Evaluation of quinoa (Chenopodium quinoa Willd.) genotypes using genotype by trait (GT) and genotype by yield × trait (GYT) methods

Abstract

Quinoa (Chenopodium quinoa Willd.), a native South American crop with high nutritional value, is a promising option for sustainable agriculture in arid and semi-arid regions of Iran, due to its environmental tolerance and valuable composition. This study aimed to evaluate quinoa genotypes using genotype by trait (GT) and genotype by yield × trait (GYT) graphical methods. Twenty genotypes obtained from the IPK Gene Bank in Germany were evaluated in a randomized complete block design with three replications over two cropping seasons (2023 and 2024) in Rasht, Iran. The evaluated traits comprised morphological, phenological, yield-related characteristics, and grain saponin content. The combined analysis of variance (ANOVA) revealed highly significant genetic variation among the genotypes for all traits, with significant effects of year and genotype × year interaction on key traits, including grain yield. GT analysis indicated that the first and second principal components accounted for 26.35% and 19.52%, respectively, explaining a total of 47% of the variance, and confirmed significant positive correlations between grain yield and traits such as panicle length and thousand-grain weight, as well as significant negative correlations between grain yield and specific phenological characteristics. Based on the GT biplot, genotypes 2 and 17, being closest to the center of the concentric circles, were identified as near-ideal genotypes with balanced performance across most traits. In contrast, GYT analysis revealed that the first two principal components accounted for 91.51% of the total variance, and the alignment of GY×PH, GY × SD, and GY×NPP vectors indicated positive correlations among these traits. The GYT biplot suggested that genotypes 6, 8, and 20 had balanced yield-trait profiles, highlighting their potential usefulness for further evaluation. Overall, this study provides preliminary evidence of quinoa performance under the tested conditions and emphasizes the theoretical applicability of the GYT approach in quinoa breeding programs.

Introduction

Quinoa is native to the Andean highlands of South America and originates primarily from the Lake Titicaca region between Peru and Bolivia^1–3. Its cultivation dates back more than 5,000 years, and it is often referred to as the “golden grain” or the “mother grains"⁴. Quinoa, as a valuable pseudo-cereal, is rich in protein, essential amino acids, beneficial fatty acids, fiber, vitamins, minerals, healthy carbohydrates, and bioactive compounds, while being naturally gluten-free^4–6. The compounds present in quinoa seeds make it a potent and beneficial antioxidant, and its polysaccharides exhibit antidiabetic properties, playing a significant role in modulating the immune system^7,8. Quinoa has a wide range of genetic diversity⁹, which allows it to grow in environments from sea level to as high as 4,500 meters¹⁰ and adapt to a variety of harsh conditions, including biotic and abiotic stresses¹¹. Generally, quinoa grain yield varies considerably depending on agroecological conditions¹². According to various studies, grain yield has been reported to range from 0.09 to 0.84 t.ha^− 1 in Morocco¹³, 0.11 to 3.05 t.ha^− 1 in Italy¹⁴, 1 to 3 t.ha^− 1 in Northern Europe¹⁵, and 2 to 3 t.ha^{− 1 16} and 2 to 4 t.ha^{− 1 17} in Iran.

Approximately 570 million farming households manage nearly 80% of the world’s agricultural land, making a significant contribution to local food supplies. A significant portion of these lands is susceptible to recurring drought, recognized as a major climate threat to global food production¹⁸. Breeding programs aimed at introducing new crop genotypes to increase grain yield and ensure food security for the growing population are of paramount importance. Moreover, the release of new crop varieties for any region requires a comprehensive understanding of environmental factors and local climatic conditions, as well as their effects on various morphological, physiological, and yield-related traits. In other words, adaptation and tolerance to regional climatic conditions constitute an effective approach to achieving sustainable production. They should be considered a key objective in breeding programs aimed at introducing new varieties¹⁹. In Iran, 85% of the agricultural land is located in arid and semi-arid regions with saline soils²⁰. Therefore, identifying new crop varieties is crucial for overcoming environmental stresses, such as salinity and drought. Quinoa, as a valuable crop with considerable potential to tolerate various environmental stresses, can be cultivated beyond its native range and represents a promising option for stress-prone agricultural lands^21–23. Quinoa is considered a novel crop in Iran. Although recent studies have aimed to identify quinoa genotypes suitable for cultivation in several regions of Iran^16,17,24,25, these efforts remain limited, and significant gaps still exist in our understanding of the genetic characteristics of different quinoa genotypes.

The primary goal of plant breeders is to increase grain yield²⁶. However, yield is a quantitative trait with low heritability, and selecting superior genotypes based solely on yield may not be effective²⁷. Therefore, to improve grain yield in many breeding programs, traits with high heritability and correlated with yield that have a significant effect on grain yield are utilized to increase the likelihood of selecting high-yielding superior genotypes. Consequently, the evaluation and selection of genotypes are often conducted simultaneously based on multiple correlated traits (multi-trait selection); however, genotype × environment (G × E) interactions and negative correlations among traits complicate this process²⁸. Conventional multi-trait selection techniques, including independent culling levels and selection indices^29,30, rely on arbitrary choices to establish thresholds or assign weights to characteristics for index development, which often yield inconsistent results³¹. An ideal genotype should possess superior levels of several key breeding traits. The genotype × trait (GT) biplot technique, developed by Yan and Kang³², categorizes genotypes based on several qualities and identifies those exhibiting balanced values across all variables as better genotypes. In contrast, the genotype × yield × trait (GYT) approach, proposed by Yan and Frégeau-Reid²⁸, considers yield as the primary and most important trait, and then groups genotypes based on yield and other traits, selecting those that exhibit optimal and balanced values for both yield and the other evaluated traits as superior genotypes. The GT and GYT methods are excellent tools for the graphical evaluation of superior genotypes and for grouping genotypes and traits, compared to traditional statistical techniques such as ANOVA, mean comparisons, linear correlations, and more complex methods like path analysis and selection indices³³. The GYT biplot provides a more comprehensive tool for ranking genotypes and identifying their strengths and weaknesses, addressing a key limitation of the previous GT method, which was affected by negative correlations among traits³⁴. This approach regards yield as a permanent and essential characteristic, with other features becoming significant only when linked to high yield³⁵. In this method, the trait value is multiplied by the yield to assign greater weights to more valuable traits. In contrast, for traits where reduced values are preferred, the yield is divided by the corresponding trait value³⁶.

