Repeatability of bunch traits in peach palm genotypes selected for table use

Lima, Leidiane de Cássia de Sousa; Oliveira, Maria do Socorro Padilha de; Brandão, Camila Pinto

doi:10.1590/0103-8478cr20250235

ABSTRACT:

Peach palm (Bactris gasipaes Kunth.) exhibits significant variability in fruit traits, which contributes to broad consumer preference for attributes such as flavor and color. Repeatability studies can support breeding programs by facilitating the selection of genotypes with desirable traits for the fruit market. This study estimated repeatability coefficients for bunch traits in peach palm genotypes selected for table use. Twenty-five plants from the Active Peach Palm Germplasm Bank (BAG Pupunha) in Tomé-Açu, Pará, Brazil, were evaluated across three consecutive bunches per plant. Nine traits were assessed: total bunch weight (TBW); number of fertile fruits (NFF); number of parthenocarpic fruits (NPF); number of rachillae per bunch (NRB); bunch rachis length (BRL); mean weight of ten fertile fruits (MW10FF); mean weight of ten parthenocarpic fruits (MW10PF); ripe fruit weight (RFW); and unripe fruit weight (UFW). Repeatability coefficients (r) were estimated using analysis of variance (ANOVA), principal component analysis (PCA) based on covariance (PCA_COV) and correlation (PCA_COR) matrices, and structural analysis (SA). Overall, the methods showed high agreement for coefficient magnitude, except for NFF, NPF, MW10FF, and MW10PF. The lowest numbers of measurements required were observed for NPF and WUF. The covariance-matrix-based approach showed the greatest efficiency. The traits TBW, NPF, WTFF, and WUF are recommended for genotype selection, and evaluating two to three bunches per genotype can achieve accuracies of up to 85% in peach palm genotypes selected for table use.

Key words:
amazon; plant breeding; Bactris gasipaes; principal components

RESUMO:

A pupunheira dispõe de variedade de frutos, tendo ampla preferência por consumidores, indo desde sabor a cor. O estudo de repetibilidade pode subsidiar programas de melhoramento, permitindo a seleção de plantas com características desejáveis ao mercado de fruto. O objetivo do estudo foi estimar os coeficientes de repetibilidade para caracteres de cacho em genótipos de pupunheiras selecionados para mesa. Para isso, foram selecionadas 25 plantas do Banco Ativo de Germoplasma de Pupunha, localizado em Tomé-Açu (PA), a partir da coleta de três cachos consecutivos por planta. Para estimar os coeficientes de repetibilidade foram mensurados nove caracteres: peso total do cacho (PTC); número de frutos férteis (NFF), número de frutos partenocárpicos (NFP); número de ráquilas por cachos (NRC); comprimento da ráque por cacho (CRC); peso de dez frutos férteis (PDFF); peso de dez frutos partenocárpicos (PDFP); peso de frutos maduros (PFMad) e peso de frutos imaturos (PFImat). Além disso, os coeficientes de repetibilidade (r) foram calculados por meio da análise de variância (ANOVA), componentes principais com matriz de covariâncias (CPCV) e de correlações (CPCOR), além da análise estrutural (AE). Os resultados mostram que houve concordância entre os métodos quanto à magnitude dos coeficientes, exceto para NFF, NFP, PDFF e PDFP. Os menores números de medições necessárias foram observados para NFP e PFImat. A metodologia baseada na matriz de covariância mostrou maior eficiência. Portanto, recomenda-se considerar os caracteres PTC, NFP, PDFF e PFImat na seleção de genótipos, sendo possível avaliar de dois a três cachos em genótipos de pupunheira selecionados para mesa, com acurácia de até 85%.

