Nutrient Requirements and Growth Response of Harumanis Mango (Mangiferaindica L.) during Vegetative Shoot Growth Stages: A Mitscherlich Law Analysis

This study investigates the nutrient requirements of Harumanis mango (Mangifera indica L) during different vegetative shoot growth stages by analyzing the soil nutrient test value-relative growth relationships. The research utilizes the Mitscherlich Law to model the response of mango yield in relation to varying nutrient levels. The data came from experimental plots, and the results show the asymptotic behavior of mango yield for three essential nutrients: nitrogen (N), phosphorus (P), and potassium (K). For vegetative shoot growth1, the asymptotic yield was estimated at 665.5 with a decline rate of -3.39 concerning N, -2.17 concerning P, and -1.35 concerning K. The coefficient of determination (R2) was 0.934, indicating a high goodness of fit for the model. Similar trends were observed for vegetative shoot growth2 and 3, where the asymptotic yields and nutrient decline rates varied accordingly. This study provides crucial insights into Harumanis mango nutrient needs across growth stages, aiding orchard management for sustainable yields. Applying the Mitscherlich Law enhances our understanding of how nutrients affect mango growth. These findings support targeted fertilization, boosting productivity and orchard efficiency. Future research can explore more growth factors and long-term nutrient impacts.


Introduction:
Mango (Mangifera indica L) is one of the most economically important fruit crops globally, cherished for its succulent, sweet, and aromatic fruits.Among the various mango varieties [1], Harumanis mango holds a special place due to its unique flavor, attractive appearance, and high market demand [2].However, to maintain sustainable mango production and optimize fruit yield, it is crucial to understand the intricate relationship between soil nutrient levels and mango growth during different stages of vegetative shoot flush [3] [4].The soil nutrient management plays a pivotal role in the growth and development of fruit trees, including mango [4].Adequate and balanced nutrient supply is essential to support the plant's physiological processes, such as photosynthesis, nutrient uptake, and fruit development.Insufficient or excessive nutrient levels can lead to reduced growth, suboptimal yields, and increased susceptibility to diseases and pests [5] [6].
In an optimized mango cultivation practices, it is imperative to investigate the soil nutrient-test value relative growthrelationships [7].The Mitscherlich Law, is a well-established model in agricultural research, which was widely used to understand the impact of nutrient availability on plant growth [8][9].By employing this model, the objective is to explore the asymptotic behavior of mango yield concerning three vital nutrients: N P K during different Vegetative Shoot growth stages [8][10].
In this study, the results of the comprehensive analysis of soil nutrient-test value relative growth relationships for Harumanis mango using the Mitscherlich Law were presented [14] [15].The experiments were conducted in controlled plot conditions to gather data on mango yield responses to varying nutrient levels.Subsequently, the asymptotic yield and nutrient decline rates was calculated for each nutrient across different Vegetative Shoot growth stages [12] [13].The outcomes of this research are anticipated to contribute significantly to mango cultivation practices and orchard management.By discerning the specific nutrient requirements of Harumanis mango during various growth phases, it's possible to develop targeted fertilization strategies that maximize fruit yield while ensuring efficient.
This study sheds light on the complex interplay between soil nutrient levels and mango yield, offering valuable insights for farmers, agronomists, and researchers to make informed decisions in optimizing mango production and sustaining the cultivation of the beloved Harumanis mango variety.The integration of the Mitscherlich Law as a modeling tool enhances our understanding of mango growth dynamics, paving the way for improved orchard management practices and increased fruit productivity.Moreover, the findings may serve as a foundation for future research endeavors aimed at exploring additional factors influencing mango growth and expanding our knowledge of sustainable fruit cultivation techniques

Experimental Design:
To ensure robustness and reduce potential bias, the study was carried out utilizing a randomized complete block design (RCBD) with numerous replications.Every stage of the Harumanis mango's Vegetative Shoot growth was included in the study and treated separately.

Vegetative Shoot Growth Stages
The mango trees were monitored for Vegetative Shoot growth stages, and data were recorded for each stage separately.The stages were carefully identified based on observable growth patterns and physiological changes in the trees.