In recent years, the GT and GYT analyses have been employed to identify desirable genotypes in various crops. Afiah et al.³⁷ showed that there were significant differences among quinoa genotypes in terms of agronomic features and yield under heat stress in Egypt, and identified genotypes such as AMES22157, Q12, and Q27 as preferable. They confirmed the significance of characteristics such as plant height and branch number in enhancing grain output by correlation and path analyses, and emphasized the use of the Genotype × Trait (G×T) biplot as an effective technique for discovering and categorizing potential genotypes. According to Yan and Frégeau-Reid²⁸, the GYT biplot effectively classified oat genotypes based on yield, in conjunction with characteristics such as β-glucan content, lodging resistance, and grain weight. In contrast, the GT biplot exclusively emphasized the correlations between these characteristics. Faheem et al.³⁴ indicated that the GYT biplot, which elucidated 85.1% of the total variance, was a superior instrument for assessing advanced durum wheat lines in comparison to the GT biplot, which represented just 42.2% of the variation. This research revealed genotypes DF19D13 and DF19D14 as the most promising due to their combination of grain production with features such as earliness, short stature, and high thousand-grain weigh. Yang et al.³⁶ applied the GYT biplot analysis in peas (Pisum sativum L.) and demonstrated that genotype Yunwan52 performed best in terms of combining grain yield with traits such as the number of primary branches, seeds per plant, hundred-seed weight, pod length, and number of seeded pods. In addition, genotype Yunwan50 showed superiority when grain yield was combined with plant height. These findings confirmed the effectiveness of the GYT graphical approach in selecting superior pea genotypes. Taherian and Bagheri²⁵ evaluated ten quinoa (Chenopodium quinoa Willd.) genotypes using the graphical GT and GYT approaches at the Kashmar Agricultural Research Station, Iran, over two growing seasons. The GT analysis revealed that high-yielding genotypes were characterized by greater inflorescence length and thousand-seed weight but fewer inflorescences, smaller collar diameter, and shorter plant height. The GYT biplot revealed that Titicaca, Giza1, and Redcarina were the most promising genotypes in the Kashmar area, with greater grain yield, thousand-seed weight, and panicle length. Sadegh Ghol Moghadam et al.³⁸ investigated winter wheat genotypes grown under rainfed conditions to identify suitable genotypes based on root characteristics, yield, and yield components. Their results showed that the GYT biplot performed better than the GT biplot. Xinwang et al.³⁹ assessed agronomic attributes and genotype × yield × trait (GYT) interaction in 16 sugar beet cultivars in seven environments in northern and northeastern China. Their findings demonstrated that cultivar KWS7748 shown enhanced adaptability and production efficacy. Moreover, the GYT biplot provided more reliable insights for multi-trait evaluation of sugar beet compared with Genotype plus Genotype-by-Environment (GGE) and GT biplots.

The objectives of this study were to examine the correlations among agronomic traits and to evaluate and compare the performance of quinoa genotypes by trait (GT) and genotype by yield × trait (GYT) analytical approaches in order to identify promising quinoa genotypes based on multi-trait and yield–trait relationships under the studied conditions.

Materials and methods

The plant materials consisted of 20 quinoa genotypes of diverse origin, native to Bolivia, Chile, and Peru, which were obtained from the IPK Gene Bank, Leibniz Institute of Plant Genetics and Crop Plant Research, Germany (Table 1). The studied genotypes were selected from a larger set of quinoa accessions that had been previously tested in different regions of Iran, due to their satisfactory performance and sufficient variability in key morphological and agronomic traits^16,17. The experiment was conducted in a randomized complete block design (RCBD) with three replications in a research field in Rasht, Iran (latitude 37° 04’ N, longitude 49° 39’ E, with an altitude of 71 m) during two cropping years (2023 and 2024). Meteorological data during plant growth period in 2023 and 2024 and the physico-chemical properties of the experimental soil are presented in Tables 2 and 3, respectively.

Table 1.

Description, identification code, and origin of quinoa (Chenopodium quinoa Willd.) genotypes used in this experiment.

Number	Genotype	ID (Code)	Origin	Number	Genotype	ID (Code)	Origin
1	CHEN68	D2191	Bolivia	11	CHEN156	D9390	Peru
2	CHEN71	D2196	Chile	12	CHEN179	D9358	Chile
3	CHEN83	D2194	Bolivia	13	CHEN205	D9416	Chile
4	CHEN84	D2195	Bolivia	14	CHEN220	D9439	Peru
5	CHEN159	D9376	Bolivia	15	CHEN255	D9502	Chile
6	CHEN215	D9730	Peru	16	CHEN217	D9432	Peru
7	CHEN210	D9421	Chile	17	CHEN225	D9443	Peru
8	CHEN123	D9428	Peru	18	CHEN223	D9442	Chile
9	CHEN115	D9316	Bolivia	19	CHEN206	D9417	Chile
10	CHEN133	D9361	Bolivia	20	CHEN171	D9350	Chile

Table 2.

Meteorological statistics during the years 2023–2024 in the rasht region of guilan province.

Months	Temperature (°C)				Relative humidity		Total rainfall		Total evaporation
	min		max		(%)		(mm)		(mm)
	2023	2024	2023	2024	2023	2024	2023	2024	2023	2024
April	9.32	8.85	20.37	20.16	76.55	74.27	53.90	31.70	79.00	82.00
May	13.24	13.84	23.03	24.61	81.77	76.02	116.20	94.10	78.80	99.10
June	19.26	18.95	29.33	29.49	79.16	73.95	62.80	7.00	132.80	152.60
July	20.09	21.17	29.83	30.57	77.66	74.84	131.80	73.70	126.20	142.30
August	20.81	21.66	33.04	30.60	73.76	79.40	47.50	115.20	150.00	96.60
September	19.67	20.06	28.27	30.04	82.70	76.04	184.60	87.10	78.00	109.20
October	14.44	16.42	24.45	24.63	83.71	86.00	150.10	185.20	53.10	54.60
November	12.34	9.65	24.26	17.51	80.48	89.29	77.70	208.60	55.10	33.10
December	7.54	6.22	18.94	15.04	91.18	88.08	120.00	62.50	42.20	25.70

Table 3.

Physical and chemical properties of the experimental soil.

EC (dS/m)	pH	Organic matter (%)	N (%)	P (ppm)	K (ppm)	Density	Silt (%)	Clay (%)	Sand (%)	Soil texture
1.62	7.61	1.04	0.18	7.2	320	1.51	49.4	30	20.6	Clay loam

Each experimental plot consisted of seven rows, with a spacing of 40 cm between rows and 12 cm between plants, resulting in a planting density of 16 plants per square meter. The spacing between plots and between blocks was 50 cm and 1 m, respectively. Soil moisture of the experimental field was measured using a tensiometer and irrigation was performed using a sprinkler system, according to the plant requirements. Nitrogen (N), phosphorus (P), and potassium (K) fertilizers were applied based on soil test results at rates of 48, 69, and 20 kg/ha of pure N, P, and K, respectively. Weeds were controlled manually by hand-weeding at three times from the four-leaf stage to the end of flowering.