Palavras-chave:
amazônia; melhoramento genético; Bactris gasipaes; componentes principais

INTRODUCTION

Peach palm (Bactris gasipaes Kunth.) is a palm native to the humid tropics with considerable economic potential for multiple applications, contributing to food security, economic development, sustainability, and biodiversity conservation (CARVALHO et al., 2013; BOLANHO et al., 2013; CLEMENT et al., 2017; SPACKI et al., 2022). The species provides two main food products: heart of palm and fruits (GONZÁLEZ-JARAMILLO et al., 2022). Peach palm fruits are notable for their nutritional value and versatility, with applications in oil extraction, baking, animal feed formulation, and table consumption (after appropriate preparation) (MELO SILVA, 2013). For table consumption, they also meet a wide range of consumer preferences in terms of flavor, processing characteristics, and color, especially in the dietary habits of the population of Northern Brazil, where they are typically cooked in water with salt and also incorporated into various dishes, as well as processed into flour (CARVALHO et al., 2013; SPACKI et al., 2022; BUITRAGO ACOSTA et al., 2022). Despite the market preference for peach palm fruits, producers still lack high-quality genetic materials for fruit production (BORGES et al., 2017) because planting material is often derived from seeds used without selection criteria, which directly affects the quality of the products offered to the market (CLEMENT et al., 2009; KRAMER et al., 2023). Historically, peach palm breeding has focused on heart of palm production due to its higher added value and established demand in the agro-industrial market (CLEMENT et al., 2009). However, fruit-oriented research remains limited, underscoring the need for greater investment in studies targeting fruit production.

Fruit-oriented domestication and the selection of superior genotypes are further constrained by the species’ high phenotypic variability. This variability reflects multiple domestication stages across different cultivation regions, particularly for fruit traits (CLEMENT & SANTOS, 2002; SANTOS et al., 2011; CARVALHO et al., 2013). Successful breeding depends on the careful selection of individuals to serve as parents in subsequent generations, thereby reducing the time and resources required to obtain genotypes with improved genetic performance (FARIAS NETO et al., 2013).

In this context, repeatability analysis is a useful statistical tool in breeding programs (CRUZ et al., 2012). It facilitates the selection of superior genotypes by estimating the stability of an individual’s genetic performance across harvests or evaluation periods, based on repeated measurements of the same trait (AZEVEDO et al., 2016). In palms, repeatability analysis has been widely applied to enhance selection efficiency. Examples include bunch traits in açaí palm (OLIVEIRA & FERNANDES, 2001), traits related to heart of palm production in peach palm (FARIAS NETO et al., 2002; PADILHA et al., 2003; BERGO et al., 2013), interspecific hybrids of caiaué and oil palm (CHIA et al., 2009; LOPES et al., 2012), bunch traits in bacabeiras (OLIVEIRA & MOURA, 2010), plant and bunch traits in bacabeiras (MARCIEL et al., 2022), and fruit traits in bacabão (SILVA SOUZA et al., 2023), among others. However, to the best of our knowledge, repeatability estimates for bunch traits in peach palm genotypes selected for table use have not yet been reported. Repeatability analysis may therefore serve as a strategic tool to guide fruit-oriented breeding and expand the agronomic potential of this species.

Thus, the present study aimed to estimate repeatability coefficients for bunch traits in peach palm genotypes selected for table use, thereby providing information to support the advancement of breeding efforts in this species

MATERIALS AND METHODS

Three consecutive mature bunches were harvested from 25 peach palm genotypes previously selected from the Active Peach Palm Germplasm Bank (BAG Pupunha), located at the Embrapa Eastern Amazon experimental field in Tomé-Açu, northeastern Pará State, Brazil. The region has a hot, humid climate, with mean annual rainfall and temperature of 1,791 mm and 26 °C, respectively (INMET, 2024). The genotypes were established in 1993 and planted in rows of five plants at 5 m × 5 m spacing, under upland (non-flooded) conditions, in heavy-textured Yellow Latosol.

Nine bunch and fruit traits were evaluated for each genotype: total bunch weight (TBW); number of fertile fruits (NFF); number of parthenocarpic fruits (NPF); number of rachillae per bunch (NRB); bunch rachis length (BRL); mean weight of ten fertile fruits (MW10FF); mean weight of ten parthenocarpic fruits (MW10PF); ripe fruit weight (RFW); and unripe fruit weight (UFW).

