Comprehensive study of a Thithonia diversifolia material using mathematical modeling

The overall purpose of the study was describing of the component morphological behaviour of the vegetal material as Tithonia diversifolia. In this case, it was used statistical criteria for modelling, where best-fit models were selected. Different linear and non-linear models were adjusted to know the variable behavior of seedling height (cm), 100 sheet weight (g MV), total weight of plant (green matter, g) and total weight of a linear meter (g green matter), which were taken during the rainy and dry seasons in the Granma province from Cuba. The data were processed in the softwares Statistical Infostat (2001) and IBM - SPSS (V22). In the rainy season, height and weight of 1 m seedlings fitted the linear model, where higher values were reached at the 18th weeks with 174.98 cm and 4927.3 g, respectively. Moreover, weight of 100 sheets MV was adjusted to the quadratic model with a value of 220.59 g at 14th weeks. On the other hand, total weight of plant continued to increase at 18th weeks, reaching 109.70 g. (este valor no coincide con lo anterior) In the dry season, the variables presented significant adjustments for the exponential model and expressed slow behavior during the first three measurements, increasing from 10th to 18th week. Where, the weight of 100 green leaves increased to values above 300 g at 18th week. Last of all, this article reports for the first time about the growth of T. diversifolia in the eastern part of Cuba.


Introduction
The integral study of the potential of Tithonia diversifolia this shrub plant in silvopastoral systems contributing to the biodiversity and sustainability and productive in tropical livestock has been carried out by different authors in Cuba, among them [1][2][3] and in other countries of the Southern Cone such as Colombia.
The materials of T. diversifolia were evaluated for their adaptive, botanical, growth characteristics, chemical, nutritional and productive constituents. It has also been addressed using mathematical modeling. It has been a useful methodology for the evaluation of this forage shrub species. In the eastern region of Cuba, evaluations of different materials of this plant have been carried out and their modeling has allowed the comparison of their behavior using the statistical criteria described by [4] In a previous investigation [2], made the discrimination of 29 Tithonia plant materials through the Statistical Model of Impact Measurement [5], selecting 5 (23, 5, 10, 16 and 17), representative of four groups according to this methodology and recommended as plant materials intended for food by the options offered for the production of biomass .
The objective of this research was to describe the behavior of some morphological components of the plant material 23 of T. diversifolia to determine, through the use of statistical and modeling criteria, the best fit models for different yield components.

Materials and Methods
In this investigation, plant material 23 was analyzed, a member of the group of materials that showed the greatest indicators of biomass production.
Statistical methodology. Different linear and non-linear models were adjusted to know the behavior of the variables height of the seedling (cm), weight of 100 leaves (g MV), weight of the whole plant (green matter, g) and total weight of a linear meter (g green matter) during 2006 and 2007, from June to October (rainy season), and from January to June (rainy season) of the Granma province in Cuba. The adjusted models were linear, quadratic, cubic, Gompertz, Logistic and Exponential as a function of time. The criteria described by [4] were used to select the best fit models .presented the criteria to be considered and clarifies that they are essential The models used in the adjustment of the variables were the following: Later clarifies this same author that are essential to make a correct selection of models criteria 1, 2, 5, 6 and 12 The processing was performed for the two weather stations. The information was organized in Excel databases to determine the statisticians and to plot the data. Subsequently, the statistical software Infostat (2001) and IBM-SPSS (V 22) were used to adjust the models.

Results and Discussion
To facilitate the discussion, the results with the plant material 23 is analyzed for each climatic season. A table is presented first with the mean squares of the error of the analysis of variance of the model and the significance of this, for each model and variable analyzed to make their selection with better MOL2NET, 2019, 5, doi:10.3390/mol2net-05-xxxx 4 goodness of fit. Subsequently, the information of the selected models is completed with the coefficient of determination (R²), the estimated parameters and their corresponding standard errors.
Rainy .The indicators of seedling height and total weight of 1m were better adjusted to the linear model, while the weight of 100 MV sheets was more adjusted to the quadratic model. The weight of the entire plant achieved a better fit to the exponential model (table 1). Although this variable did not have an important significance, the 10% level was considered to determine the trend of the variable over time.
From the application of the selected models it was found that the height of the seedling and the total weight of 1m (table 2) (figure 1) reached the highest values at 18 weeks, with 174.98 cm and 4927.3 g, respectively.
These variables increased by 6.13 cm and 216.38 g on average. The maximum weight of 100 MV sheets was at 14 weeks, with 220.59 g. The weight of the whole plant continued to increase at 18 weeks, reaching 109.70 g.    All variables presented significant adjustments for the exponential model and linear but due to their lower square means the first selected. The exponential dynamics for material 23 (table 4)   They increased from week 10 to 18, and continued with this behavior without reaching stable or maximum values. Of the three variables, the weight of 100 green leaves increased with values greater than 300 g at 18 weeks ( Figure 3).
The total weight of 1 m MV of plant material 23 reached more than 3000 g at 18 weeks (figure 4) and presented a considerable amount of leaves. The characteristics of the growth of this plant were totally different in the dry season with respect to the rainy season. The best fit model is always the exponential.
This indicated that the material presents slow growth in the rainy season, although it reached appreciable values in the leaves.
In a work carried out in Cuba, Ruiz and Febles (2000), found the usefulness of modeling, when evaluating the best fit models to study the growth ofa group of tropical tree species. They determined the best model when sowing in two moments of the rainy period. This enabled recommendationsmore precise about it.   The total weight of 1 m MV of this collection 23 were much higher because they reach more than 3000 g at 18 weeks. The material 23 exceeds almost 1,000 g to other collections, especially considering that the heights of the plant are similar.
This study reports for the first time about the growth of materials 23 of Tithoniadiversifoliain different areas of Cuba. This information will be very useful to exploit better species.

Conclusions
It is concluded that Tithonia diversifolia, plant material 23, presented the best growth characteristics during the rainy season until week14. In the rainy season, the best growth was from week 10.
Knowing the behavior of different components of the plant over time allows the development of future work related to the production of biomass, whether for cutting or grazing.