The traits evaluated in this study included days to 90% seedling emergence (DSE), days to four-leaf stage (DFL), days to 50% flowering (DF), days to pollination (DP), days to grain coloring (DGC), days to maturity (DM), panicle length (PL, cm), plant height (PH, cm), stem diameter (SD, cm), root length (RL, cm), number of panicles per plant (NPP), thousand-grain weight (TGW, g), and grain yield (GY, t.ha^− 1). All traits, except GY, were measured on five randomly selected plants from each experimental unit. For GY, all plants from the four central rows of each plot, excluding border rows and edge plants to avoid border effects, were harvested and GY was recorded in t.ha^− 1. SD was measured at the middle of the lower third of the stem using a digital caliper with 0.01 mm accuracy⁴⁰. RL was measured by carefully uprooting and washing the plants, with five plants randomly selected per plot at physiological maturity. Roots were excavated up to 30 cm depth using a spade, washed, and then measured as the linear distance from the crown (root-shoot junction) to the root apex in centimeters⁴¹. GS was determined using the standard afrosimetric method described by Koziol (1991), with minor modifications. Quinoa seed flour (0.50 ± 0.02 g) was directly weighed into a screw-cap test tube (15 cm in length and 15 mm in diameter). After adding 5 mL of distilled water, the tube was capped and shaken vigorously (approximately 4 shakes.s⁻¹, up-and-down movement) for 30 s, then left to stand for 30 min. The tube was shaken vigorously again for 30 s and allowed to rest for a further 30 min. Subsequently, the tube was shaken vigorously for another 30 s as a final shakedown and left to rest for 5 min before reading the foam height. Foam height (FH) was measured to the nearest 0.1 cm using a ruler. Grain saponin content was calculated according to Eq. (1):

1

Where GS is the grain saponin content (mg.g^− 1 of fresh seed weight), FH is the foam height measured 5 min after the final shaking (cm), and SW is the seed weight of fresh sample (g).

Statistical analyses

After data collection, the normality of experimental errors and the homogeneity of error variances were first tested by SPSS 27 software using the Kolmogorov–Smirnov test⁴³ and Bartlett’s test⁴⁴, respectively. Upon confirmation of normal distribution and variance homogeneity, a combined analysis of variance (ANOVA) for the studied traits was performed using SAS 9.4 software. We used the R software (version 4.5.1) and the heatmaply package to perform correlation analyses of the GT and GYT datasets. Pearson’s correlation coefficients among quinoa traits were calculated and visualized as heatmaps, providing a clear representation of the interrelationships among traits. Following that, the genotype ranking was done using the genotype × trait (GT) and genotype × yield × trait (GYT) biplot approaches. For this purpose, the two-year mean values of the traits were used for the GT analysis, while for the GYT analysis, standardized combinations of trait × yield were employed. Standardization was conducted to remove the effects of different measurement units and to homogenize variances²⁸, according to Eq. (2):

2

Where P_ij is the standardized value of genotype i for trait or yield–trait combination j, T_ij is the observed value of genotype i for trait or yield–trait combination j, and and are the mean and standard deviation of the trait or yield–trait combination j across all studied genotypes, respectively. The superiority index (SI) was calculated as the sum of all standardized yield–trait combinations for each genotype, followed by computing the mean superiority index for each genotype. The GT and GYT biplot analyses were also performed according to Eq. (3)²⁸:

3

where and are the eigen values of PC1 and PC2 for trait i, respectively; and are the eigen values of PC1 and PC2 for trait j, respectively; is the residual of fitting PC1 and PC2 of genotype i on trait j; and are the singular values for PC1 and PC2, respectively; α is the singular value partitioning factor. When α = 1 (i.e. SVP = 1 for a two-dimensional GGE biplot), the biplot is genotype-focused, which is suitable for comparing genotypes. When α = 0 (i.e. SVP = 2), the biplot is trait-focused, which is appropriate for visualizing trait relationships. The relationships among genotypes based on traits are not affected by the choice of α. The scalar d is chosen such that the length of the longest vector among genotypes equals the length of the longest vector among traits, which is important for generating a functional two-dimensional biplot²⁸. The GT biplot was constructed by plotting against for genotypes and plotting against for traits on the same graph. The procedure for constructing the GYT biplot was the same as that for the GT biplot, except that the term “trait” was replaced with “yield–trait combination”.

In the GYT analysis, ideotype directions and trait-specific weights were determined to represent the relative biological significance and breeding relevance of each trait in the multi-trait evaluation. Phenological traits, including DSE, DFL, DF, DP, DM and DGC, were assigned a “low” ideotype with moderate weights (0.4). In contrast, morphological and yield-related traits, such as DM, PH, SD, PL, NPP, RL, TGW, and GY, were defined with a “high” ideotype and assigned higher weights (ranging from 0.8 to 1.0) to highlight their greater contribution to overall genotype performance, particularly grain yield. The grain saponin content (GS) was assigned a “low” ideotype with a relatively low weight (0.2), given its lower breeding priority within the analytical framework of this study. Trait weighting was applied solely during the construction of the GYT biplots to improve the interpretability of multi-trait relationships and genotype ranking patterns, and it was not included in the calculation of the superiority index (SI). The figures related to these analyses were plotted using the Metan package in R 4.5.1 software.

Results

Normality test

The results of Kolmogorov–Smirnov test to evaluate the normality of the experimental errors distribution (Table 4), demonstrated that all studied traits conformed to a normal distribution. Similarly, the outcomes of Bartlett’s test for homogeneity of error variances (Table 4) indicated that the Chi-square statistic wasn’t significant across all characteristics, hence affirming the homogeneity of error variances.

Table 4.

Normality and homogeneity of variance tests of experimental errors.