Repeatability coefficients (r) were estimated for all traits using three approaches: (i) two-way analysis of variance (ANOVA), with genotype and bunch as factors; (ii) principal component analysis (PCA) based on covariance (PCA_COV) and correlation (PCA_COR) matrices; and (iii) structural analysis based on the correlation matrix. For PCA-based methods (PCA_COV and PCA_COR), mean values across bunches were used to construct the matrices, and evaluation times were treated as independent variables.

ANOVA-based repeatability

Repeatability was estimated using the model described by (CRUZ et al., 2012): Yij = μ + gi + aj + ɛij, where Yij = is the observation for the i-th genotype in the j-th bunch, μ the overall mean, g_i the random effect of the i-th genotype under permanent environmental influence (i = 1, ..., 25 genotypes), a_j the fixed effect of bunch j (j = 1, 2, 3), and ɛij the experimental error.

Repeatability was calculated as:

$r = \frac{C o v (Y_{i j}, Y_{i^{'} j}}{\sqrt{{V (Y}_{i j}) (Y_{i^{'} j})}} = \frac{{\hat{σ}}_{g}^{2}}{{\hat{σ}}_{g}^{2} + {\hat{σ}}_{ε}^{2}}$

where: r is the coefficient of repeatability, Cov (Y _ij , Y _i’j ) the covariance between two measurements of the same genotype in different evaluation times/environments, V (Y _ij ) and V (Y _i’j ) are the variances of the observations, ${\hat{σ}}_{g}^{2}$ is the genotypic variance (permanent differences among genotypes), and ${\hat{σ}}_{ε}^{2}$ the residual variance, representing temporary environmental effects (within-type variation).

PCA-based repeatability

The principal component method proposed by ABEYWARDENA (1972) estimates repeatability from either the correlation matrix or the phenotypic variance-covariance matrix (Γ).

PCA based on the correlation matrix (PC _COR )

This approach quantifies the correlation among repeated measurements of the same genotype across evaluation times. Ther largest eigenvalue (λ₁) represents the proportion of total variation explained by the tendency of genotypes to maintain their relative ranking across evaluations (CRUZ et al., 2012). Repeatability was estimated as:

$r = \frac{{\hat{λ}}_{1} - 1}{- 1}$

where λ1 is the largest eigenvalue associated with the eigenvector whose elements have the same sign and similar magnitudes, and η the number of evaluations.

PCA based on the covariance matrix (PC _COV )

In this approach, repeatability was estimated from the phenotypic variance-covariance matrix (Γ) as:

$r = \frac{{\hat{λ}}_{1} - {\hat{σ}}_{Y}^{2}}{{\hat{σ}}_{Y}^{2} (- 1)}$

where λ1 is the eigenvalue of Γ associated with the eigenvector whose elements have the same sign and similar magnitudes.

Structural analysis

The structural analysis method proposed by MANSOUR et al. (1981) uses R as the parametric correlation matrix among genotype means for each pair of evaluations, with R as its estimator. Repeatability was estimated as:

$r = \frac{α^{'} R α - 1}{- 1} = \frac{2}{(- 1)} \sum_{j < j^{'}} \sum R_{j j^{'}}$

Where $α^{'} = [1 / \sqrt{η}, 1 / \sqrt{η}, \dots, 1 / \sqrt{η}]$ is the eigenvector associated with the largest eigenvalue of R, η the number of evaluations, and R_jj’ the estimated correlations between repeated measures.

Repeatability coefficients were used to determine the minimum number of evaluations required to obtain reliable estimates, thereby optimizing time, cost, and effort in genotype selection (CRUZ et al., 2012). For each trait, the required number of evaluations (ŋ₀) to predict the true genotype value was calculated for predetermined coefficients of determination (R² = 0.85, 0.90, and 0.95), using the expression proposed by CRUZ et al. (2012):

$_{0} = \frac{R^{2} (1 - \hat{r})}{(1 - R^{2}) \hat{r}}$

where ղ₀ is the number of branches required to predict the true value, R² the coefficient of determination, and r the repeatability coefficient.