Mango Yield Measurement:
Mango yield was quantified for each experimental plot during the respective Vegetative Shoot growth stage.
The number of fruits per tree and fruit weight were recorded to calculate the total yield per plot.

Application of Mitscherlich Law:
The Mitscherlich Law model was utilized to analyze the soil nutrient test value-relative growth relationships.The model considers the asymptotic behavior of yield response concerning nutrient levels in the soil.The following equation represents the Mitscherlich Law model: Where: Asymptote: Represents the maximum achievable response as X increases.b: Indicates the rate of decline in yield concerning nutrient levels.X: Indicates the concentration of the particular nutrient (N, P, or K) within the soil in terms of nutrient level. 8th

Curve Fitting
The Mitscherlich Law model was fitted to the yield data for each nutrient (N, P, and K) and Vegetative Shoot growthstage using appropriate statistical R software.The general form of the curve fitting equation for the Mitscherlich Law model is represented in equation 1.The curve fitting process involves finding the best-fitting values for the parameters Asymptote and b that minimize the difference between the observed mango yield data and the model's predictions based on the nutrient levels in the soil.This is usually done through optimization techniques such as least squares fitting, which aims to minimize the sum of squared differences between the observed and predicted yield values.

Coefficient of Determination (R 2 ) and Root Mean Square Error (RMSE)
The goodness of fit of the model was assessed by calculating the coefficient of determination (R 2 ) and the root mean square error (RMSE).R 2 provides a measure of how well the model explains the variance in the data, while RMSE represents the average difference between the observed and predicted values.The coefficient of determination, denoted as R 2 , is a statistical measure that represents the proportion of the variation in the dependent variable (in this case, mango yield) that is explained by the independent variable(s) (nutrient levels).In the context of the Mitscherlich Law analysis, R 2 indicates how well the model fits the observed mango yield data based on the nutrient levels in the soil.R 2 ranges from 0 to 1, where: x R 2 = 0 indicates that the model does not explain any of the variation in the data, and the model's predictions are no better than simply using the mean value of the dependent variable (yield) as a predictor.
x R 2 = 1 signifies a perfect fit of the model to the data, where all the variation in the dependent variable can be explained by the independent variable(s) in the model.

Root Mean Square Error (RMSE):
Root Mean Square Error, denoted as RMSE, is a measure of the average difference between the observed values (mango yield data) and the predicted values from the Mitscherlich Law model.It quantifies the accuracy of the model's predictions, reflecting how well the model fits the observed data.
RMSE is calculated as follows: where n is the number of data points (number of experimental plots in this study).yi represents the observed mango yield for the i-th experimental plot.‫ݕ‬ ො denotes the predicted mango yield from the Mitscherlich Law model for the i-th experimental plot.
R 2 and RMSE are important statistical metrics used to evaluate the goodness of fit of the Mitscherlich Law model in explaining the mango yield response concerning variations in nutrient levels.A high R 2 value and a low RMSE value together indicate a well-fitted model that effectively captures the relationship between nutrient availability in the soil and mango yield during different Vegetative Shoot growth stages.

Results
The results were thoroughly analyzed to identify trends and patterns in the nutrient-yield relationships for Harumanis mango during various Vegetative Shoot growth stages.The significance of each nutrient's impact on mango yield was determined based on p-values obtained from the statistical analysis.

Target and CSTV90:
The "target" column represents the target value for each nutrient, which is presumably the desired level of the nutrient in the soil for optimal yield.CSTV90 refers to the Coefficient of Soil Test Value at 90%, which may be an indicator of the soil nutrient level where 90% of the asymptotic yield is achieved.

Model Comparison:
The AIC, AICc, and BIC values are provided for model comparison.Lower values of AIC, AICc, and BIC indicate better model fits.It is important to consider these criteria when selecting the bestfitted model for explaining the relationship between nutrient levels and mango yield.

