non linear regression

Recently, pseudo-continuous transfer functions (PC-PTFs) have been introduced for estimating soil water retention curve (SWRC). The M5 tree method is similar to regression trees, where linear functions are located in its leaves, and it has a high capability in creating transfer functions. These functions are highly sensitive to the power of machine learning algorithms. However, so far, the powerful M5 tree method has not been used to develop PC-PTFs for a wide range of soil textures. Additionally, the effectiveness of some soil structural variables in improving PC-PTFs has not been investigated, so far. Furthermore, the dependency of the error distribution of PC-PTFs on soil textural triangles to various factors has not been deeply examined. Therefore, the objectives of this study were to develop PC-PTFs using the M5 method, investigate the effect of soil structural variables on the performance of these functions, and examine the error dependence of these functions on different factors. A total of 120 soil samples were collected from depths of 10 to 60 centimeters, with agricultural, orchard, and pastureland uses of Tehran and Hamedan provinces, and soil texture, bulk density (BD), SWRC, saturated hydraulic conductivity (Ks), organic matter (OM), mean weight diameter (MWD) of soil aggregates, and penetration resistance at 300 hectopascals (PR300) were measured. Thirteen PC-PTFs, in three groups of inputs, were developed to estimate SWRC, using M5 tree and non-linear regression methods. The error distribution of all PC-PTFs was plotted on the soil texture triangle, according to root mean square error (RMSE). In the first function, soil suction was used as the only estimator. A non-linear regression model produced an acceptable model for the first function with a R2 of 0.718. In PC-PTFs 3 to 6, components of soil texture, BD, and FC (at 300 hPa matric suction) and PWP (at 15000 hPa matric suction) moisture contents were used to estimate SWRC. The R2for these functions ranged from 0.719 to 0.990, indicating an improvement in the performance of SWRC estimation. In the M5 method, the use of FC significantly improved the model performance and created an optimal model, resulting in RMSE of 0.015 and 0.020 cm³cm⁻³, and R² of 0.987 and 0.973 in the training and validation stages, respectively. In the M5 method, any function using Ks and MWD as estimators showed significant improvement compared to PC-PTF4, which used soil texture components and BD as estimators. The AIC values in both training and validation stages in the M5 method were 37% to 283% and 111% to 157% lower compared to non-linear regression, respectively. The error distribution on the soil texture triangle showed no dependence on soil texture but was related to the method of creating PC-PTFs and relevant input variables. A powerful artificial intelligence methods can be employed to create a comprehensive model for SWRC. This would eliminate the need for users to rely on various SWRC models such as van Genuchten for different soils. Incorporating a set of soil texture and structure variables increases the accuracy of SWRC estimation. However, among structural variables, those indicating pore size distribution were more suitable for SWRC estimation. The greater impact of FC compared to PWP demonstrated the higher efficiency of moisture in intermediate matric suctions for SWRC estimation. The robust algorithm of the M5 tree method identified some patterns of relationships between input and output variables that were not detectable by non-linear regression. Considering the dependence of error distribution on the soil texture triangle to the method of creating PC-PTFs and input variables, categorizing error distribution maps should be done based on the mentioned factors.

Growth traits (such as body weights at different ages) in most of the birds have been often considered in most of the poultry breeding programs. Changes in growth pattern can be evaluated through measuring body weight traits at regular intervals and using mathematical functions (growth curve functions). For this purpose, data from 1182 wild (including 905 female and 277 male) and 674 Italian speckled (including 499 female and 175 male) quails were utilized. Accordingly, after body weight at hatch, body weights of the birds were recorded through 45 days in a 5-day interval manner. Gompertz, Logistic, Lopez, Richards, and von Bertalanffy were used to estimate growth curve parameters. To evaluate/ rank the goodness of fit for functions, the BIC, AIC, MSE, and  were used. Based on results, Richards’ function for both studied populations (wild and Italian speckled quails) and for both genders (females and males) were the best fitted model. The relatively same growth pattern and same function for describing growth pattern in these two quail strains refer to the same growth traits, therefore simultaneous production of them can be achieved under same management practices. Moreover, comparing results of the current studies with other researches, by comparing other studies with this study’s results, it can be concluded that increasing the number of records and shortening the weighing intervals can be effective in determining the appropriate function.