Trait	Chi-Square	Significant level	Kolm.-Smir.	Significant level
DSE= Days to 90% seedling emergence	2.0447	0.1527	0.136	0.200
DFL= Days to four-leaf stage	0.0323	0.8574	0.200	0.055
DF= Days to 50% flowering	0.0968	0.7557	0.151	0.200
DP= Days to pollination	0.0744	0.7850	0.174	0.116
DGC= Days to grain coloring	0.0199	0.8880	0.120	0.200
DM= Days to maturity	0.0738	0.7859	0.171	0.130
PH= Plant height (cm)	0.2429	0.6221	0.148	0.200
SD= Stem diameter (cm)	0.1557	0.6932	0.139	0.200
PL= Panicle length (cm)	0.3197	0.5718	0.116	0.200
RL= Root length (cm)	0.9495	0.3298	0.167	0.147
NPP = No. of panicles per plant	0.00322	0.9548	0.122	0.200
TGW = 1000-grain weight (g)	2.4291	0.1191	0.203	0.051
GY or Y= Grain yield (t.ha− 1)	0.5004	0.4793	0.119	0.200
GS= Grain saponin (%)	1.7451	0.1865	0.110	0.200

Combined analysis of variance

The combined analysis of variance for the studied traits in 20 quinoa genotypes over two years is presented in Table 6. The results showed that the effect of year was significant for DSE, DF, DGC, SD, PL, NPP, and GY (p < 0.01), and for DM and GS (p < 0.05), while it was not significant for DP, PH, RL, and TGW. Based on the results in Table 2, the differences observed between years appear to be mainly influenced by the region’s climatic conditions, particularly rainfall and evapotranspiration during the growing season. Significant differences were also found among genotypes for all measured traits at the 1% probability level, indicating the presence of considerable genetic diversity among the evaluated quinoa genotypes. In addition, the genotype × year interaction was significant for DF, DP, DM, NPP, TGW, and GY, suggesting differential responses of quinoa genotypes to environmental variation across the two experimental years, particularly for GY. This implies that the genotypes did not maintain the same level or ranking of performance across years, and different genotypes achieved the highest yield in each year.

Table 6.

Continue.

Source of variation	df	SD	PL	NPP	RL	TGW	GY	GS
Year	1	37.341**	327.030**	78.408**	1.204ns	0.038ns	0.863**	0.341*
Block (Year)	4	28.940**	21.531ns	18.616**	4.859ns	0.097**	0.217**	0.017ns
Genotype	19	44.619**	157.433**	136.075**	57.732**	0.233**	3.112**	0.647**
Genotype × Year	19	4.862ns	21.671ns	10.583*	3.767ns	0.043*	0.142**	0.050ns
Error	76	5.357	15.140	5.204	3.702	0.025	0.053	0.089
C.V%	-	18.862	16.313	9.495	11.796	8.349	9.753	26.932

ns, *, **: non-significant, significant at P < 0.05 and P < 0.01, respectively.

Relationships among the studied traits

The Pearson’s correlation matrix among the studied traits is presented in Fig. 1. and Fig. 2. The results of correlations based on the GT analysis (Fig. 1) showed that DP had the highest positive correlations with DGC (r = 0.763^**) and DF (r = 0.603^**). Also, SD was positively correlated with PH (r = 0.604^**), while GY exhibited significant negative correlations with DP (r = − 0.567^**) and DM (r = − 0.529^*). The results of trait correlations based on the GYT analysis are presented in Fig. 2, which revealed predominantly positive and significant associations among traits, reflecting favorable yield–trait combinations and providing a useful basis for comparative multi-trait assessment of quinoa genotypes under the evaluated conditions^34,36,45.

Fig. 1.

Pearson’s correlation coefficients for the studied traits in quinoa genotypes based on the GT data. The abbreviations of the studied traits are shown in Table 4.

Fig. 2.

Pearson’s correlation coefficients for the studied traits in quinoa genotypes based on the GYT data. The abbreviations of the studied traits are shown in Table 4.

The genotype by trait (GT) data based on the mean values of the studied traits across the two separate cropping seasons (2023 and 2024) are presented in Table 7. The results showed considerable variation in the agronomic traits of the 20 quinoa genotypes. For example, grain yield (GY) had a standard deviation of 0.72 t.ha^− 1 with an average of 2.36 t.ha^− 1, ranging from 0.93 t.ha^− 1 in genotype No. 10 to 3.41 t.ha^− 1 in genotype No. 1. Regarding phenological traits and earliness, genotype 14 was identified as the late-maturing genotype with a growth period of 151.33 days, while genotypes 5 and 11 were recognized as the early-maturing genotypes with a growth period of about 120 days. The mean for this trait was 134.43 days with a standard deviation of 8.08 days. Plant height (PH) also exhibited the largest variation among genotypes, with a mean of 130.56 cm and a standard deviation of 32.97 cm. Genotype 5 with 182.67 cm was the tallest, whereas genotype 15 with 74.50 cm was the shortest. Such variation is crucial distinguishing promising genotypes⁴⁶.

Table 7.

Genotype by trait (GT) data for the studied 20 quinoa genotypes based on an average of two years, 2023 and 2024. The abbreviations of the studied traits are shown in Table 4.

Genotype	DSE	DFL	DF	DP	DGC	DM	PH	SD	PL	NPP	RL	TGW	GY	GS
1	3.67	8.33	34.50	48.33	61.17	127.00	148.07	14.47	27.08	23.00	20.83	2.14	3.41	1.07
2	4.50	11.17	44.17	58.50	67.33	140.50	125.03	15.54	23.65	30.17	15.62	2.07	1.91	0.69
3	4.83	11.00	48.33	60.33	65.00	135.33	119.17	14.95	26.92	20.50	17.93	1.72	1.84	0.87
4	5.67	12.83	37.17	53.50	61.67	132.83	172.50	15.74	23.41	28.50	12.87	1.86	2.40	1.10
5	5.50	10.83	42.83	55.50	64.83	120.50	182.67	10.89	20.67	23.17	11.17	2.05	2.42	0.70
6	4.17	11.50	42.67	58.17	67.50	129.00	139.83	15.20	24.43	31.50	16.50	1.80	3.36	1.05
7	5.67	11.67	45.67	59.00	63.50	127.83	121.99	13.48	26.72	17.83	11.78	2.19	3.01	1.66
8	5.33	10.50	37.00	60.33	69.00	126.50	136.30	10.01	19.48	18.67	17.00	2.08	3.42	1.41
9	5.17	8.33	40.00	57.50	67.67	138.33	130.83	9.02	27.67	24.00	18.57	1.66	1.40	1.27
10	5.33	11.17	43.33	61.67	67.00	129.17	103.67	9.78	22.57	19.50	12.27	1.76	0.93	1.47
11	5.33	10.33	32.67	52.83	64.67	120.00	100.50	9.92	33.48	20.33	11.82	2.03	3.30	1.39
12	5.17	12.50	36.33	56.83	64.33	140.50	116.40	12.71	23.32	19.67	12.75	1.81	2.35	1.16
13	5.50	9.83	38.50	61.33	66.67	141.83	91.83	11.43	19.92	18.33	16.13	1.77	1.37	1.04
14	4.17	10.83	51.00	59.17	66.17	151.33	115.83	12.55	13.50	24.67	18.67	1.70	2.19	0.68
15	5.00	11.17	39.67	60.00	64.50	141.83	74.50	8.19	13.83	22.67	18.33	1.92	1.86	1.02
16	4.50	10.33	42.67	57.33	65.00	139.33	173.67	14.83	28.63	25.83	17.42	2.07	2.74	0.69
17	6.17	11.17	44.33	61.00	68.67	139.00	179.00	13.06	28.05	34.00	19.93	2.09	2.20	0.86
18	6.67	10.83	33.00	57.50	66.17	138.00	180.00	15.86	29.46	27.33	19.60	2.04	2.16	0.95
19	6.00	11.50	45.33	60.33	67.33	141.00	87.83	7.04	18.22	21.50	19.22	1.70	2.06	1.24
20	5.50	10.83	33.67	52.17	60.83	128.83	111.50	10.78	26.05	29.33	17.83	1.46	2.92	1.85
Mean	5.19	10.83	40.64	57.57	65.45	134.43	130.56	12.27	23.85	24.02	16.31	1.90	2.36	1.11
Standard deviation	0.730	1.10	5.22	3.52	2.35	8.08	32.97	2.73	5.12	4.76	3.10	0.20	0.72	0.33

