Acta Biológica Colombiana

INTRODUCTION

The açaí (Euterpe oleracea Mart.) is a palm of the Arecaceae family, widely disseminated and cultivated in the Brazilian Amazon. It occurs naturally in the Amazon region and has great economic importance for regional fruit production, especially for Pará, whose pulp production, commercialization and consumption generate large markets (Neves et al., 2015), with açaí juice being an iconic regional product of this state, representing the main product extracted from the palm tree (Silvestre et al., 2016).

With the popularization of the ecological appeal and the discoveries of nutritional qualities, the açaí pulp commercialization has gradually grown along with an expansion to other national markets and reaching international levels (Pagliarussi, 2010). This production makes Brazil the largest açaí pulp producer, consumer, and exporter (Menezes, 2005), which produced in 2020 the amount close to 1500 thousand t, in an area of 221 thousand ha, generating about R$ 4754 billion, with the North region representing 99 % of these values, highlighting Pará with more than 96 % of the total Brazilian (Instituto Brasileiro de Geografia e Estatística [IBGE], 2020).

An inherent aspect of man is that over time, traditional communities in the process of domestication of different species selected a wide intraspecific diversity. The result of this process is reflected in the large number of existing varieties, which are generally considered a cultural artifact of these communities and can therefore be called ethno-varieties (Peroni and Martins, 2000), in this way, it can be considered that the açaí tree is spread throughout the Amazon region and fits perfectly into this denomination.

The açaí tree fits as an ethno-variety, where there is a diversity of types for various morphological characters. Jardim (2000) and Pimentel and Jardim (2009) defined different types or ethno-varieties of açaí trees, based on differentiation in morphological structures, such as fruit color, the shape of inflorescences, bunches, and others, naming them as black açaí, tinga açaí, spotted açaí, mulatto açaí, sword açaí, and white açaí, additionally Jardim and Oliveira (2014) add chumbinho açaí. With white açaí being, the second most consumed, behind black açaí with almost the entire volume. It is worth noting that the fruits when ripe have a color ranging from dark purple to black, except the white type açaí, which produces light green fruits (Nogueira et al., 2005); (Oliveira and Tavares, 2016).

Regarding the location, it is noteworthy that in some areas of the Marajó Island and the estuary of the Amazon River, one can find the white açaí or açaí-tinga (Oliveira et al., 2002), sword açaí on the island of Combu and in the municipality of Acará and bovine blood açaí in the southern part of Amazonas and Santarém (Simonian, 2014).

Recently, with the growth of açaí demand beyond the regional market in the North of the country, açaí planting and domestication began, to meet this growing market (Homma, 2014). Despite the increase in açaí production, stimulated by technological advances, cultivation practices, and high prices, the environmental conservation and the social return of populations have not evolved at the same pace (Teixeira, 2018). The expansion without due environmental care in this way can become an obstacle to biodiversity, by promoting the felling of other species (reduction of competition). Inserting in this context the white açaí plants loss, transforming the forest into homogeneous extensions of black açaí palms (Homma et al., 2006), that is, management practices are failing to achieve a balance between productivity and environmental conservation, corroborated by the records of Homma (2014).

Additionally, Tagore et al. (2018) affirm that the increase in market value and the amount consumed has generated the adoption of intensive and aggressive management practices for the predominance of açaí trees with black fruits. This pressure generates risk to the natural environment by stimulating the elimination of other species and, consequently, the local landscape alteration, which changes the soil and climate conditions in these regions. On the opposite side, the traditional extractive production system does not have the adoption of a cultivation process. Production occurs naturally and respects local heterogeneity. The product, in general, is intended for the maintenance of families and, therefore, is suitable as a sustainable activity with lower risks (Tagore, 2017), preserving the species present and thus avoiding the genetic erosion of white açaí that could be present.

A complicating factor in research with açaí trees in terms of selection is the evaluation of many characteristics and the effect that the environment has on the behavior of genetic material. Variations due to the response to environmental factors generate changes in its phenotypic aspects, a phenomenon known as genotypes versus environments interaction (GxA), making it difficult to select and recommend adapted and stable genotypes (Cruz et al., 2014). An important option is the use of multivariate statistics, which makes it possible to obtain the correct information and allows a joint interpretation of the characteristics under study, which are not perceptible with the use of univariate statistical analysis that works with each one in isolation (Cruz et al., 2014).