Nowadays, identification of the yield limiting factors in the field particularly the various yield components including number of panicle per unit area, number of seeds per panicle and seed weight) is one of the most important methods to increase the production of rice. The yield gap (YG) analysis can be performed by measuring the yield related characteristics. Yield gap was estimated as the difference between actual and potential yield that has been used in various studies as an important indicator to increase the yield in crops and different areas. One of the most powerful methods to evaluate the reasons of yield potential and yield gap is boundary line analysis. The purpose of this research was to select an appropriate function for describing the relationship between yield and yield components in the Fumann plain of Guilan province. Furthermore, after selecting the superior function, the parameters of the yield and yield components were estimated  to calculate the yield gap in the region. The present study was carried out during two cropping seasons: 2012-13 and 2013-14 in Foumanat plain (cv. ‘Tarom Hashemi’). We recorded the geographic coordinates of 53 fields. At the end of growing season (harvesting time), paddy yield and yield components (panicle number, filled grain number and 100- grain weight) were calculated in each field. The correlation coefficients between yield components and yield were studied. Segmented, quadratic and dent-like models were applied to describe the relationship between yield and yield components. Root mean square error (RMSE), determination coefficient (R2), regression simple coefficients (a & b) and coefficient of variation (CV) were used to identify the appropriate model. After selecting a superior model, the boundary line method was used to calculate yield gap and its percentage, optimum yield and optimum amount of yield components for each field. According to the results, a positive and significant correlation was existed between paddy yield with panicle number and filled grain number with 100- grain weight and a negative and significant correlation was existed between 100- grain weights with panicle number. Linear regression simple coefficients for all traits studied in the quadratic function and for two traits of panicles number per square meter and of filled grains number in the panicle in the segmented model were significant. Among the fitted models, segmented model has the lowest RMSE (respectively equal to 0.082 and 0.472) and coefficient of variation (equal to 1.26 and 6.39, respectively) in terms of two characteristics of panicle number and 100- grain weight and was able to describe the trend of the experimental data. In addition, dent-like model with the lowest RMSE (equal to 0.484) and coefficient of variation (equal to 6.60) used to describe the changes of filled grain number. In Foumanat plain, YG was recorded 3.63 t.ha-1with the average optimum yield and actual yield of 8.44 and 4.81 t.ha-1, respectively (40% reduction in yield). Also, the optimum amount of panicle number, filled grain number and 100- grain weight were 560, 47-83.9, and 2.18 g, respectively. Although, the area of Foumanat plain in the west of Guilan province has low actual yield, there is a good potential to increase the current yield. In this study, two segmented and dent-like models were identified as superior models. The highest YG in this study was related to the number of panicles per square meter followed by the number of filled grains and the 100- grain weight. Therefore, proper crop management for improving the yield components could be an important step towards reducing the YG and increasing the yield potential in the studied area.

Regardingthe climate change and recent droughts, the proper management of irrigation systems and water resources is very important. However, achieving the optimum crop yields due to lack of water requires, the accuracy estimating the amount of water by the plants to prevent water loss and or water stress in plants is needed. In this study, the reference evapotranspiration using lysimeter was measured during three cropping seasons. Applying Ref-ET software, the reference evapotranspiration with 16 empirical equations using meteorological data were estimated, the significant difference between measured and estimated was determined using SPSS software. The empirical equations Hargreaves, Priestley-Taylor and Penman (FAO) were determined as the most suitable methods for the studied area. For the obtained data from two growing seasons and by applying nonlinear regression in SPSS software, optimized coefficients for the two Priestley-Taylor and Hargreaves equations were estimated, and then by using obtained data in the third year, thevalidation was done and RMSE as well as nRMSE values were calculated to assess the equations that for optimized Hargreaves were 0.20 mm/day and 4.60% and for optimized Priestley-Taylor equation were 0.22 mm/day and 4.5%, respectively.

Nowadays, due to population growth and changes in eating habits, there is a need to increase agricultural productions to meet consumer demand all around the world. Increasing the area under cultivation is one of the solutions for this problem, which cannot be appropriate in future because this needs to use of marginal lands with low yield and stability. Hence, increased yield is an effective strategy in this regard which can resolve the problem by decreasing yield gap. Considering the fact that there is an urgent need to increase rice production in the country as well as improving the productivity of soil resources, planning for the proper use of chemical fertilizers to achieve the maximum performance seems to be required. Accordingly, the aim of this study was to evaluate rice potential yield and yield gap in Foumanat plain using boundary line analysis, moreover, to find the relationship between soil properties and rice yield.
In order to investigate the yield gap (YG) of rice (cv. ‘Tarom Hashemi’) related to soil properties, a field experiment was carried out in Foumanat plain during two cropping seasons: 2012-13 and 2013-14. We recorded the information of 53 fields as soil samples were taken and geographic coordinates were recorded. Some soil characteristics such as total nitrogen, potassium, phosphorus, organic matter and cation-exchange capacity were measured. At the end of growing season (harvesting time) grain yield was calculated in each field (1 m-2). The boundary line method was used to calculate yield gap, optimum yield and optimum amount of soil properties for each field. Data analysis done by nonlinear regression of quadratic function, dent-like and segmented models based on PROC NLIN procedures.
Segmented functions were well able to describe the trend of pH and electrical conductivity of soil. In addition, dent-like function used to describe the process of changes in available phosphorus, available potassium, organic matter and cation exchange capacity. Also, a quadratic function was used to describe the trend of total nitrogen . The average of optimum yield and actual yield were 7. 67 and 4.81 ton ha-1, respectively, in Foumanat plain with an YG of 2.86 ton ha-1 (37.3 percent). The optimum concentration of total nitrogen, phosphorus, potassium, organic matter, cation exchange capacity, pH and electrical conductivity were 0.266 percent, 13.49-30.35 mg kg-1, 102.2-173.4 mg kg-1, 2.7-3.2 percent, 25.43-30.8 meq 100 g-1, 6.36 and 1.92 dS.m-1 respectively.
Based on the results of this study, some of the main factors for rice YG in this area could be inappropriate management of chemical fertilizer usage (nitrogen, phosphorus and potassium) as well as ignored role of organic matter and cation exchange capacity in providing essential nutrients for rice. Boundary line analysis method could clearly calculate the soil properties potential in response to yield. In general, the results of this study can help to conclude a good strategy for achieving optimal production and gap reduction due to fertility situation of the area.

