Best linear unbiased prediction in combination with path analysis in processing grapes

ABSTRACT

The knowledge of correlations between multiple characteristics in plant breeding leads to more effective selection strategies. The path analysis allows refining these correlations and partitioning them into direct and indirect effects on the main variable. The path analysis becomes more effective when based on predicted genotypic values rather than phenotypic values. The objective was to evaluate correlations between the main agronomic characteristics of grapevine cultivation and their direct and indirect effects on yield per plant to improve selection strategies to reach superior progenies. A randomized complete block design was installed using four cultivars and two rootstocks, five repetitions, and plots of four plants. Data from three crop seasons were analyzed from a mixed model and genetic correlations were subject to the path analysis. A high and positive significant correlation was found between average fruit production and the number of clusters per plant. On the other hand, the average production per plant showed a low correlation to cluster width and height per grapevine. Wider and higher berries tend to increase berry fresh mass and therefore increase the contents of soluble solids and reducing sugars. Among the features, the number of clusters per plant has the strongest direct effect on fruit production in grape cultivars. Berry fresh mass, berry length, and berry width were indirectly influenced by the number of clusters and showed high heritability compared to yield and number of clusters. These characteristics could be used in indirect selection.

Vitis spp; correlation; genotypic values; mixed models; tropical vitiviniculture

Introduction

Plant breeding programs seek improvements in agronomic features of interest. In this regard, multiple characteristics are simultaneously considered during the evaluation. Correlation studies aim to understand the relationship between such characteristics, which may result in genetic enhancement in future generations or the selection of a genotype of interest (Cargnin, 2019; Moreira et al., 2019). Thus, the selection for a main feature with low heritability and/or measuring difficulties can be performed based on one or more characteristics of moderate to high heritability, allowing the breeder to advance the use of indirect selection, saving time and effort (Diniz and Oliveira, 2019).

The correlation estimates a connection between pair of variables, regardless of their causes. However, the correlation allows estimating only the magnitude and the sense of linear association between two features, which may not represent their actual association, since a high or low relation may result either from the biased of a third characteristic or a set of characteristics (Cruz et al., 2012). For that reason, more detailed studies about relationships between characteristics become crucial, such as the path analysis developed by Wright (1921), which allows a better analysis of the coefficients that determine the influence that one characteristic has on another. The path analysis allows to unfold biased correlations into direct and indirect effects of features on the main variable, generating more accurate estimates of cause and effect (Lombardi et al., 2015).

The results of the path analysis become more effective when based on predicted genotypic values rather than phenotypic ones. The use of components of variance estimated by maximum restricted likelihood (REML) and by predicted genotypic values by the best linear unbiased prediction (BLUP) leads to more precise and accurate inferences, increasing accuracy of the analysis and efficiency of breeding programs (Olivoto et al., 2017), since the phenotypic values are corrected to the environmental effects and weighed by the character heritability through BLUP (Butler et al., 2017).

This study aimed to evaluate the correlations between the main agronomic characteristics of vine cultures and their direct and indirect effects on average production by the plant of promising grapes varieties for processing using the path analysis based on genotypic values via BLUP.

Materials and Methods

Study site

The experiment was conducted at the Centro de Seringueira e Sistemas Agroflorestais of the Instituto Agronômico (IAC) in Votuporanga, São Paulo State, Brazil (20°15’ S, 50°30’ W, 483 m altitude). According to the Köppen classification, the climate in the region is humid tropical (Aw) (Beck et al., 2018).

The vineyard was implanted in Aug 2013. The plants were spaced in 2.0 m × 1.1 m and sustained in an espalier system with a unilateral cordon. Cultural practices followed the recommendations for regional viticulture, with daily micro-sprinklers irrigation, and installation of polyethylene screens. For all seasons, vines were cane pruned to leave one to two nodes, as well as the usual cultivation practices in the region. Subsequently, 5 % hydrogen cyanamide was applied to the buds to induce and standardize the sprouting.