As stated earlier, almost all studies evaluated and analyzed a large number of characteristics in a univariate way, but this approach is extremely limited because it does not consider the possible correlation that may be present between the characteristics. To overcome this obstacle, multivariate analysis has been used, especially principal components analysis (PCA) and canonical discriminant analysis (CDA). The first transforms an original variables set correlated with each other into a new set of variables, called principal components, whose function is to linearly reduce the size of a data set, generating a set of p uncorrelated variables, retaining as much information as possible, holding the total variation, ordered in descending order (Hair et al., 2014); (Johnson and Wichern, 2019). CDA, like PCA, reduces the dimensionality and standardizes the data. The derivation of canonical coefficients, together with a multivariate analysis of variance is the CDA base (Johnson and Wichern, 2019).

Based on the aspects of the possible loss of genetic material from white açaí, research that can stimulate and show the existence and importance of this type is essential, with their analysis not based only on the univariate dimension, but in multivariate statistical methods for the interpretation of the phenotypic variations produced by the different characteristics. Therefore, the objective of this work was to analyze the characteristics of behavior in progenies of this ethno-variety, by the multivariate and the main components analysis, to determine which attributes present the greatest contribution in the phenotypic manifestations and to verify if there is an effect of plant age on these characteristics.

MATERIALS AND METHODS

This study is part of the açaí tree genetic improvement program for fruit production in the Amazon estuary, conducting an experimental area containing a total of 52 white açaí progenies located in the Germplasm of Embrapa Amazônia Oriental, Belém, PA (1º 27'21" S and 48º 30'16" W, 10.8m). This experiment was installed in February 2003, in a completely randomized design with ten replications of one plant per plot, spaced 5 m x 5 m. The matrices were collected in municipalities of the Amazon estuary, being Curralinho (01º48'49" S and 49º47'43" W), Breves (01º40'56" S and 50º28'49" W), São Sebastião da Boa Vista (01º43'03" S and 49º32'27" W), Muaná (1º53'51" S and 49º23'71" W), Limoeiro do Ajurú (01º53'42" S and 49º22'51" W) and Ponta de Pedras (1º39'28" S e 48º87'05" W), located in the Marajó Archipelago, at the mouth of the Amazon River (Pará state, Brazil).

For the morphoagronomic characterization of the accessions, carried out between 2009 and 2018 were used, total bunch weight (PTC) in kg; fruit weight per bunch (PFC) in kg; fruit yield per bunch (RFC), in %, obtained by dividing PFC and PTC, multiplied by 100; one hundred fruits weight (PCF) in grams; rachillas number per bunch (NRC); and rachilla length in the bunch (CRC), expressed in cm.

In the collected data initially, the univariate analysis of variance (ANOVA) to verify the existence of differences that allow performing the other analyses. A multivariate analysis was carried out, allowing observing and understanding of the differences in behavior to the six characteristics simultaneously. The principal component analysis (PCA) and canonical discriminant analysis (CDA) were the multivariate analysis methodologies employed.

Canonical Discriminant Analysis

Canonical discriminant analysis (CDA) or canonical variables analysis is applied to the results of principal component analysis, aiming to differentiate treatments based on the most important characteristics. The first stage of the CDA verifies the assumptions and then the multivariate analysis of variance (MANOVA) is performed with verification of significant differences between treatments in the canonical functions using the multivariate Lambda tests of Wilkis, Pillai, Wilks, Hotelling-Lawley, and Roy (Johnson and Wichern, 2019).

The use of CDA makes it possible to determine functions of the variables X = (X1, X2, …, Xp), which separate g groups as much as possible, using Z a linear combination of the original variables, and the mean value of Z changes from one group to another and thus generating separate groups. The approach aims to build linear combinations of Xi variables, in which the indices a = (a1, a2, …, ap) can maximize the F ratio for a one-way analysis of variance (Hair et al., 2014); (Johnson and Wichern, 2019). The linear combination of variables is given by: Z = a₁X₁ + a₂X₂ + a₃X₃ + … + a_pX_p.

Fig. 1.: Scree Plot of principal component axes eigenvalues in white açaí progenies.

A biplot is structured for the first two canonical variables (CAN1 and CAN2), managing to discriminate the treatments jointly in terms of the most important characteristics in the canonical variables. All analyses were performed using the R 3.4.1 software (R Foundation, n.d.), considering α = 5%.