The GT biplots with settings SVP = 2, Centering = 2, and Scaling = 1 are presented in Figs. 3 and 4, and Fig. 5. Additionally, the genotype by yield–trait (GYT) data and the standardized GYT data are shown in Tables 8 and 9, respectively. The graphical biplots for the GYT analysis with the same specifications (SVP = 2, Centering = 2, and Scaling = 1) are illustrated in Figs. 6, 7 and 8, and Fig. 9. The GYT data (Table 8) was derived from the GY data (Table 7), where each column represents a specific yield–trait combination. In this table, higher values indicate that a genotype performs better in that particular combination of conditions. Furthermore, based on the superiority index (SI) in Table 9, the genotypes were ranked as 1 > 6 > 8 > 11 > 16 > 20. These tables and figures offer an integrated view of genotype performance across numerous variables and demonstrate the usefulness of combining GT and GYT approaches for multi-trait assessment.

Fig. 3.

The genotype by trait (GT) biplot based on standardized data. The abbreviations of the studied traits are shown in Table 4.

Fig. 4.

Polygon diagram of the genotype by trait (GT) biplot to determine the best quinoa genotype. The abbreviations of the studied traits are shown in Table 4.

Fig. 5.

GT biplot ranking of 20 quinoa genotypes compared to the ideal genotype. The abbreviations of the studied traits are shown in Table 4.

Table 8.

Genotype by yield × trait (GYT) data for the studied 20 quinoa genotypes based on the average of two years, 2023 and 2024. The abbreviations of the studied traits are shown in Table 4.

Genotype	GY/DSE	GY/DFL	GY/DF	GY/DP	GY/DGC	GY×DM	GY×PH	GY × SD	GY×PL	GY×NPP	GY×RL	GY×TGW	GY/GS
1	0.931	0.410	0.099	0.071	0.056	433.07	504.919	49.343	92.343	78.430	71.030	7.297	3.20
2	0.424	0.171	0.043	0.033	0.028	268.355	238.807	29.681	45.172	57.625	29.834	3.954	2.77
3	0.382	0.168	0.038	0.031	0.028	249.007	219.273	27.508	49.533	37.720	32.991	3.165	2.12
4	0.424	0.187	0.065	0.045	0.039	318.792	414.000	37.776	56.184	68.400	30.888	4.464	2.18
5	0.440	0.223	0.056	0.044	0.037	291.61	442.061	26.354	50.021	56.071	27.031	4.961	3.44
6	0.807	0.292	0.079	0.058	0.050	433.44	469.829	51.072	82.085	105.840	55.440	6.048	3.21
7	0.531	0.258	0.066	0.051	0.047	384.768	367.190	40.575	80.427	53.668	35.458	6.592	1.81
8	0.641	0.325	0.092	0.057	0.050	432.63	466.146	34.234	66.622	63.851	58.140	7.114	2.43
9	0.271	0.168	0.035	0.024	0.021	193.662	183.162	12.628	38.738	33.600	25.998	2.324	1.10
10	0.174	0.083	0.021	0.015	0.014	120.128	96.413	9.095	20.990	18.135	11.411	1.637	0.63
11	0.619	0.319	0.101	0.062	0.051	396	331.650	32.736	110.484	67.089	39.006	6.699	2.38
12	0.455	0.188	0.065	0.041	0.037	330.175	273.540	29.869	54.802	46.225	29.963	4.254	2.02
13	0.249	0.139	0.036	0.022	0.021	194.307	125.807	15.659	27.290	25.112	22.098	2.425	1.31
14	0.525	0.202	0.043	0.037	0.033	331.412	253.668	27.485	29.565	54.027	40.887	3.723	3.21
15	0.372	0.167	0.047	0.031	0.029	263.803	138.570	15.233	25.724	42.166	34.094	3.571	1.82
16	0.610	0.266	0.064	0.048	0.042	381.764	475.856	40.634	78.446	70.774	47.731	5.672	4.01
17	0.357	0.197	0.050	0.036	0.032	305.8	393.800	28.732	61.710	74.800	43.846	4.598	2.57
18	0.324	0.199	0.065	0.038	0.033	298.08	388.800	34.258	63.634	59.033	42.336	4.406	2.26
19	0.344	0.179	0.045	0.034	0.031	290.46	180.930	14.502	37.533	44.290	39.593	3.502	1.66
20	0.531	0.270	0.087	0.056	0.048	376.183	325.580	31.478	76.066	85.644	52.064	4.263	1.58
Mean	0.471	0.221	0.060	0.042	0.036	314.672	314.500	29.443	57.368	57.125	38.492	4.533	2.286
Standard deviation	0.186	0.076	0.023	0.014	0.011	85.803	129.773	11.638	24.214	21.051	13.777	1.618	0.850

Table 9.

Standardized genotype by yield × trait (GYT) data and superiority index for the studied 20 quinoa genotypes. The abbreviations of the studied traits are shown in Table 4.

