Maternal effects, reciprocal differences and combining ability study for yield and its component traits in maize (Zea mays L.) through modified diallel analysis

Field evaluation of diallel crosses

The selected eight parental inbred lines of maize (Table 1) were planted during October, 2019 (Rabi season) and crossing was done in full diallel method (including reciprocal crosses) and harvested in the month of April, 2020. The harvested ears were shelled, processed and the seed packets were prepared. These, 56 F₁ hybrids along with four checks: 900-M Gold, NK-6240, GH-0727 and GH-150125 and the parent lines were planted in the month of June, 2020 (Kharif season) at the All India Co-ordinated Maize Improvement Project, UAS, Dharwad in completely randomized block design with three replications for evaluation. The specific weather conditions for the growing season are provided in Table 2. The soil at the experimental site was medium-deep black soil (Vertic Inseptisol) and evaluation was under optimal situation. All the genotypes (hybrids and parental lines) were raised in two rows of four meters length by following a spacing of 60 cm × 20 cm. The recommended maize package of practices for maize were followed to raise a healthy crop (Zaidi et al., 2017; http://aicrpmaize.icar.gov.in/karnataka;k0162_3.pdf (icar.gov.in)).

Data collection

The data on eight quantitative traits was measured across all the replications. The traits studied were: days to 50% tasseling (DTT), days to 50% silking (DTS), number of kernel rows per cob (NKRC), number of kernels per row (NKR), cob girth (CG) (cm), cob length (CL) (cm), hundred grain weight (HGW) (g) and grain yield (GY) (q/ha). Below is a detailed description of the method used to measure these traits.

DTT: Number of days from the day of sowing to the day on which 50 per cent of the plants in the treatment showed anthesis was recorded as days to 50% tasseling.

DTS: Number of days from the day of sowing to the day on which 50 per cent of the plants in the treatment showed silk emergence was recorded as days to 50% silking.

NKR: The average number of kernels per row from five cobs from the base to tip of ear counted physically and recorded.

NKRC: The number of kernel rows counted physically and recorded from five cobs and averaged.

CG: Average cob girth of five cobs measured using vernier caliper after removing the husk at the middle portion of the ear and measured in centimeters (cm).

CL: Average length of five cobs in centimeters (cm) after harvest measured from the base to the tip of the ear.

HGW: Weight of hundred grains drawn from a random sun-dried sample and measured in grams (g).

GY: Weight of the de-husked ears/plot recorded at the time of harvest and then converted to grain yield at 15 per cent moisture and expressed in quintals per hectare (q/ha).

Statistical analysis

With the aid of the statistical software package Rstudio version 2022.07.1 (RStudio Team, 2022) and Microsoft Excel, the data gathered for the traits was put together and examined according to Griffing (1956a). The diallel analysis with R package (Yaseen, 2018) was used to examine various effects and combining ability of method 1 and model I of the diallel analysis. The model used was ${\displaystyle Y_{ij}=\mu +g_i+g_j+s_{ij}+r_{ij}+\frac{1}{c}\sum k{e}_{ij}}$

where Y_ij is the observed measurement of parents i and j; µ is the population mean; gi and gj are the GCA effects of parent i and j respectively; s_ij is the SCA effect of the cross between parents i and j; r_ij is RECs and e_ij is the random environmental effects associated with ij^th individual. The restrictions imposed on the combining ability effects were: ∑g_i = 0 and ∑s_ij = 0 for each j (Griffing, 1956b).

According to Singh & Chaudhary (1985) the genetic components or variance due to GCA (σ²_GCA), SCA (σ²_SCA), and RCA (σ²_RCA) were estimated. The ratio of GCA variance to SCA variance was also calculated, with ratios greater than unity indicating additive gene action and ratios less than unity indicating dominance genetic effect (i.e., non-additive gene action) for the particular trait.