Treatments and experimental design

The experimental design was randomized blocks in plots with four cultivars grafted onto two rootstocks, totaling eight cultivar/rootstock combinations. Five replicates with four plants per plot were used. The treatments consisted of the cultivars Isabel Precoce (Isabella mutation), BRS Carmem (Muscat Belly A × H 65.9.14), BRS Cora (Muscat Belly A × H. 65.9.14), and IAC 138-22 Máximo (Seibel 11342 × Syrah) grafted on the most commonly used rootstocks IAC 766 ‘Campinas’ (106-8 Mgt × Vitis caribaea) and IAC 572 ‘Jales’ (V. caribaea × 101-14 Mgt). All the cultivars are grapes intended for juice production, with IAC 138-22 Máximo used for juice and wine productions.

Three production cycles were evaluated in the first halves of three years: cycle 1 - from Mar 2017 (pruning) to June 2017 (harvest); cycle 2 - from Mar 2018 (pruning) to June 2018 (harvest); cycle 3 - from Mar 2019 (pruning) to July 2019. In all pruning events, four to six buds per branch were kept.

Evaluated variants

The components evaluated were as follows: cluster fresh mass (CM), berry fresh mass (BM), rachis fresh mass (RM), cluster length (CL) and width (CW), berry length (BL) and width (BW), total soluble solids (SS) expressed in °Brix, titratable acidity (AT) expressed in tartaric acid percentage, pH, maturation index (MI), and reducing sugars content (RS) in glucose percentage. At harvesting, the number of clusters per vine (NCV) was measured and the production (kg) per vine was obtained (Yield) through plant mass.

For the evaluation of the physical characteristics of clusters, rachis, and berries, ten representative clusters were used per experimental plot, and in each cluster, ten berries were collected from the upper, middle, and lower parts of the clusters (3:4:3), totaling 100 berries per plots size. Following the physical analysis, the same berries from each cluster were smashed to obtain grape must determine SS, AT, pH, MI, and RS in triplicates.

An analytically accurate scale was used to measure CM, BM, and RM (in g). A graduated measuring ruler with a length of 30 cm was used to quantify CL, CW, BL, and BW (in cm). SS was determined by an Atago® digital refractometer using the juice extracted from the grape pulp. RS was determined according to the colorimetric method proposed by Somogyi-Nelson (Nelson, 1944), which is based on an analytical glucose curve at the absorbance of 510 nm. AT was obtained by titration of 0.1 N NaOH to the equivalence point of pH = 8.2 as indicated by a color change, the MI corresponds to SS/AT ratio, and the pH was determined by a potentiometer Micronal brand, model B274.

Statistical analysis

The joint analysis of crop seasons from 2017, 2018, and 2019 was analyzed according to the following mixed linear model described:

$Y=Xr+Zg+Wi+e$

where: Y is the data vector; r is the vector of plot effects within different seasons (fixed); g is the vector of genetic values effects (random), where σ²_g corresponds to genetic variance; i is the vector effects of cultivars × seasons interaction (random), where σ²_i is the variance of cultivars × seasons interaction; e is the vector of random errors, where σ²_e the variance of errors. X, Z, and W represent the incidence matrices that fit r, g, and i to the Y data vector.

The estimation of the effects of random effects (best unbiased linear prediction - BLUP) of the model was carried out by the equation system of Henderson (1975). The residual maximum likelihood (REML) method was used to estimate the variance components (σ²_g, σ²_i and σ²_e ), as described by Butler et al. (2017).

The significance of variance components was verified by the likelihood ratio test (LRT), according to Resende (2007). The genetic correlations between the characteristics studied were estimated based on the predictions of genetic values, and each characteristic was used to calculate broad sense heritability values and selective accuracy. The statistical analysis was carried out applying R version 3.6.3 using Imer functions and ranef from lme4 library to estimate and predict the mixed model.

For the path analysis, the genetic correlation matrix of the explanatory variables was verified in relation to multicollinearity. The test used was the assessment of the condition number (CN) as proposed by Montgomery and Peck (1981), which examines the ratio between the highest and lowest eigenvalues of the correlation matrix. Multicollinearity is considered low when CN < 100, moderate to high if 100 < CN < 1000, and severe if CN >100. When severe multicollinearity was identified, a constant k was added to the main diagonal of the correlation matrix, similar to the ridge regression method (Carvalho and Cruz, 1996).