Genotype	GY/DSE	GY/DFL	GY/DF	GY/DP	GY/DGC	GY×DM	GY×PH	GY × SD	GY×PL	GY×NPP	GY×RL	GY×TGW	GY/GS	Mean SI
1	2.48	2.49	1.73	2.02	1.70	1.380	1.47	1.71	1.44	1.01	2.36	1.71	1.08	1.74
2	−0.25	−0.65	−0.74	−0.63	−0.69	−0.540	−0.58	0.02	−0.50	0.02	−0.63	−0.36	0.57	−0.38
3	−0.48	−0.70	−0.96	−0.77	−0.69	−0.765	−0.73	−0.17	−0.32	−0.92	−0.40	−0.85	−0.19	−0.61
4	−0.25	−0.44	0.21	0.23	0.23	0.048	0.77	0.72	−0.05	0.54	−0.55	−0.04	−0.12	0.10
5	−0.17	0.04	−0.15	0.13	0.09	−0.269	0.98	−0.27	−0.30	−0.05	−0.83	0.26	1.36	0.06
6	1.81	0.95	0.84	1.12	1.18	1.384	1.20	1.86	1.02	2.31	1.23	0.94	1.09	1.30
7	0.33	0.49	0.27	0.65	0.97	0.817	0.41	0.96	0.95	−0.16	−0.22	1.27	−0.56	0.48
8	0.91	1.38	1.44	1.04	1.15	1.375	1.17	0.41	0.38	0.32	1.43	1.59	0.17	0.98
9	−1.08	−0.70	−1.10	−1.21	−1.36	−1.410	−1.01	−1.44	−0.77	−1.12	−0.91	−1.37	−1.39	−1.14
10	−1.59	−1.81	−1.70	−1.85	−1.95	−2.267	−1.68	−1.75	−1.50	−1.85	−1.97	−1.79	−1.95	−1.82
11	0.80	1.30	1.82	1.45	1.28	0.948	0.13	0.28	2.19	0.47	0.04	1.34	0.11	0.94
12	−0.08	−0.43	0.22	−0.02	0.03	0.181	−0.32	0.04	−0.11	−0.52	−0.62	−0.17	−0.31	−0.16
13	−1.19	−1.08	−1.08	−1.35	−1.37	−1.403	−1.45	−1.18	−1.24	−1.52	−1.19	−1.30	−1.15	−1.27
14	0.30	−0.24	−0.75	−0.32	−0.28	0.195	−0.47	−0.17	−1.15	−0.15	0.17	−0.50	1.09	−0.18
15	−0.53	−0.71	−0.57	−0.74	−0.64	−0.593	−1.36	−1.22	−1.31	−0.71	−0.32	−0.59	−0.55	−0.76
16	0.75	0.59	0.20	0.43	0.52	0.782	1.24	0.96	0.87	0.65	0.67	0.70	2.03	0.80
17	−0.61	−0.31	−0.45	−0.39	−0.37	−0.103	0.61	−0.06	0.18	0.84	0.39	0.04	0.33	0.01
18	−0.79	−0.28	0.24	−0.29	−0.32	−0.193	0.57	0.41	0.26	0.09	0.28	−0.08	−0.03	−0.01
19	−0.68	−0.55	−0.64	−0.52	−0.49	−0.282	−1.03	−1.28	−0.82	−0.61	0.08	−0.64	−0.74	−0.63
20	0.32	0.65	1.19	1.00	1.02	0.717	0.09	0.17	0.77	1.35	0.99	−0.17	−0.83	0.56
Mean	0	0	0	0	0	0	0	0	0	0	0	0	0	0
Standard deviation	1	1	1	1	1	1	1	1	1	1	1	1	1	1

Fig. 6.

Genotype-by-yield × trait values across two years. The relationship based on GYT combination data. The abbreviations of the studied traits are shown in Table 4.

Fig. 7.

Genotype-by-yield × trait values across two years. Which-won-where view based on GYT combination data. The abbreviations of the studied traits are shown in Table 4.

Fig. 8.

Genotype-by-yield × trait values across two years. Average tester coordination view of the GYT biplot. The abbreviations of the studied traits are shown in Table 4.

Fig. 9.

Genotype-by-yield × trait values across two years. Ranking genotypes based on GYT biplot analysis. The abbreviations of the studied traits are shown in Table 4.

Table 5.

Combined analysis of variance for the studied traits of quinoa genotypes in Rasht, Iran, in 2023 and 2024. The abbreviations of the studied traits are shown in Table 4.

Source of variation	df	DSE	DFL	DF	DP	DGC	DM	PH
Year	1	25.208**	6.533*	69.008 **	6.533ns	128.133**	73.633*	0.061ns
Block (Year)	4	3.633ns	3.733ns	3.958 ns	37.533ns	1.941ns	7.783ns	98.098ns
Genotype	19	3.197**	7.245**	163.653**	1414.466**	33.282**	391.849**	6523.545**
Genotype × Year	19	1.471ns	2.375ns	6.025**	469.133**	3.361ns	55.721**	15.70ns
Error	76	1.475	1.505	2.089	12.260	3.310	13.485	50.169
C.V%	-	23.396	11.325	3.557	6.082	2.779	2.731	5.425

ns, *, **: non-significant, significant at P < 0.05 and P < 0.01, respectively.

Genotype by trait (GT) biplot

The results of GT biplot indicated that the first and second principal components explained 26.35% and 19.52% of the total variance, respectively, accounting for approximately 47% of the overall variation in the data (Fig. 3). The cosine of the angle between vectors in this biplot is a useful way to illustrate how traits are related and how they interact with each other. Acute angles between traits indicate positive correlations, right angles (90°) indicate independence, and obtuse angles indicate negative correlations³². As shown, traits such as DM, DF, DGC, and DP were aligned and positively correlated with each other. In contrast, traits such as GY, PL, and TGW exhibited positive correlations among themselves (angles < 90°). However, they were positioned in the opposite direction of the phenological traits (angles > 90°), indicating negative correlations between these two groups of traits. The findings align with the Pearson correlation data (Fig. 1), particularly in the temperate climate of Rasht, northern Iran, where early-maturing quinoa genotypes showed superior grain yield^47,48. Furthermore, traits such as DSE, DFL, and RL showed weak correlations with other traits, as reflected by their shorter vector lengths in the biplot. Additionally, the results of biplot indicated that genotypes 1, 4, and 5, which were aligned with the yield-related vectors, exhibited higher yield potential. In contrast, genotypes 9, 10, 13, 15, and 19, which were positioned in the opposite direction and not aligned with the grain yield vector, exhibited lower grain yield.

Figure 4. illustrates the polygon view of the GT biplot. At the vertices of the polygon, seven genotypes (14, 17, 16, 1, 11, 10, and 19) were positioned. These genotypes, due to their greater distance from the origin, were identified as those with the highest values of the studied traits, either in positive or negative directions. Examination of this biplot showed that genotype 1 had the highest values for GY and PL; genotype 16 for SD, PH, and NPP; genotype 17 for RL; genotype 14 for DM, DFL, DGC, and DP; genotypes 9 and 19 for DSE; and finally genotype 11 for GS.