The additive and dominant variances, heritability was also calculated from σ²_GCA, σ²_SCA, σ²_RCA as follows,

σ²_A = 2 σ_GCA

σ²_D = σ_SCA ${\displaystyle \begin{array}{c}{H}_{bs}^2=\frac{{\sigma }_A^2+{\sigma }_D^2}{{\sigma }_P^2}\hfill \\ h_{ns}^2=\frac{{\sigma }_A^2}{{\sigma }_P^2}\hfill \end{array}}$

where r = Number of replications, σ²_GCA = Variance due to GCA, σ²_SCA = Variance due to SCA, σ²_RCA = Reciprocal variance, σ²error = Error variance, σ²_P = Phenotypic variance, σ²_A = Additive variance, σ²_D = Dominance variance, H²_bs = Broad sense heritability, h²_ns = Narrow sense heritability (Singh & Chaudhary, 1985).

Baker’s ratio was used to determine the relative importance of GCA and SCA effects for each trait (Baker, 1978).

Baker’s ratio = $\frac{2{\sigma }_{GCA}^2}{\left[2{\sigma }_{GCA}^2+{\sigma }_{SCA}^2\right]}$

Griffing’s model formula

Griffing’s method of combining ability effects was estimated using the following model, ${\displaystyle \begin{array}{c}\hfill {\hat{g}}_i=\frac{1}{2n}\left({x_i}_{.}+{x_{.}}_i\right)–\frac{1}{n^2}\left({x_{.}}_{.}\right)\hfill \\ \hfill {\hat{s}}_{ij}=\frac{1}{2}\left({x_i}_j+{x_j}_i\right)-\frac{1}{2n}\left({x_i}_{.}+x_{.i}+{x_j}_{.}+x_{.j}\right)+\frac{1}{n^2}\left({x_{.}}_{.}\right)\hfill \\ \hfill \widehat{r_{ij}}=\frac{1}{2}\left(x_{ij}-x_{ji}\right)\hfill \end{array}}$

Modified model formula

For the precise estimation, the GCA effect is $\widehat{g_i}$ partitioned according to Mahgoub (2011) to estimate GCA effect for the parent when it is used as a female in its hybrid combination $\widehat{g_{fi}}$ and GCA effect for the same parent when it is used as a male in its hybrid combination $\widehat{g_{mi}}$ as follows: ${\displaystyle \begin{array}{c}\hfill \widehat{g_{fi}}=\frac{1}{n}\left(x_{i.}\right)-\frac{1}{n^2}\left(x_{..}\right)\hfill \\ \hfill \widehat{g_{mi}}=\frac{1}{n}\left(x_{.i}\right)-\frac{1}{n^2}\left(x_{..}\right)\hfill \\ \hfill \widehat{g_i}=\frac{1}{2}\left(\widehat{g_{fi}}+\widehat{g_{mi}}\right)\hfill \end{array}}$

where, $\sum \widehat{g_{fi}}=0,\sum \widehat{g_{mi}}=0$ and $\sum \widehat{g_i}=0$ ${\displaystyle \begin{array}{c}\hfill \frac{1}{2}\left(\widehat{g_{fi}}-\widehat{g_{mi}}\right)=\frac{1}{2}\left[\frac{1}{n}\left(x_{i.}\right)-\frac{1}{n^2}\left(x_{..}\right)-\frac{1}{n}\left(x_{.i}\right)+\frac{1}{n^2}\left(x_{..}\right)\right]\hfill \\ \hfill \frac{1}{2}\left(\widehat{g_{fi}}-\widehat{g_{mi}}\right)=\frac{1}{2}\left[\frac{1}{n}\left(x_{i.}\right)-\frac{1}{n}\left(x_{.i}\right)\right]=\frac{1}{2}\left(x_{i.}-x_{.i}\right)\hfill \\ \hfill \widehat{m_i}=\frac{1}{2}\left(\widehat{g_{fi}}-\widehat{g_{mi}}\right)\hfill \end{array}}$

where $\sum \hat{m}=0$.

The average difference between the $\widehat{g_{fi}}$ and $\widehat{g_{mi}}$ was proved to be equal to of maternal effects. It is exactly equal to maternal effect estimated according to Cockerham (1963) $\hat{m}=\left(\frac{x_{i.}-x_{.i}}{2n}\right)$. Thus, it proves the $\widehat{g_{fi}}-\widehat{g_{mi}}$ estimate provides the precise estimation of maternal effects.