RESULTS

The results in Table 1, which is a preliminary univariate analysis, show statistical differences in the effect of years for all traits among the different progenies. Visualize that there are different behaviors between the progenies and thus also allowing the multivariate analysis was performed after verifying the presence of differences in univariate analysis.

In principal component analysis (PCA), the explained variance is how much each component can explain the eigenvalue, given as a percentage, and the accumulated proportion is how much each component successively accumulates from its previous ones until reaching 100 % (Araujo and Coelho, 2009). The results obtained by the principal components technique are in Table 2. The first two PCs were responsible for 61.47 % of the total variation, on the effect of years on the evaluated characteristics, where PC1 was responsible for 42.24 % and the second, PC2, for 19.24 % of the data variations.

Fig. 2.: Eigenvectors of PTC: total bunch weight; PFC: fruit weight per bunch; RFC: fruit yield per bunch; PCF: one hundred fruits weight; NRC: rachillas number per bunch and; CRC: rachilla length in the bunch, in the first two principal components (PC1 and PC2) in white açaí progenies.

Table 1.: Summary of univariate analysis of variance for PTC, PFC, RFC, CRC, NRC, and PCF in white açaí progenies.

PTC: total bunch weight; PFC: fruit weight per bunch; RFC: fruit yield per bunch; PCF: one hundred fruits weight; NRC: rachillas number per bunch and; CRC: rachilla length in the bunch.

Table 2.: Principal component axes (PC), eigenvalues (λ i), percentage of variance explained by the components (PCV), cumulative percentage (aVPC) scores (Weights), and correlations (Correl) in the component axes (PC1, PC2 and PC3) for six characteristics evaluated in white açaí progenies.

PTC: total bunch weight; PFC: fruit weight per bunch; RFC: fruit yield per bunch; PCF: one hundred fruits weight; NRC: rachillas number per bunch and; CRC: rachilla length in the bunch.

The Scree Plot is a line plot of the eigenvalues of factors or principal components in evaluated characteristics. The generate graphic is employed to determine the number of factors to retain in an exploratory factor analysis or principal components to retain in a principal component analysis (PCA) according to Matos and Rodrigues (2019).

The inflection point occurs at number two in the horizontal axis, which represents the second component axis (Fig. 1).

The graphics to components axis (Fig. 2) showed the proximity among NRC, PCF and RFC, close to the positive vertical axis and PFC, PTC close to positive horizontal axis, with CRC close to these.

For Manova, according to Song (2013), four alternative statistics were used to test the hypothesis that all samples come from populations with the same mean vector. Being considered robust (ie, they can be applied even if the assumptions do not hold for all groups or variables) if the sample sizes are approximately equal for the m samples. Thus, through the multivariate Lambda tests of Wilkis, Pillai, Hotelling-Lawley, and Roy, the F test between the different years of evaluation (Table 3) to identify the presence of significant differences.

The four different methodologies for multivariate analysis (Table 3) indicate at 1% significance that the white açaí progenies behave differently in the set of characteristics evaluated.

In (Table 4), the six canonical functions were needed to explain the 100 % of the variability of the data, but only the first two were considered since the percentage above 80 % is sufficient for reliable and satisfactory interpretation of the results, which allows the understanding of behavior in the set of parameters analyzed (Cruz et al., 2014).

In the first and second canonical component discriminant function (Table 5) the most important features (positive and/or negative) were in order, PTC, CRC, and PFC, so these variables are important in the discrimination of progenies between the years, whose absolute values were higher. The years also had different effects in phenotypic values to evaluated characteristics.

Table 3.: Summary of multivariate analysis of variance, using four statistical tests, indicating the degrees of freedom of the numerator (NGL) and denominator (DGL) and the probability for the F test for the response variables (six characteristics) evaluated simultaneously.

PTC: total bunch weight; PFC: fruit weight per bunch; RFC: fruit yield per bunch; PCF: one hundred fruits weight; NRC: rachillas number per bunch and; CRC: rachilla length in the bunch.

Table 4.: Canonical variables (CV), canonical discriminant function (Can), approximation of the F value (Fap), eigenvalues (λ i), percentage of variance explained by the canonical variables (CVV) and cumulative percentage (aCVV) in the characteristics evaluated in white açaí progenies.