Figure 5. presents the ideal genotype biplot (GT), a tool for ranking genotypes and comparing them to the ideal genotype. This plot, based on the set of phenological, morphological, and agronomic traits evaluated, specifies the position of the hypothetical ideal genotype on the coordinate axes and then displays the positions of the other genotypes within concentric circles around the hypothetical ideal genotype³². Accordingly, genotypes with shorter distances from the hypothetical ideal genotype are those that exhibit balanced values for all traits studied and are considered as promising genotypes. In contrast, genotypes with greater distances from the ideal genotype do not have favorable performance across the set of traits, although they may exhibit desirable values for certain specific traits. Thus, the ideal genotype biplot provides a clear interpretation of the efficiency of genotypes, delivering key information for breeders to select superior genotypes. The tip of the blue arrow in this biplot, representing the center of the concentric circles, indicates the position of the hypothetical ideal genotype (the genotype with the most desirable values for all studied traits). Based on this analysis, genotypes 17, 2, and 16, followed by genotypes 6 and 18, were the closest to the ideal genotype and had the most desirable values for the set of traits, while genotypes 11 and 20, being the farthest from the ideal genotype, showed unfavorable performance for the overall traits. However, genotypes 11 and 20 had the highest values for the undesirable trait, grain saponin content (GS), while genotype 1 recorded the highest value for grain yield (GY).

Genotype × yield × trait (GYT) biplot

The results of the GYT biplot analysis showed that the first and second principal components explained 86.76% and 4.75% of the total variance, respectively, accounting for a cumulative 91.51% of the total variation among the studied quinoa genotypes (Fig. 6). In contrast, the GT analysis (Fig. 3) yielded a value of only 46.87%. Since in the GYT two-dimensional plot, all yield–trait combinations are considered as components of yield, one of the main characteristics of this analysis is the presence of high and consistent positive associations among traits²⁸. The GYT biplot polygon is presented in Fig. 7. This polygon was constructed by connecting the genotypes farthest from the origin to each other. Based on the polygon (Fig. 7), genotypes 1, 6, 8, 7, 12, 10, and 9, located at the vertices of the polygon, were identified as the most responsive genotypes in this study, meaning that these genotypes show pronounced responses in different yield–trait combinations, exhibiting either the highest or lowest values. Identifying such genotypes plays a key role in enhancing crop productivity and developing effective breeding programs⁴⁹. Additionally, radial lines from the center of the biplot divided the polygon into three significant sections. In the first section, genotype 1, followed by genotypes 6 and 16, exhibited the highest values in terms of the GY × RL and GY × NPP combinations. Genotype 8, followed by 20, was positioned in the second section of the polygon. This area mainly includes traits located near the horizontal axis (PC1) and opposite to the PC2 axis. Traits such as GY × SD and GY×PL, due to their smaller factor loadings in the principal components, played a minor role in explaining the total variance in this section and had limited influence in differentiating genotypes 8 and 20. In contrast, traits such as GY×TGW, GY/DP, GY/DFL, and GY/DGC, which are farther from the origin and form acute angles with the positions of these genotypes, made a more substantial contribution to the ranking of these genotypes within this section. In the third section of the GYT biplot, genotypes 7 and 11 were mainly ranked based on the GY/GS and GY/DSE combinations. Among these, the GY/GS combination, being closer to the origin, contributed less to the overall variance explanation for this group of genotypes, indicating a relatively uniform and low saponin content among these lines. In contrast, the GY/DSE combination, being farther from the origin and closely aligned with these genotypes, played a more significant role in distinguishing and differentiating them. The average tester coordination (ATC) plot (Fig. 8) shows that traits like GY/DFL, GY/DSE, GY/DP, GY×TGW, and GY/DGC (combinations of grain yield with phenological and morphological traits) are clearly on the left half of the horizontal axis. Genotypes 8 and 20 are the best matches for these traits. This suggests that these two genotypes exhibit relatively favorable performance in terms of both physiological and agronomic traits. Notably, genotype 8 is located near the intersection of the axes, suggesting relative stability across most of the combined traits. Genotype 20, followed by genotype 6, is slightly further from the center but aligned in a similar direction, while genotype 10 was ultimately ranked as the weakest genotype. The ideal genotype biplot is presented in Fig. 9. According to this plot, a hypothetical genotype with the most favorable values for all studied traits is positioned at the center of the concentric circles (indicated by the blue arrow), and all other studied genotypes are ranked based on their distance from this hypothetical genotype. Genotypes 8 and 6, having the shortest distance from the center of the concentric circles, were identified as the most balanced and closest to the ideal genotype.

Discussion

A key goal of plant breeding is to suggest new high-yielding cultivars. However, both positive and negative correlations with numerous other traits influence grain yield, which typically has low heritability. As a result, breeders must carefully consider morphological, agronomic, and physiological traits when choosing the best genotypes. This is because these traits can affect grain yield indirectly through their interactions. Correlated traits serve as indirect selection criteria for improving yield. While classical approaches, such as multi-trait selection indices, can be employed for this purpose, they often rely on trait weighting to construct indices, which can result in inconsistent outcomes. In contrast, graphical statistical tools such as the genotype × trait (GT) biplot and the genotype–yield × trait (GYT) biplot provide strong visual frameworks for assessing cultivars and traits simultaneously. This makes it easier to find genotypes that have balanced and acceptable levels across all traits, especially yield, along with other important characteristics.

The results of the combined ANOVA (Table 6) indicated that variations in climatic conditions across the experimental years (Table 2), particularly precipitation patterns, evapotranspiration, and temperature, had a significant influence on the growth and development of quinoa genotypes. Most traits exhibited high sensitivity to inter-annual environmental fluctuations. Consistently, previous studies have reported that environmental variability, including rainfall and temperature, directly affects the phenological and physiological traits of quinoa^50,51. In particular, recent research has highlighted that genotype, environment, and their interaction (G × E) significantly impact quinoa seed yield^16,52. The significant genotypic variation observed for all evaluated traits indicates the presence of considerable genetic diversity among the studied quinoa genotypes. Such diversity provides a useful basis for comparative evaluation and for identifying genotypes with desirable trait combinations. This aspect is particularly relevant for grain yield, which remains a primary target in quinoa breeding programs⁴⁷. Both genetic and environmental factors, as well as their interaction (G×E), are known to influence phenological and yield-related traits; however, the limited number of environments evaluated in the present study restricts the extent to which these effects can be fully characterized. Previous studies have shown that single-environment or limited-environment evaluations may be insufficient for drawing broad conclusions regarding genotype performance, as genotype rankings can vary across years or environments. In this context, the use of multivariate approaches, such as GT and GYT analyses, offers a practical framework for multi-trait assessment and comparative interpretation of genotype performance under the tested conditions.