Coefficient of Determination (R 2 ) and Root Mean Square Error (RMSE):
The coefficient of determination (R 2 ) measures how well the model explains the variance in the data.Higher R 2 values (closer to 1) indicate a better fit of the model to the observed data.Root mean square error (RMSE) represents the average difference between the observed and predicted values.Lower RMSE values indicate a better fit of the model to the data.

P-values:
The p-values are provided for each nutrient and Vegetative Shoot growth stage.P-values indicate the statistical significance of the nutrient's effect on mango yield during a specific Vegetative Shoot growth stage.A smaller p-value (usually less than 0.05) suggests that the nutrient significantly influences mango yield during that particular stage.
Overall, the results demonstrate that the Mitscherlich Law model has been applied to the data to study the impact of NPKon mango yield during different Vegetative Shoot growth stages.The model provides insights into the nutrient requirements of Harumanis mango at various growth stages, contributing to improved mango orchard management and sustainable fruit production practices.The statistical analysis and model comparisons provide a robust basis for making informed decisions about nutrient management strategies, tailored to optimize mango productivity and ensure efficient resource utilization.

Conclusion
In order to assess the soil nutrient test value-relative growth connections for the Harumanis mango during various Vegetative Shoot growth stages, this study used the Mitscherlich Law model.The findings have important ramifications for mango cultivation and orchard management by delivering vital insights into the nutrient requirements and their effect on mango yield.The investigation showed that NPK had a big impact on mango yield at different Vegetative Shoot growth phases.As the mango trees grew and developed, their nutrient requirements altered, as shown by the asymptotic yield values and decline rates (b) for each nutrient across the various stages.The comparison of models using the Akaike Information Criterion (AIC), corrected AIC (AICc), and Bayesian Information Criterion (BIC) allowed us to identify the best-fitted models for each nutrient and Vegetative Shoot growth stage.These model selection criteria ensured that the chosen models strike a balance between goodness of fit and complexity, enhancing the reliability of the findings.
The coefficient of determination (R 2 ) indicated a high degree of variation in mango yield explained by the Mitscherlich Law model, reflecting its suitability in capturing the nutrient-yield relationships.Additionally, the low root mean square error (RMSE) values demonstrated the model's accuracy in predicting mango yield based on soil nutrient levels.
The study's findings have practical implications for mango farmers, agronomists, and researchers.By understanding the specific nutrient requirements of Harumanis mango during distinct Vegetative Shoot growth stages, tailored fertilization strategies can be developed to optimize fruit production and improve overall orchard efficiency.The results offer valuable guidance to farmers in making informed decisions about nutrient management practices, leading to sustainable mango cultivation and increased fruit productivity.
Moreover, the application of the Mitscherlich Law model has enriched our understanding of mango growth dynamics concerning nutrient availability in the soil.This research provides a foundation for further studies exploring additional factors influencing mango growth and the long-term effects of nutrient management on mango orchards.
In conclusion, this study contributes to the body of knowledge surrounding mango cultivation practices, providing essential data to support evidence-based decisions for sustainable mango production.The insights gained from this research have implications not only for the cultivation of Harumanis mango but also for other fruit crops, promoting efficient and environmentally responsible agricultural practices. 8th

2 .
Sampling Time: Data collection took place daily from 7:00 am to 3:00 pm throughout the research period.3. Daily Data Collection: On each day, eight data samples were taken.4. Data Sampling Procedure: For each data sampling event, measurements were recorded at tenminute intervals for six consecutive samples (10 minutes x 6 samples = 1 hour (1 data)) one day will get 8 sample data (7.00am to 3.00pm).Subsequently, the average value of these six data points was calculated. 5. Frequency of Sampling: A total of 2920 (8 sample per day x 365 days) data points were collected in one season (14 May2020 -21 May 2021).

Table 1
Results Analysis of Soil Nutrients (N, P and K) at various vegetative shoot growths.
The table presents the results of the analysis of soil nutrient test value-relative growth relationships for Harumanis mango during different Vegetative Shoot growth (VSG) stages (Vegetative Shoot growth1, Vegetative Shoot growth2, and Vegetative Shoot growth3).
International Conference on Man Machine Systems 2023 Journal of Physics: Conference Series 2641 (2023) 012007