaluate and estimate date fruits’ quality in cold storage, whereas standard destructive methods require time in the laboratory. Mohammed and others [7], and Rybacki et al. [70] used a convolutional neural network to build an automatic classification model for different varieties of date palm fruits based on two crucial factors: differences in color and assessment of the geometric limitations of dates. The selection of the classification criteria determined the validation accuracy of the model presented in that study. Fruit color-based categorization had an accuracy of 85.24%, while geometric limitations alone produced an accuracy of 87.62%. However, when the dates’ geometry and color were carefully considered, the accuracy increased to 93.41%. Overall, according to the authors, good accuracy was achieved via the experiment. These ANN models’ reliance on data for training presented a challenge. In order to accomplish a certain job, the internal depiction of the model is updated during the training stage of the models [72]. Furthermore, it alters the network’s architecture by adjusting individual neurons’ firing rules, altering the linkages’ weights, and changing the connecting links by adding or deleting links [74].

3.4. Outcome of the Sensitivity Analysis

The independent variables made different contributions to the pollen grains’ productivity and the viability of male date palms’ attributes in the newly developed ANN model of 15-30-8. By using the input node interrogator in Qnet v2000 software, the inputs influence on the outputs could be understood by the percentages of contribution.

Table 7. Percentages of contribution of the inputs to outputs using the ANN model of 15-30-8.

Output Node’s Number	Output Node’s Name	Input Node’s Number	Input Node’s Name	Percentage Contributed
1	Number of strands per spathe	1	Leaf length	10.96
		2	Leaf width	2.77
		3	Length of the pinna part	4.93
		4	Number of pinnae per leaf	9.61
		5	Pinna length	7.16
		6	Pinna width	12.5
		7	Spathe length	4.52
		8	Spathe width	8.72
		9	Length of spathe stem	17.66
		10	Spathe weight	6.66
		11	N	3.16
		12	P	4.16
		13	K	1.80
		14	Ca	2.47
		15	Mg	2.93
2	Strand length	1	Leaf length	4.50
		2	Leaf width	4.89
		3	Length of the pinna part	7.65
		4	Number of pinnae per leaf	5.90
		5	Pinna length	2.03
		6	Pinna width	6.21
		7	Spathe length	4.92
		8	Spathe width	4.35
		9	Length of spathe stem	4.68
		10	Spathe weight	26.29
		11	N	6.38
		12	P	4.71
		13	K	2.83
		14	Ca	10.67
		15	Mg	3.98
3	Number of flowers per strand	1	Leaf length	8.28
		2	Leaf width	13.18
		3	Length of the pinna part	3.33
		4	Number of pinnae per leaf	10.69
		5	Pinna length	3.82
		6	Pinna width	1.39
		7	Spathe length	11.85
		8	Spathe width	2.59
		9	Length of spathe stem	10.45
		10	Spathe weight	6.62
		11	N	4.98
		12	P	2.54
		13	K	13.98
		14	Ca	3.14
		15	Mg	3.17
4	Number of flowers per spathe	1	Leaf length	11.38
		2	Leaf width	12.55
		3	Length of the pinna part	4.54
		4	Number of pinnae per leaf	7.01
		5	Pinna length	4.56
		6	Pinna width	6.23
		7	Spathe length	12.37
		8	Spathe width	5.94
		9	Length of spathe stem	4.66
		10	Spathe weight	7.35
		11	N	4.4
		12	P	2.37
		13	K	10.99
		14	Ca	3.27
		15	Mg	2.38
5	Weight of pollen grains per spathe	1	Leaf length	12.57
		2	Leaf width	8.15
		3	Length of the pinna part	2.23
		4	Number of pinnae per leaf	9.4
		5	Pinna length	2.97
		6	Pinna width	2.17
		7	Spathe length	2.32
		8	Spathe width	10.09
		9	Length of spathe stem	17.85
		10	Spathe weight	2.44
		11	N	5.90
		12	P	1.91
		13	K	12.14
		14	Ca	5.37
		15	Mg	4.48
6	Pollen grains’ viability	1	Leaf length	9.40
		2	Leaf width	4.65
		3	Length of the pinna part	9.44
		4	Number of pinnae per leaf	2.89
		5	Pinna length	6.25
		6	Pinna width	7.24
		7	Spathe length	6.23
		8	Spathe width	3.28
		9	Length of spathe stem	9.37
		10	Spathe weight	14.92
		11	N	5.76
		12	P	3.41
		13	K	4.95
		14	Ca	3.75
		15	Mg	8.46
7	Pollen grains’ length	1	Leaf length	4.60
		2	Leaf width	5.24
		3	Length of the pinna part	3.97
		4	Number of pinnae per leaf	3.46
		5	Pinna length	5.16
		6	Pinna width	8.70
		7	Spathe length	8.37
		8	Spathe width	13.35
		9	Length of spathe stem	19.78
		10	Spathe weight	2.87
		11	N	5.99
		12	P	3.47
		13	K	3.52
		14	Ca	6.16
		15	Mg	5.36
8	Pollen grains’ width	1	Leaf length	5.98
		2	Leaf width	4.51
		3	Length of the pinna part	2.69
		4	Number of pinnae per leaf	3.69
		5	Pinna length	3.35
		6	Pinna width	8.80
		7	Spathe length	4.51
		8	Spathe width	4.80
		9	Length of spathe stem	30.59
		10	Spathe weight	7.03
		11	N	2.23
		12	P	3.86
		13	K	7.97
		14	Ca	4.75
		15	Mg	5.23

shows the percentages of contribution for all the dependent variables. As a result, the length of the spathe stem had the most critical effect on how the ANN predicted the values of the dependent variables, i.e., the number of strands per spathe, weight of pollen grains per spathe, pollen grains’ length, and pollen grains’ width, with percentages of 17.66%, 17.85%, 19.78%, and 30.59%, respectively. Spathe weight had the most critical effect on strand length and pollen grains’ viability, with percentages of 26.29% and 14.92%, respectively. Leaf width has the most critical effect on the number of flowers per spathe, with a percentage of 12.55%. The concentration of K in the leaves of male date palms had the most critical effect on the number of flowers per strand, with a percentage of 13.98%. Hence, these variables could impact the choice type of subordinate contractor associations.

4. Conclusions

One of the most significant characteristics of pollen grains that influence pollination is the morphological properties. This study was undertaken to model the performance parameters of the pollen grains of male date palms using an artificial neural network (ANN). The inputs to the ANN model were based on the morphological properties of the male date palms’ leaves and the leaves’ mineral compositions. The nonlinear connections between many variables were used by the ANN model to generate a novel solution based on data that were measured in the field. A 15-neuron input layer, a 30-neuron hidden layer, and an 8-neuron output layer made up the ideal ANN model. With a higher coefficient of determination and a lower root mean squared error, this model improved its quick and simple predictions of the pollen grains’ viability, strand length, weight of pollen grains per spathe, number of strands per spathe, number of flowers per strand, pollen grains’ length, and pollen grains’ width. The findings demonstrated that the ANN model is an effective means of predicting the performance characteristics of male date palms, with a coefficient of determination (R²) ranging from 0.902 to 0.992 for the parameters under investigation when the testing data were used. The limitation of the research is the small training dataset used to make the model more generalizable. Although the ANN modeling analysis in the present study relied on data from only one growth season during the building of the ANN model, because of the encouraging results, consequently, this research work could be a starting point for mathematical analysis associated with the physiological mechanisms of male date palms. In addition, the performance parameters of the pollen grains of male date palms (Phoenix dactylifera L.) could be examined in real time with the ease of measuring some features and an ANN prediction model.