Specific combining ability effect is partitioned to estimate SCA effect for the cross $\widehat{s_{ij}}$ and for its reciprocal $\widehat{s_{ji}}$ as follows: ${\displaystyle \begin{array}{c}\widehat{s_{ij}}=x_{ij}-\frac{1}{2}\left(x_{i.}+x_{.i}+x_{j.}+x_{.j}\right)+\frac{1}{n^2}\left(x_{..}\right)\hfill \\ \widehat{s_{ji}}=x_{ji}-\frac{1}{2}\left(x_{i.}+x_{.i}+x_{j.}+x_{.j}\right)+\frac{1}{n^2}\left(x_{..}\right)\hfill \end{array}}$

where, $\sum \widehat{s_{ij}}+\widehat{s_{ji}}=2Griffin{g}^{\prime }s\widehat{s_{ij}}$

Reciprocal effects were calculated from partitioned specific combining ability as follow, ${\displaystyle r_{ij}=\frac{1}{2}\left(\widehat{s_{ij}}-\widehat{s_{ji}}\right)and{r}_{ji}=-r_{ij}}$

As a result, the difference between the SCA effect of a cross and its reciprocal equals the estimated reciprocal effect. Therefore, this difference provides a precise estimate of the reciprocal effect. Testing the significance differences was estimated according to Griffing’s method.

where

$\widehat{g_i}$ = Griffing’s GCA effect of i^th parent,

$\widehat{g_{fi}}$ = Mean deviation of the i^th parent as a female, averaged over a set of n males, from the grand mean,

$\widehat{g_{mi}}$ = Mean deviation of the i^th parent as a male, averaged over a set of n females, from the grand mean,

$\widehat{m_i}$ = Maternal effect of i^th parent,

$\widehat{s_{ij}}$ = SCA effect of the cross combination with i^th female and the j^th male parent,

$\widehat{s_{ji}}$ = SCA effect of the cross combination with j^th female and the i^th male parent,

r_ij = reciprocal effect involving the i^th female and the j^th male parent,

x_ij = The mean of cross resulting from crossing the i^th female with the j^th male,

x_ji = The mean of cross resulting from crossing the j^th female with the i^th male,

x_i. = The sum of i^th female over all males,

x_.i = The sum of i^th male over all females,

x_j. = The sum of j^th female over all males,

x_.j = The sum of j ^th male over all females,

x_.. = Grand total.

Correlation analysis

The mean values, mid-parent, and better-parent heterosis were correlated with the Griffing’s GCA, SCA, and adjusted GCA and SCA effects. The heterosis values of straight and reciprocal hybrids (S3-6) and the mean performance of straight and reciprocal hybrids (S1-2) were listed in the supporting files. Using MS-Excel, the correlation analysis was carried out.

Analysis of variance for combining ability

To understand source of variability and how it is manifested in the experimental material the analysis of variance was computed (Table 3). The results of the statistical analysis of variance showed that the treatments were significant for each of the traits, which suggests that the experimental material was varied. The GCA was significant for all the examined traits, but for the traits DTT, DTS and NKRC it was higher than the SCA indicating that these traits are regulated by additive gene action. SCA was also significant for all the traits, but for NKR, CL, HGW and GY it was higher than GCA, indicating the significance of non-additive gene action in regulating these traits. For cob girth (CG) even though GCA and SCA were significant but their effects were very low. The value of the maternal effect is demonstrated by the significance of RECs in every trait. Maternal and non-maternal components make up the reciprocal effect but it is the maternal component that is important.

