عنوان مقاله [English]
Introduction: Persian walnut (Juglans regia L.) is a large, wind-pollinated, monoecious, dichogamous, long lived, perennial tree cultivated for its high quality wood and nuts throughout the temperate regions of the world. Growth model methodology has been widely used in the modeling of plant growth. Mathematical models are important tools to study the plant growth and agricultural systems. These models can be applied for decision-making anddesigning management procedures in horticulture. Through growth analysis, planning for planting systems, fertilization, pruning operations, harvest time as well as obtaining economical yield can be more accessible.Non-linear models are more difficult to specify and estimate than linear models. This research was aimed to studynon-linear regression models based on data obtained from fruit weight, length and width. Selecting the best models which explain that fruit inherent growth pattern of Persian walnut was a further goal of this study.
Materials and Methods: The experimental material comprising 14 Persian walnut genotypes propagated by seed collected from a walnut orchard in Golestan province, Minoudasht region, Iran, at latitude 37◦04’N; longitude 55◦32’E; altitude 1060 m, in a silt loam soil type. These genotypes were selected as a representative sampling of the many walnut genotypes available throughout the Northeastern Iran. The age range of walnut trees was 30 to 50 years. The annual mean temperature at the location is16.3◦C, with annual mean rainfall of 690 mm.The data used here is the average of walnut fresh fruit and measured withgram/millimeter/day in2011.According to the data distribution pattern, several equations have been proposed to describesigmoidal growth patterns. Here, we used double-sigmoid and logistic–monomolecular models to evaluate fruit growth based on fruit weight and4different regression models in cluding Richards, Gompertz, Logistic and Exponential growth for evaluation of fruit growth according to length and width(diameter) of fruit. Then to determine the most efficient model, different parameters of evaluation of model fitting were used. The best model was selected based on the highest value of R2and the lowest values for RMSE, AIC and BIC. The data were analyzed using SAS software (version 9.2) and Solver in Microsoft Excel.
Results and Discussion
Growth model based on fruit weight: According to the actual and estimated growth model based on fruit weight, double sigmoid function and logistic–monomolecular model showed a good prediction of fruit weight changes versus time data (days after full bloom). However, in general according to evaluation criteria, double sigmoid model was the best model to predict walnut fruit weight. Based on total fruit weight, fruit growth occurs at two stages: in the beginning of the growth phase, there is a slow growth for 30 days and then it is continued with a rapid growth until 60 days after full bloom. Thereafter, growth was again slow. At the beginning of the second phase of growth (70 to 85 days after full bloom), fruit growth increased again and then, walnut fruits started to ripe on the tree in summer, bright green husk (outer pericarp layer) changed to a yellowish color and the growth again decreased (130 days after full bloom).
Growth model based on fruit length and width measurements: Based on the actual and estimated growth pattern the Richard model describes the growth of fruit better than other models. The first phase lasted for about 15 days and the second phase of growth was very rapid and it lasted for 35 daysin most of genotypes. Then, fruit length and width did not change significantly until harvesting time. However, due to subtle changes of fruit length and width following fruit rapid growth stage, fruit weight is preferred for describing fruit growth of the Persian walnut. During the first phase of development, increasing size and weight are associated with the formation of new and larger cells and tissues. The second phase includes attainment of final nut form, and it is characterized mainly by chemical changes. These include changes in the shell as the cells become lignified and more important changes in kernel composition.
Conclusion: Based on thes tatistical testing and goodness of the fit, the best model between six nonlinear growth models, was double-sigmoid and Richard model swhich can be used to accurately predict fruit growth based on fruit weight, fruit lengt hand width, respectively.