The coefficient of determination (R²), which represents the expected accuracy of predicting the true genotype value based on η₀ evaluations, was calculated as:

$R^{2} = \frac{r}{1 + r (- 1)}$

where R² is the coefficient of determination for the number of repetitions tested, ղ₀ the number of branches evaluated, and r the repeatability coefficient.

All analyses were performed using GENES (Computational Application in Genetics and Statistics), a software package for statistical and quantitative genetic analyses in biometrics (CRUZ, 2013; 2016).

RESULTS AND DISCUSSION

Repeatability coefficients (r) and the number of measurements (ηo) required to achieve predefined coefficients of determination (R²) for the nine peach palm bunch traits are presented in table 1. Overall, repeatability estimates were consistent across methods, with similar magnitudes for most traits. Exceptions were observed for NFF, NPF, MW10FF, and MW10PF, which showed greater variation among methods, reflecting differences in the underlying statistical approaches.

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Table 1
Repeatability coefficients (r), coefficients of determination (R²), and the estimated number of bunch evaluations (η0) required under different statistical methods-analysis of variance (ANOVA), principal component analysis based on the covariance matrix (PCA_COV) and correlation (PCA_COR) matrices, and structural analysis based on the correlation matrix (SA_COR)-for nine traits evaluated in 25 peach palm genotypes.

NFF and MW10PF exhibited the lowest repeatability values (0.13-0.48), resulting in low prediction accuracy (31.8%-73.1%) and requiring more evaluations to achieve satisfactory determination. This pattern is expected, since lower r values require more repeated measurements to accurately predict genotype values (CRUZ et al., 2012). Low repeatability in NFF may be attributed to biotic and abiotic sources of variation and limitations in experimental control (FERREIRA et al., 2005), including reduced pollinator activity, given the species’ reliance on entomophilous pollination, and flowering asynchrony in the region (DEPRÁ & GAGLIANONE, 2018; MOLDOLO et al., 2021). For MW10PF, practical sources of variation may also contribute, particularly the large weight differences between fertile and parthenocarpic fruits (FERREIRA, 2005), which increase within-genotype variability and reduce measurement consistency.

By contrast, TBW, NPF, NRB, MW10FF, RFW, and UFW showed higher repeatability (0.51-0.75), with R² values ranging from 75.9% to 90.1%, indicating greater stability across consecutive evaluations and stronger genetic control relative to environmental influence (VENCOVSKY, 1973; AMBRÓSIO et al., 2023; CRUZ et al., 2012). NPF, MW10FF, and UFW exhibited the highest repeatability values, supporting their use as promising parameters for early and indirect selection of superior genotypes due to their greater phenotypic stability (COSTA et al., 2003).

ANOVA generally produced lower or similar repeatability estimates compared to PCA and structural analysis, except for TBW and MW10PF. PCA-based approaches yielded the most favorable estimates, likely because they better isolate the alternation effect (CRUZ et al., 2012). Similar patterns have been reported for palms, including peach palm (FARIAS NETO et al., 2002; BERGO et al., 2013), oil palm (CEDILLO et al., 2008; CHIA et al., 2009), and species of the genus Oenocarpus (OLIVEIRA & MOURA, 2010; MACIEL et al., 2022). These studies reinforce that PCA-based methods provide more accurate repeatability estimates when cyclic variation occurs in production traits (ABEYWARDENA, 1972; CRUZ et al., 2012). By contrast, ANOVA tends to underestimate repeatability under these conditions because alternation is absorbed into the experimental error term (ABEYWARDENA, 1972; KENDALL, 1975; VASCONCELLOS et al., 1985; CHIA et al., 2009; CRUZ et al., 2012). In the present study, the combined use of multiple analytical methods increased confidence in the estimates, since each approach partitions genetic and environmental sources of variation differently, supporting more robust genotype selection.