The adequate value regarding constant K was determined by examining the ridge (Hoerl and Kennard, 1970), which was obtained by plotting the estimated parameters (path coefficients) as a function of K values within the range of 0 < K < 1. The smallest K value capable of stabilizing most estimates of path coefficient was used. Therefore, path analysis was used to analyze all variables, considering a characteristic yield per vine as a basic variable and the other variables as independent or explanatory. GENES computational program (Cruz, 2013) was applied for the path analysis.

Results and Discussion

The treatments, constituted of different grape cultivar/rootstock combinations for processing, showed significant differences by the likelihood ratio test (LRT) for CM, CL, CW, BM, BL, BW, RM, RM/CM, SS, AT, and RS (Table 1). Essential characteristics, such as the number of clusters per vine (NCV) and average fruit production per vine, did not differ genetically among the grapevine cultivars evaluated, which proceeded in low estimates of heritability. These results point to the need to investigate and select based on the features that are less influenced by the environment and that affect fruit production, allowing indirect genetic progress.

Table 1
– Genetic parameters for the characteristics: NCV = number of clusters per vine; Yield; CM = cluster mass; CL = cluster length; CW = cluster width; BM = berry mass; BL = berry length; BW = berry width; RM = rachis mass; RM/CM; SS = total soluble solids; pH; AT = titratable acidity; MI = maturation index; RS = reducing sugar – estimated by the analysis of cultivars assessed in the harvests of 2017, 2018, and 2019, in Votuporanga, São Paulo State, Brazil.

Parameters	NCV	YIELD	CM	CL	CW
σ2g	27.98	5.80E-05	570.35**	0.67**	0.52**
σ2i	110.81**	1.50**	374.39**	0.98**	0.49**
σ2e	33.08	4.26E-01	268.42	0.78	2.90E-01
h2	31.67	0.0034	78.19	62.14	73.12
rgg	56.23	0.6	88.42	78.82	85.51
Cve	15.23	17.8	13.77	7.23	7.67E+00
Average	37.76	3.67	119.11	12.2	7.02E+00
	BM	BL	BW	RM	RM/CM
σ2g	5.348e-01**	0.045**	0.023**	1.36**	0.653**
σ2i	0.02685**	0.0061	0.0012**	0.26**	0.060 **
σ2e	3.21E-02	0.0316	1.69E-03	0.43	0.149
h2	97	90.5	97.47	92	94.5
rgg	98	95	98.7	95.9	97.2
Cve	7.9	9.98	2.72	19.4	13.5
Average	2.53	1.78	1.513	3.389	2.87
	SS	pH	AT	MI	RS
σ2g	0.36**	2.93E-04	3.900e-02**	13.7458	3.189**
σ2i	0.83**	0.008**	0.03971**	20.052**	0.3672**
σ2e	6.49E-01	3.53E-03	5.87E-03	7.542	9.09E-01
h2	52	9	74	65.39	92
rgg	72.2	30	86	80.8	95.9
Cve	4.72	1.87	7.08	15.6	6.98
Average	3.17	3.17	1.08	17.56	13.67

• ** and * Significant at 1 and 5 %, respectively, by likelihood ratio test (LRT); σ²_g= genotypic variance between cultivar/rootstock combinations; σ²_i= variance of cultivars × season interaction; σ²_e= residual variance; h² = heritability; rgg = selective accuracy; Cve = coefficient of variation.

The interaction of the cultivars × seasons affected almost all characteristics evaluated, except for BL. In other words, the cultivars did not show similar behavior in different seasons for this feature (Table 1). The presence of the genotype × environment interaction makes the selection process difficult and may alter the estimates of several parameters, such as heritability, genetic variance, and even correlation. Correlation is a changeable parameter; thus, it might be underestimated if one of the characteristics offers slight variation due to low environmental control or a strong interaction between genotypes × seasons (Lira et al., 2017). Therefore, evaluating the genotypes in different seasons is essential for a more liable selection. When genotypes are evaluated in a more significant number of places or seasons, the effect of environments and genotypes × environment is estimated with greater precision, and, consequently, the contribution of the genetic effect on phenotypic variation is more accurate (Zambiazzi et al., 2017).