Evolution of resistance in weeds leads to induction of fitness cost. Five winter wild oat biotypes resistant to haloxyfop R methyl ester collected from Kalaleh Township located in Golestan province were evaluated along with the susceptible biotype in terms of variation in cardinal temperatures in the following study. The experiment was conducted at laboratories of Gorgan University of Agricultural Sciences and Natural Resources as completely randomized design with 4 replications each consisting of 25 seeds. Petri dishes containing seeds were incubated and monitored continuously at temperatures 5-40 °C (at 5°C intervals) following a 72 hours vernalization at 4°C. Non-linear regression models were used to quantify germination response to temperature. No notable difference was observed among winter wild oat biotypes and beta model at 50 percentile was the most suitable model to describe cardinal temperatures. Base, optimum and ceiling temperatures were estimated between -4.21 to -5.91, 23.37-23.94 and 36.99-37.54 °C, respectively. Thermal tolerance range of susceptible and resistant biotypes were not significantly different. Susceptible and resistant biotypes showed similar response. Lack of fitness cost regarding cardinal temperatures demonstrates that similar non-chemical management practices including early sowing may be implemented to control resistant and susceptible biotypes germination and emergence

Investigating the process of pollutant dispersion in natural rivers is important in pollution control and its distribution and management of aquatic environments. The process of pollution distribution is a function of dispersion coefficient that has been used in Advection-Diffusion equation. Since the one-dimensional models are applied for river water quality modeling, the first step in modeling the quality of river water is determining the Longitudinal Dispersion Coefficient (LDC). Many methods such as empirical, analytical, statistical, field measurements, and more sophisticated approaches, i.e., artificial intelligence techniques have been suggested for LDC estimation. By now, Laboratory methods are associated with many limitations. These methods are along with high costs and detrimental effects on the aquatic environment due to the application of some specific and harmful tracers. Artificial Intelligence Models have had a good prediction for LDC in recent years, but uncertainty in these models, as an annoying factor, always limited their results for practical purposes. These techniques act exactly like a black box model. Also, although different studies have been carried out for LDC estimation in natural rivers, the absence of a comprehensive study to investigate the effects of different patterns of dimensionless hydraulic and geometric parameters on LDC is still felt. Another challenge is the inaccuracy and less user-friendliness of the provided models to predict LDC. Thus, the main objective of this study is to investigate different types of LDC prediction by application of regression analysis.
The data used in this study for estimation of LDC contains 61 datasets of hydraulic parameters such as velocity U (m/s), shear velocity u*(m/s) and flow rate (Q), and also the geometric specifications measuring in cross-section of rivers like water depth H(m), stream width (W) and curvature of the river σ. This dataset was taken from different sections of 31 rivers in the United States of America. This information was used as input parameters (about 70 percent, i.e 43 data for calibration and 30 percent, i.e. 18 data for testing) for the non-linear regression model.
Many of researchers have used equations based on establishing a relationship between LDC and hydraulic-geometric specifications of rivers. Some researchers have used other parameters such as Q and σ to improve LDC estimation. So, in this research, all combination of input parameters for application of non-linear equations have been investigated. Non-linear equations could be changed to linear equations by a logarithmic method. Thus, all of the unknown coefficients of equations could be known by a linear Least Squares Regression.
Calibration and test steps were carried out using various patterns of hydraulic and geometric data of the rivers in the United States of America. The obtained equations have been compared by the statistics of regression method such as coefficient of determination (R2), t-value, p-value and Variance Inflation Factor (VIF). Higher values of t-value led to the lower value of p-value that indicated the importance of parameter in equation. VIF shows the existence of multi-collinearity in equation. Results showed that the pattern including the river curvature parameter had the best performance for LDC prediction model, while discharge parameter had the least effects on the LDC prediction model. Also, if the constant number is eliminated from the equation, the model’s performance is increased. The R2 of calibration and test stages of the best tuned model were 0.993 and 0.938, respectively. Selected equations in this research (with the best performance) compared with the models suggested by other researchers based on Root Mean Square Error (RMSE), Mean Related Error (MRE), Developed Discrepancy Ratio (DDR), and Threshold Statistics (TS) indices. The comparison of the developed model with the past studies revealed that it had a better performance in LDC estimation. Although the model proposed by Zeng and Huai (2014) had the second best performance, its statistical indices (RMSE and MRE)were about 2 and 83 times greater than that those obtained for the developed model. The best model based on the DDR graphic statistic has the largest crest and lowest width. So the comparison of models based on DDR indicated that the developed model in this research had the best performance. Also, the graph of the TS showed that the model developed in this research had the lowest threshold of errors in 100 percent of datasets. Thus, this research provides an LDC estimator model that outperforms the other existence equations.