The correlation matrix (Fig. 1) revealed strong positive associations between DP and DGC (r = 0.763^**), DP and DF (r = 0.603^**), and SD and PH (r = 0.604^**), suggesting a coordinated pattern of phenological and morphological development in quinoa. These relationships may highlight the close linkage between key vegetative and reproductive growth stages, whereby genotypes with synchronized flowering and pollination may also tend to progress through subsequent stages, such as inflorescence development, in a coordinated manner. Such correlations may be related to shared physiological and genetic regulatory pathways that govern quinoa growth and development^54,55. Additionally, the positive correlation between SD and PH may be attributed to the plant’s structural characteristics. Genotypes with stronger stems are more likely to reach a higher altitude, which optimizes light capture and increases resistance to mechanical stresses such as wind or grain weight^56,57. This coordination across phenological and morphological traits can be leveraged as a selective advantage in breeding programs. Interestingly, our findings also demonstrated that grain yield (GY) was significantly and negatively correlated with late-maturing phenological traits, suggesting that early-maturing genotypes tended to show higher grain yield under the evaluated conditions. This result is consistent with numerous studies that have identified days to flowering and maturity as key determinants of quinoa performance and yield potential. For instance, research conducted in Morocco, Italy, and Brazil has shown that early sowing dates in temperate environments are often associated with favorable growth conditions reduced exposure to terminal stresses, which may contribute to accelerated maturation and improved grain yield^58–60. Consequently, the selection and further evaluation of early-maturing genotypes may represent a promising approach for improving quinoa productivity under the evaluated temperate conditions.

Based on the two-dimensional GT biplot (Fig. 3), traits such as PL, TGW, PH, SD, and NPP were identified as influential variables with high variation for discriminating high-yielding quinoa genotypes. A positive association was evident between GY and both PL and TGW. Although these correlations were not statistically significant in the present study (Fig. 1), several previous reports have consistently confirmed the positive relationships between GY and TGW or PL^17,61,62. Such associations suggest that these traits are likely governed by shared genetic regulation or may be influenced by pleiotropic QTLs^63,64. Overall, the GT biplot indicated that Genotypes 1, 4, and 5 were closely associated with GY. However, this relationship did not account for other important traits, such as DM. This limitation highlights that the GT analysis alone cannot reliably identify superior genotypes, as it may overemphasize yield performance while neglecting other agronomically essential attributes. Therefore, GT should not be considered a comprehensive tool for genotype ranking in breeding programs.

According to several published reports, the GYT method has proven to be more precise and effective than GT when selecting simultaneously for multiple traits across environments^28,34,39. By integrating yield with other key agronomic and physiological traits, GYT facilitates a more targeted and efficient identification of superior genotypes^35,65. In the first GYT biplot presented by Yan and Frégeau-Reid²⁸, yield–trait combinations were regarded as unweighted and of equal significance. However, in breeding programs with specific objectives, assigning differential weights to traits can enhance the precision of selection⁶⁶. In this study, lower weights were assigned to traits such as grain saponin content and phenological traits (e.g., DSE, DFL, DF, DP, DM, and DGC), while higher weights were assigned to traits that directly influence yield. This weighting strategy increased the accuracy of genotype ranking based on breeding priorities and improved the identification of desirable genotypes with balanced trait combinations. The GYT analysis revealed that the initial two principal components accounted for 91.51% of the total variance. This indicated that the biplots were experienced in describing the variation in genotype × yield × trait data. Other studies have reported similar levels of explained variance, including 85.49%⁶⁷, 85%³⁴, 96.96%³⁶, and 91.1%⁴⁵.

In the Average Tester Coordination (ATC) biplot (Fig. 6), constructed according to the framework proposed by Yan and Frégeau-Reid²⁸, the orientation of yield–trait combination vectors played a key role in interpreting genotype performance. Unlike the classical GGE biplot, where the positive PC1 axis generally reflects superior genotypes and mainly emphasizes overall yield, the GYT approach defines desirability based on the direction of combined traits. The ATC view revealed that genotypes 8 and 20 showed the most substantial alignment with yield–trait combinations involving phenological and morphological attributes (GY/DFL, GY/DSE, GY/DP, GY×TGW, and GY/DGC). Notably, Genotype 8 was situated close to the biplot origin, indicating a more balanced and consistent performance across the evaluated yield–trait combinations. In contrast, genotype 10 was ranked lowest in the ATC view, reflecting its weak association with key traits and, consequently, lower overall usefulness compared to the superior genotypes. These results underscore the value of the GYT approach, which not only evaluates overall yield performance but also highlights the ability of genotypes to effectively combine yield with essential agronomic and physiological traits, thereby facilitating a more comprehensive multi-trait assessment of genotype performance.

Overall, the GYT analysis identified genotypes 8, 6, and 20 as promising performers based on their balanced yield–trait combinations within the scope of the present experiment. The GYT biplot provided a comprehensive visualization of the relationships between traits and grain yield, where the length, direction, and angles of trait vectors clearly revealed the structure of positive and negative correlations. This approach enabled the identification of favorable yield–trait combinations, offering a clearer and more objective understanding of genotype performance under the evaluated conditions. By simultaneously integrating multiple traits with yield, the GYT method enhanced the interpretation of genotype behavior and supported more informed breeding decisions compared with univariate analyses, providing a holistic assessment of overall genotype desirability.

Conclusion

This study evaluated 20 quinoa genotypes for agronomic traits and grain yield using the graphical methods of GT and GYT under the semi-Mediterranean climate of Rasht, Iran, during two cropping seasons (2023–2024). The combined ANOVA revealed significant genetic variation among genotypes and a year effect on traits such as grain yield, days to flowering, No. of panicles per plant, and stem diameter. Pearson Correlation analysis and GT biplot revealed positive correlation between panicle length, thousand-grain weight, stem diameter, and grain yield. In contrast, phenological traits, including days to pollination and days to maturity, showed significant negative correlations. The GYT analysis, which explained 91.51% of the total variation, showed higher discriminatory power than the GT approach and identified genotypes 6, 8, and 20 as promising genotypes, combining high yield with favorable agronomic traits. These results demonstrate that the comprehensive and effective GYT approach allows quinoa genotypes to be ranked based on combined trait performance, simultaneously identifying strengths and weaknesses across different traits. Nevertheless, genotype × year interactions and climatic variability were limiting factors. Future studies should test the selected genotypes across a broader range of environments, with a focus on drought and salinity tolerance. This study represents an essential step toward improving quinoa genotypes for food security and sustainable agriculture in Iran.

Author contributions

Amir Forghani Saravani: Investigation, data collection and analysis, writing original draft. Babak Rabiei: Supervision, conceptualization, visualization, methodology, funding acquisition, writing - original draft, writing - review & editing, Ebrahim Souri Laki: Writing original draft, writing - review & editing, supervision. All the authors read and approved the final manuscript. All the authors have agreed with the published version of the manuscript.

Funding

This research was funded by the University of Guilan, Iran, with Grant No. 176,129/1403.

Data availability

Data will be made available by the corresponding author.

Declarations

Competing interests

The authors declare no competing interests.