Repeatability estimates were then used to calculate the minimum number of bunch evaluations (η₀) required to achieve R² values of 0.85, 0.90, and 0.95. NPF and UFW consistently required the fewest evaluations across methods and R² levels (η=2 to 9 branches), indicating high measurement consistency, suggesting that these traits are efficient and cost-effective candidates for selection programs (DANNER et al., 2010). Conversely, MW10PF-particularly under ANOVA-was impractical for achieving 90% (η=58) and 95% (η=122) thresholds due to the high number of required evaluations. Under the PCA_COV approach, R² = 85% was achieved with relatively few bunches: TBW (η = 3), NFF (η = 6), NPF (η = 2), NRB (η = 5), BRL (η = 4), MW10FF (η = 3), MW10PF (η = 1), RFW (η = 5), and UFW (η = 2). This result demonstrated both statistical efficiency and practical feasibility for field evaluations. Higher accuracy levels are attainable by increasing the number of evaluations, with the expectation of reaching R² = 95%.

According to RESENDE (2002), R² values above 80% are adequate for predicting an individual’s true genetic value. Therefore, the evaluation of three bunches per genotype in this study was sufficient to identify superior genotypes for TBW, NPF, MW10FF, and UFW, ensuring R² = 85% accuracy while minimizing experimental costs and time (VALENTE et al., 2017). This approach optimizes breeding resources without compromising the reliability of the estimates (CHIA et al., 2009).

Overall, TBW, NPF, MW10FF, RFW, and UFW were the most promising traits for selection in peach palm breeding programs due to their high repeatability and stability. Conversely, NFF and MW10PF exhibited lower repeatability, requiring more evaluations and stricter environmental control. Finally, PCA_COV provided the most reliable estimates, enabling more efficient and economical selection of productive genotypes to advance peach palm fruit production and quality.

CONCLUSION

The traits TBW (η = 3), NPF (η = 2), MW10FF (η = 3), and UFW (η = 2) were the most consistent across evaluations at R² = 0.85, supporting their use for early and indirect selection in peach palm breeding programs.

Overall, the statistical methods showed good agreement for most traits (TBW, NRB, BRL, RFW, and UFW). PCA_COV was the most efficient approach for identifying stable traits, thereby reducing the number of required measurements and, consequently, evaluation costs. These results highlighted the utility of multivariate methods for early selection and optimizing breeding resources. Because this study was conducted in a single environment and production cycle, further validation across diverse environmental conditions and harvest seasons is recommended to confirm the estimated parameters and broaden their applicability in peach palm breeding programs.

ACKNOWLEDGMENTS

The authors thank Embrapa Amazônia Oriental for providing a DTI-C fellowship to the first author through Project 10.20.02.001.00.00 (CNPq/Embrapa). And was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES), Brazil - Finance Code 001.

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CR-2025-0235.R1
DATA AVAILABILITY STATEMENT
All data generated or analysed during this study are included in this published article.
DECLARATION OF USE OF ARTIFICIAL INTELLIGENCE
The authors declare that they did not use artificial intelligence to realize this study and prepare the manuscript.

Edited by

ASSOCIATE EDITOR:
Alessandro Dal’Col Lúcio (0000-0003-0761-4200)

SCIENTIFIC EDITOR:
Tiago Olivoto (000-0002-0241-9636)

Data availability

All data generated or analysed during this study are included in this published article.

Publication Dates

Publication in this collection
14 Aug 2026
Date of issue
2026

History

Received
02 May 2025
Accepted
13 Jan 2026
Received
30 May 2026

This is an open-access article distributed under the terms of the Creative Commons Attribution License