Table 5.: Contribution of the six characteristics and the years in the first and second canonical discriminant function

PTC: total bunch weight; PFC: fruit weight per bunch; RFC: fruit yield per bunch; PCF: one hundred fruits weight; NRC: rachillas number per bunch and; CRC: rachilla length in the bunch.

The Box Plot of the first canonical function (Fig 3) shows that the characteristics RFC, NRC and PCF contributed positively to the behavior of the set of white açaí progenies, between the years 2008 to 2012 and 2014 to 2017. While PTC, PFC and CRC contributed to the years 2013 and 2018. This result shows different contributions of the characteristics evaluated in relation to each year of evaluation.

The Figure 4 shows the canonical biplot for the characteristics evaluated in white açaí, considering the years of study. The canonical biplot objective is to prospect the main variables responsible for generating the differentiations (González-Martín et al., 2016). In CDA the approach is direct, based on a simple visual analysis, watching the projection of the two canonical discriminant functions (Sorbolini et al., 2016).

The canonical discriminant biplot (Fig. 4) results in that the characteristics, PCF and RFC present the highest specificity of the years that were similar, except for 2013 and 2018, where CRC presents specificity to this first year mentioned and PTC and PFC to the second year. NRC differentiated itself from other characteristics.

DISCUSSION

The results in Table 1 indicate the progenies presence whose performance can be highly promising for future actions of genetic improvement, Sousa et al. (2017), also found significant differences in violet-type açaí. Multivariate analysis was performed after verifying the presence of differences in univariate analysis.

In the Table 2 the first two PCs were responsible for 61.47 % of the total variation, on the effect of years on the evaluated characteristics, where PC1 was responsible for 42.24 % and the second, PC2, for 19.24 % of the data variations, close to what informed in cassava by Gonçalves et al. (2021). Thus, the sum of these first two component axes can be considered sufficient as stated by Yang et al. (2009) in which the first two principal components must explain more than 60 % of the total variance. Therefore, in the continuation of the analyses, only these first two component axes are considered. Likewise, Venturini et al. (2013) in egg production in certain weeks found that three CPS were sufficient to explain 70.93 % of the total variance of the genetic values of the traits, even with a different species from the present study, the results obtained by these authors corroborate those found in this work.

It can be said that the portion captured by the first two axes is relevant, and it can be considered sufficient to capture the variations of genetic origin, ignoring possible noise effects, or defined also by stochastic effects, which would generate difficulties for the interpretation of the analyzes (Maia et al., 2019). Additionally, when considering that the PCA was performed on the covariance matrix of standardized variables where there is retention only of the principal components whose eigenvalue is greater than unity, it follows that only the first two principal components can be considered in the analysis (Table 2), as they were the only components with an eigenvalue greater than one.

In (Table 2), to understand the importance of each variable in the structuring of the first two components with the greatest contribution and thus the PTC and PFC characteristics stood out in the first main component, and for the second component RFC and PCF stand out.

Complementarily, in the figure of the Scree Plot, the inflection starts from the second component axis, confirming the option of retaining only these two for the analysis (Figure 1), similar to those observed in Eucalyptus clones by age according to Protásio et al. (2014), that is, the most relevant information from the original sample data is contained in the first two main components.

Fig. 3.: Boxplot plots with canonical discriminant functions for the years in the characteristics, PTC: total bunch weight; PFC: fruit weight per bunch; RFC: fruit yield per bunch; PCF: one hundred fruits weight; NRC: rachillas number per bunch and; CRC: rachilla length in the bunch.

Fig. 4.: Canonical discriminant biplot for the correlation between treatments years and characteristics (PTC: total bunch weight; PFC: fruit weight per bunch; RFC: fruit yield per bunch; PCF: one hundred fruits weight; NRC: rachillas number per bunch and; CRC: rachilla length in the bunch) evaluated in white açaí progenies.

Comparing the results observed in (Table 2) with (Fig. 2), the first component axis with the greatest contributions is those with longer vectors and closer to the component axis. In the case of the first component axis to PTC and PFC, and for the second PCF and RFC, with longer vectors and closer to the component axes, can be considered that the first axis refers more strongly to the weight characteristics inherent to the bunch and the fruits present in this bunch and, the second specifically with the fruits (RFC and PCF) more strongly associated with the interaction effects with the years of evaluation.