Genetic parameters

The information on genetic parameters and heritability are shown in Table 4 with their estimates. The σ²e was significantly lower indicating that all the traits had lesser impact from the environment. The NKRC trait had a σ²A value higher than σ²D, indicating that additive genes were primarily responsible for this trait. The fact that SCA variance for all the traits was greater than GCA variance shows that non-additive gene action plays an important role in governing all traits primarily (Table 4). The additive to dominance variance ratio for NKRC was greater than unity, indicating additive gene action. The trait DTS (H²bs = 94.54) showed the highest broad sense heritability. All other traits also demonstrated high broad sense heritability. The narrow sense heritability of all other traits was low, except for the NKRC (h²ns = 45.26), which had a medium narrow sense heritability. The relative significance of GCA and SCA effects in predicting progeny performance was examined using Baker’s ratio. For the traits like NKRC, the Baker’s ratio was greater than 0.5, whereas it was less than 0.5 and close to zero for the traits NKR, CL, HSW, and GY.

General combining ability

Griffing’s method and modified method were used to estimate the GCA effects, and Table 5 shows Griffing’s GCA effect and partitioned adjusted GCA values. The parental lines P1 (−1.43, −0.72) and P3 (−2.47, −1.66) are found to be good general combiners for earliness based on the estimates for the traits DTT and DTS, respectively, according to Griffing’s GCA effects (g_i). For grain yield the parental line P7 recorded significantly highest and positive GCA effects for GY (4.98). Apart from this, the line P7 also recorded significant GCA values for other yield contributing traits like NKR (2.01), NKRC (0.94), CL (0.69), and CG (0.11). This was followed by the parental lines P3 (2.65) and P4 (1.75) recording significant values for GY. Therefore, these three lines P7, P3 and P4 can be used as source of good general combiners for grain yield trait. Similarly, the parental lines P5 (1.86) and P4 (1.2) recorded highest and significant GCA values for HGW and were found to be good general combiners.

How a particular line will behave as a male and female parent in the hybrid combination can be determined by comparing the adjusted GCA values after partitioning into male (g_mi) and female GCA (g_fi) effects (Table 5). The parental line P7 exhibited a significant GCA effect for GY [g_mi (3.42) and g_fi (6.54)] followed by for other traits also NKR [g_mi (2.11) and g_fi (1.91)], NKRC [g_mi (0.80) and g_fi (1.08)], CG [g_mi (0.05) and g_fi (0.17)] and CL[g_mi (0.45) and g_fi (0.93)] respectively based on the adjusted values. The parental line P5 recorded highest and significant breeding value in a negative direction [g_mi (−12.20)] when used as male parent for GY. It recorded highest and significant values in a positive direction [gfi (13.90)] when used as a female parent, as opposed to gi (0.85), indicating that it is a potential line when used as a female parent for grain yield as opposed to other lines. Similarly, among the remaining parental lines P6 (7.21), P4 (6.55), P3 (5.10) followed by P7 (3.42) recorded significant g_mi values for GY in a positive direction as compared to g_i (−0.38, 1.75, 2.65, and 4.98). Likewise, for HGW the parental lines P5 (3.02), P2 (0.83), and P8 (0.83) recorded high GCA values when used as females as compared to g_mi (−0.92, 0.70, and −0.05). Only one parental line P4 recorded highest GCA for the HGW trait when used as a male parent (1.70), indicating that it contributes more when used as a male parent. Griffing’s GCA and partitioned GCA values of all eight parents is presented in Fig. 1. The figure clearly indicates that the parental lines P5 and P6 behaved differently when used as female and male parent based on the partitioned GCA values as compared to Griffing’s value for GY, while the parental lines P1 and P7 did not differ significantly for Griffing’s GCA and partitioned GCA values for GY. These results highlight that different genetic background (both nucleus and cytoplasmic factors) of a line plays a crucial role in deciding the breeding value of a crop.

Maternal effect

The adjusted maternal effects, which are shown in Table 6, were determined by averaging the g_fi and g_mi differences. The average of the female over all the males is typically used to estimate the maternal effect. Estimating maternal effects for some specific cross combinations might be more crucial than using the ratio of all females to all associated males as a baseline. If it estimates taking into account all males over all females, it may underestimate the maternal effect of a few cross combinations. The estimation of the reciprocal effects follows the partitioning of the maternal effects, which results from the estimation of the maternal effects on a hybrid combination basis rather than on the average of all the associated male parents.