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Traits ⁽²⁾	Estimates based on 3 evaluations			Number of bunches required for different R²
				R²	ANOVA	PCA_COV	PCA_COR	SA_COR
					ղ₀ ⁽¹⁾	ղ₀ ⁽¹⁾	ղ₀ ⁽¹⁾	ղ₀ ⁽¹⁾
		r	R² (%)
TBW, kg	ANOVA	0.64	84.0	0.85	3.2(3)	2.7(3)	3.3(3)	3.4(3)
	PCA_COV	0.68	86.5	0.90	5.2(5)	4.2(4)	5.3(5)	5.4(5)
	PCA_COR	0.63	83.6	0.95	11.0(11)	8.9(9)	11.2(11)	11.4(11)
	SA_COR	0.63	83.5
		r	R² (%)
NFF, no.	ANOVA	0.35	62.0	0.85	10.4(10)	6.4(6)	9.7(10)	9.9(10)
	PCA_COV	0.47	72.6	0.90	16.5(17)	10.2(10)	15.4(15)	15.7(16)
	PCA_COR	0.37	63.6	0.95	34.9(35)	21.6(22)	32.6(33)	33.1(33)
	SA_COR	0.34	61.1
		r	R² (%)
NPF, no.	ANOVA	0.69	87.2	0.85	2.5(3)	1.9(2)	1.9(2)	1.9(2)
	PCA_COV	0.75	90.1	0.90	4.0(4)	3.0(3)	3.0(3)	3.0(3)
	PCA_COR	0.75	90.0	0.95	8.4(8)	6.3(6)	6.3(6)	6.4(6)
	SA_COR	0.71	87.9
		r	-------------------------------------------------R² (%)-----------------------------------------------------
NRB, no.	ANOVA	0.55	78.4	0.85	4.7(5)	4.7(5)	4.5(5)	4.8(5)
	PCA_COV	0.55	78.4	0.90	7.4(7)	7.4(7)	7.2(7)	7.7(7)
	PCA_COR	0.56	79.0	0.95	15.7(16)	15.7(16)	15.1(15)	16.3(16)
	SA_COR	0.54	77.6
		r	------------------------------------------------R² (%)------------------------------------------------------
BRL, cm	ANOVA	0.58	80.3	0.85	4.2(4)	3.8(4)	3.8(4)	3.8(4)
	PCA_COV	0.60	81.9	0.90	6.6(7)	6.0(6)	6.1(6)	6.1(6)
	PCA_COR	060	81.7	0.95	14.0(14)	12.6(13)	12.8(13)	12.8(13)
	SA_COR	0.60	81.4
		r	R² (%)
MW10FF, g	ANOVA	0.61	82.4	0.85	3.6(4)	2.8(3)	2.9(3)	2.9(3)
	PCA_COV	0.67	85.7	0.90	5.8(6)	4.5(5)	4.6(5)	4.6(5)
	PCA_COR	0.66	85.6	0.95	12.2(12)	9.5(10)	9.6(10)	9.6(10)
	AE_COR	0.66	85.6
		r	R² (%)
MW10PF, g	ANOVA	0.13	31.8	0.85	36.4(36)	0.9(1)	6.3(6)	7.5(8)
	PCA_COV	0.86	94.8	0.90	57.9(58)	1.5(2)	9.9(10)	12.0(12)
	PCA_COR	0.48	73.1	0.95	122.2(122)	3.1(3)	21.0(21)	25.2(25)
	SA_COR	0.14	32.1
		r	R² (%)
RFW, kg	ANOVA	0.51	75.7	0.85	5.5(6)	5.1(5)	5.1(5)	5.4(5)
	PCA_COV	0.53	76.9	0.90	8.7(9)	8.1(8)	8.2(8)	8.6(9)
	PCA_COR	0.52	76.8	0.95	18.3(18)	17.1(17)	17.2(17)	18.2(18)
	SA_COR	0.51	75.9
		r	R² (%)
UFW, kg	ANOVA	0.69	86.9	0.85	2.6(3)	2.2(2)	2.5(3)	2.6(3)
	PCA_COV	0.72	88.6	0.90	4.1(4)	3.5(4)	4.0(4)	4.1(4)
	PCA_COR	0.69	87.0	0.95	8.6(9)	7.3(7)	8.5(9)	8.7(9)
	SA_COR	0.69	86.9