The PTC and PFC characteristics are more intensely correlated by the proximity between the lines, with CRC having less interaction with both. Since CRC does not correlate with NRC, PCF, and RFC, due to the angle close to or greater than 90°. The PTC and PFC traits also correlate intermediately with RFC but do not interact with NRC and PCF, while these last three traits correlate with average intensity with each other. Similar distribution and behavior of characteristics in cassava by Gonçalves et al. (2021). Similarly, in peanuts, yield traits showed greater contributions Costa et al. (2021) compared to vegetative aspects.

The results from multivariate analysis (Table 3) indicate that there is genetic divergence between the white açaí progenies considering all characteristics simultaneously, confirming the results obtained in the univariate analysis. Important result for plant selection purpose.

The percentage accumulated in the first two canonical variables (Table 4) was higher than those obtained in coffee by Teixeira et al. (2013) and like that obtained by Morais et al. (2019) in Dalbergia ecastaphyllum, the use of the first two variables is sufficient and safe. Representing the heritable and non-environmental behavior.

In the first canonical discriminant function (Table 5) the most important features (positive and/or negative) were in order, PTC, CRC, and PFC in contrast to the others, so this main component efficiently differentiates the clusters mainly as a function of features of bunches in terms of weight and length of rachis. The second component behaved similarly to the first when observing PTC, CRC, and PFC, so these variables are important in the discrimination of progenies between the years and should therefore be considered as the ones that researchers should concentrate greater efforts on in their field evaluations, discarding the evaluation of other characteristics, as pointed out by Teixeira et al. (2013). Regarding the years of evaluation, a significant effect of the age of the progenies can also be inferred regarding the phenotypic effect of the evaluated characteristics; similar to what was mentioned by Protásio et al. (2014), in Eucalyptus clones.

According to the Box Plot of the first canonical function, the years 2008 to 2012 and 2014 to 2017 directly influenced NRC and PCF (Fig. 3). This indicates that in these years there was a trend towards an increase in the number of rachis of the bunch and the weight of one hundred fruits. However, there was a decreasing trend for PTC, PFC, and CRC in these years. Since the Box Plot was not able to differentiate, the years mentioned above from each other, that is, possibly the intrinsic characteristics of each year were extremely similar.

Unlike in 2013 and especially 2018, environmental conditions and the age of the progenies strongly influenced the variations observed in PTC, PFC, and CRC. When consulting the climatological data, where the white açaí progenies are installed, the average, maximum, and minimum temperatures can be observed, in addition to the relative humidity from the environment in percentage, were similar throughout the evaluation period, distinguishing the years 2013 and 2018 with about 200 mm of precipitation above the average of other years (Instituto Nacional de Meteorologia [INMET], 2022). Indicating that the water availability factor presents an important factor in the productivity of açaí plants.

The canonical biplot had little similarity to the main components biplot, with the variation explained by the two main components being 61.47 % of the data variation, while the first two discriminant canonical were able to explain 93.54 % of the total variation. Therefore, the information in Figure 4 has greater reliability. The results confirm the greater robustness of the canonical discriminant analysis compared to the PCA, in agreement with Traldi et al. (2018).

The axis of the first canonical discriminant function proved to be significantly the most important to order the effects of the years on the evaluated characteristics, as it contained 74.3 % of the observed variance. The variations existing are observed only in the years 2013 and 2018 allowed us to separate in (Fig. 4) the variables in different areas of study in the graph, being properly separated from the other years that did not contain characteristics that could generate distinction and thus were extremely similar. Note that the year 2013 directly influenced the CRC characteristic, and 2018 was more strongly associated with PTC and PFC. There is a great similarity between PTC and PFC, proximity between PCF and RFC while CRC and NRC did not show similarities in behavior with the other characteristics.

CONCLUSIONS

There is an evident correlation between the characteristics, some with greater intensity and others with less intensity, so the multivariate analysis undoubtedly has its appropriate use for the factors studied here.

By the Box Plot, the white açaí plants respond to the amount of water available annually in the production in terms of total weight of bunch and weight of fruits in bunches, specifically in the characteristics PTC, CRC, and PFC.

By the CDA, the characteristics with the greatest contribution to the variance were PTC, CRC, and PFC, being similar for the PCA mainly in the PTC and PFC characteristics.

By the canonical Biplot, the PTC, PFC, CRC, and NRC characteristics should be preferentially evaluated, and the work of evaluating RFC and PCF can be discarded, which requires a lot of manpower to be carried out.