The findings (Table 6) indicated that the parental line P3 recorded significant maternal effects but in an unfavorable negative direction for all of the quantitative traits measured. Apart from that none of the parental lines recorded either completely negative or positive maternal effect values for all the traits. For grain yield the line P5 recorded highest and significant maternal effects (13.05) in a positive direction followed by P8 (3.92) and P7 (1.56). The same line (P5) also recorded significant values for maternal effects in a positive direction for all other traits except DTT and DTS. On the other hand P6 recorded significant maternal effects in a negative direction for GY (−7.59) followed by P4 (−4.79). The line P6 recorded significant maternal effects but in a negative direction for yield contributing traits NKR, NKRC, CL and CG. For DTT and DTS the line recorded significant maternal effects in a positive direction. For maturity traits i.e., DTT and DTS the maternal effect observed in P3 (−1.17 and −1.08) was in a negative direction, thus the line P3 may be used as a female parent while developing the early maturing hybrids.

Specific combining ability

The partitioning of SCA provides additional information, such as the SCA of the straight cross and its reciprocal cross. Griffing’s SCA estimation assumes a single SCA value for a cross combination. The hightest value of Griffing’s SCA effect for grain yield was observed in the cross combination of P4×P7 (30.56) (Table 7). However, there was no significant difference between Griffing’s SCA and the adjusted straight and reciprocal cross SCA values for the cross P4×P7. Many crosses revealed noticeable variations between Griffing’s SCA and adjusted straight and reciprocal cross SCA values (P1×P8, P4×P5 and P2×P5). For other traits, some of the crosses did not show any variation between Griffing’s SCA and adjusted straight and reciprocal cross SCA values viz., for NKRC and CL (P4×P7 and P7×P8), HGW and CG (P4×P8).

The comparison of SCA for GY of top performing hybrids were depicted in the Fig. 2. The trend of Griffing’s SCA and the portioned effects clearly indicates the differences of the Griffing’s analysis and the partitioning methods. The cross P5×P6 recorded significant SCA values for GY (35.30) in a positive direction for the adjusted straight cross. But for the adjusted reciprocal crosses it recorded significant SCA values (−19.63) in a negative direction. Griffing’s SCA value was significant and in a positive direction (7.83). In contrast to this in the cross P4×P5, the reciprocal cross recorded significant SCA values for GY in a positive direction (33.60) and in the straight cross it was in a negative direction (−17.45), while the Griffing’s SCA effects was in a positive direction (8.07). The same trend was observed for other traits also.

Reciprocal effects

Estimates of RECs are given by the difference between the straight and its reciprocal cross based on SCA effects. Griffing’s reciprocal effect is the same, but the partitioned value (r_ij = −r_ji) is in two directions. The cross-combination of P5 and P6 was found to have the greatest reciprocal effect on grain yield (Table 8) in a positive direction (+27.46). Meanwhile, the cross combination between P1 and P8 had the highest reciprocal effect for majority of the yield contributing traits NKR (+5.82), HGW (+5.64) and CG (+0.41). The same cross combination also recorded significant reciprocal effects in desirable negative direction for DTT (−2.88) and DTS (−2.15) respectively. For other traits such as NKRC, the cross P4×P7 recorded significant reciprocal effect in a positive direction (+ 0.90) and for CL the cross between P1×P2 recorded highest value +2.40.

Correlation between heterosis, mean performance and combining ability

Mean performance, mid-parent heterosis, and better-parent heterosis (Table 9) were found to be strongly correlated with Griffing’s SCA effect and adjusted SCA effect after partitioning. It is therefore appropriate to identify potential hybrids based on the adjusted SCA effects after partition, which had the highest correlation with hybrid performance and heterosis. The sum of the adjusted GCA effects (g_fi and g_mi) and mean performance are strongly correlated. Griffing’s GCA effect (g_i) was not consistently correlated with the phenotypic performance of hybrids, mid-parent heterosis, and better parent heterosis. In light of this, the adjusted GCA effect sum is more accurate at predicting hybrid performance than the sum after dividing the GCA into male and female GCA.