The average yield per vine showed a high and positive genetic correlation with the number of clusters per vine (0.80) (Figure 1). This result was expected since the number of clusters and the cluster mass are directly related to the average production of grapevines. Gupta et al. (2015) also found a similar result while evaluating 20 cultivars of table grapes. The authors also observed that the average production per vine presented a low correlation with the cluster length and width and a high correlation with the number of clusters per vine.

Figure 1
– Estimates of the correlations between vectors of genotypic average predicted by BLUP. NCV = n° of clusters per vine; Yield; CM = cluster mass; CL = cluster length; CW = cluster width; BM = berry mass; BL = berry length; BW = berry width; RM = rachis mass; RM/CM; SS = total soluble solids; pH; AT = Titratable acidity; MI = Maturation index; RS = reducing sugar. **Significant at 5 % of probability and other nonsignificant correlations by the t test.

The correlation between CL with CW (0.94) and BL with BW (0.91) was highly positive. This means that large berries, according to measurements such as length, tend to be bigger in other measurements, such as width; thus, longer grape clusters tend to be wider (Abiri et al., 2020).

The significant and positive correlation reported between SS and RS was 0.87 (Figure 1). The fact that these features are associated suggests that high SS may be used as an indirect measurement to select genotypes with high amounts of reducing sugars. Approximately 95 % of grapes’ total soluble solids content are free sugars, which explains the highly significant correlation between SS and RS. However, the sugar content is a crucial characteristic of grapes for juice production (Borghezan, 2017).

There was also a high and positive correlation between BL and BM (0.95), BW and BM (0.96), BM and SS (0.83), BM and RS (0.98), BL and SS (0.79), BW and SS (0.87), BL and RS (0.92), and BW and RS (0.96) (Figure 1). This shows that the larger the berries, the larger their fresh mass and the higher the content of soluble solids and reducing sugars.

Sugars in ripe berries are present at high contents in the flesh, not in the skin (Coombe et al., 1987; Possner and Kliewer, 1985). Since most berry weight is located in the flesh, the high and positive correlation between reducing sugars and berry fresh mass is easily explained. Moreover, studies have indicated that the amount of sugar per berry was not constant but increased linearly with the berry size (Ferrer et al., 2014; Matthews and Nuzzo, 2007; Roby et al., 2004). These results were similar to our findings and confirmed that the sugar content is proportional to the berry size.

Nevertheless, increases in the sugar content with fresh mass may not be enough to avoid a lower SS in larger berries. Other studies have already observed an inverse correlation between SS and berry mass (Cawthon and Morris, 1982; Roby et al., 2004). The sources of variation in berry sizes, such as viticultural practices, environmental conditions, and grape cultivars, are more critical in determining composition than berry size per se (Matthews and Nuzzo, 2007; Ferrer et al., 2014).

On the other hand, there was a high and negative correlation between CL and CW with RS, providing evidence that the sugar content decreases as cluster size increases. Sugar concentration usually increases with decreasing fruit load (measured as leaf-to-fruit ratio) in many fruits, including grape (Dai et al., 2016). In grapevine, Nuzzo and Matthews (2006) showed that the rate of sugar accumulation occurred more rapidly in berries under a lower fruit load than in those under a higher fruit load.

The NCV and BL were correlated, although in opposite directions, suggesting that the more grape clusters a plant produces, the smaller the size of cluster berries. A negative correlation may be found between the production components, mainly because of competition between these components during plant development in each crop cycle. As stated by Leão et al. (2020), the negative correlation between the number of clusters and berries length arises from the competition for photoassimilates and unbalance in the source/drain.

The maturation index (MI), essential to define fruit flavor, presented a higher correlation to acidity (–0.92) than soluble solids content. These results indicate that fruits with the best flavor are readily selected based on acidity alteration. Acidity, however, is crucial for the industrial sector since it prevents deterioration by microorganisms and allows more flexibility to add sugar (Morgado et al., 2010). On the other hand, the selection to increase the SS/AT ratio is desirable to obtain fruits with good acceptance for table grapes (Ribeiro and Freitas, 2020).

There was also a negative correlation between BM with RM (–0.95), BW with RM (–0.93), BL with RM (–0.84), RM with SS (–0.76), and RM with RS (–0.93) (Figure 1), indicating that both variables move in opposite directions. A close-ratio between these characteristics could either facilitate gene introgression or make it more difficult, since a strong selection for a desirable characteristic may favor the presence of another undesirable germplasm characteristic (Dicenta and Garcia, 1992).

For the path analysis, the multicollinearity diagnosis showed NC = 4037.6, leading to severe multicollinearity (NC > 100). To minimize the adverse effects of multicollinearity, the ridge regression method was applied in which a constant (k) is added to the diagonal elements of the X’X matrix. The k value is the lowest value capable of stabilizing most estimators of the path coefficients (Viotto Del Conte et al., 2020). From there, a value k = 0.1269 is adopted, and all variables were used. In this analysis, the determination coefficient (R²) was 0.91, and the residual variable effect was 0.298, indicating a suitable model adjustment to explain the genetic effects related to the variables under analysis (Figure 2A).

Figure 2
– Path analysis on the direct (A) and indirect effects (B) of NCV = n° of clusters per vine; CM = cluster mass; CL = cluster length; CW = cluster width; BM = berry mass; BL = berry length; BW = berry width; RM = rachis mass; RM/CM; SS = total soluble solids; pH; AT = Titratable acidity; MI = Maturation index; RS = reducing sugar over the yield performed with average data of vine cultivars of grapevines in Votuporanga, São Paulo State, Brazil, in the harvests of 2017, 2018, and 2019.

Some methodologies can be used to mitigate problems caused by multicollinearity, such as the elimination of variables with interrelationships and the ridge regression method. There is difficulty in discarding variables because a variable that is not necessarily more economically important may better explain the primary variable (Bizeti et al., 2004; Viotto Del Conte et al., 2020). Additionally, it may be required to discard many variables. Therefore, the ridge regression method becomes an efficient method to avoid the multicollinearity effect and to include and analyze all variables.

The number of clusters per vine variable (NCV) provided the most significant maximum direct effect on grape production (0.599) and low indirect effects regarding the average production of grapes (Figure 2B). In other words, NCV presented a more relevant direct effect than the residual one and may be considered the most determining variation of grapevine production. In plant breeding, finding correlated variables with a high direct and favorable effect on the primary variable is desirable. In this study, the number of clusters per vine was the feature most correlated to grape production, with the most strongly direct effect on this feature (Figure 2A), confirming the relevance of this variable in the selection process to increase grape production.

Direct positive effects of low magnitude were observed for CM, RM, CL, SS, RS, and maturation indexes. These values were below the residual (Figure 2A). In comparison, direct negative smaller effects were found in CW, BM, BW, BL, RM/CM, and AT. This low magnitude indicates a small contribution of these variables to grape production.

It is known that yield per grapevine is a polygenic characteristic greatly influenced by the environment, which makes the direct increase of grape production a real challenge (Fanizza et al., 2005; Houel et al., 2015; Muñoz-Espinoza et al., 2016). Thus, it is essential to consider the variables that indirectly influence the increase in fruit production, mainly the variables with more significant heritability and easiness of evaluation. Berry mass, berry length, berry width, rachis mass, RM/CM, SS, and reducing sugar indirectly influenced fruit production through NCV. (Figure 2B). These characteristics exhibited high heritability in comparison to yield and NCV and could be used in the indirect selection in breeding programs aiming at increasing fruit production per plant.

Conclusion

The number of clusters per vine demonstrated a higher correlation and direct influence on fruit production in the grapevine. On the other hand, berry fresh mass and length and width were indirectly influenced by the number of clusters for the production variable of grapevine. However, these variables presented higher heritability and may be an excellent selective strategy to obtain indirect gains in the production of grapes for juice production.

Acknowledgments

The authors are grateful to the Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) for the financial support to implement and maintain the experimental site (grants 2013/18913 and, 2015/16440-5).

References

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Edited by

Edited by: Thiago Libório Romanelli

Publication Dates

• Publication in this collection
  23 Oct 2023
• Date of issue
  2024

History

• Received
  11 Oct 2022
• Accepted
  22 Mar 2023