1 Introduction

Pulses as nutritionally rich food, play an important role in improving the overall value of cereal based diets for low and medium income group of the people. To meet the dietary requirements particularly for the poorer section of the society, to whom animal protein is less accessible pulse, is an ideal crop. Pulses when combined with cereals provide a nutritionally balanced amino acid composition with a ratio nearing the ideal for humans [40]. Frequent consumption of pulses is now recommended by most health organizations [29]. Among the cultivated winter pulses in Bangladesh, chickpea (Cicer arietinum L.) with 17–24% protein, 41–50.8% carbohydrates and high percentage of other mineral nutrients and unsaturated linoleic and oleic acid is one of the most important crops for human consumption [11]. Unfortunately, despite its nutritional values, the area, yield rate and production of chickpea are relatively low and decline in the subsequent year compared to other pulses in Bangladesh [4].On the other hand, in 2018, world production of chickpeas increased over 2017 levels by 16%, rising to a total of 17.2 million tonnes [10].Chickpea belong in the family Fabaceae, commonly known as gram or Bengal gram is one of the most favoured of all pulses in Bangladeshi society. In Bangladesh and surrounding countries, chickpea serves as food in many ways. The cooked dhal, called soopah (soup) in Sanskrit, constituted a common food item. During the holy month of Ramadan, chickpea is used to make most favoured item ghugni for iftary. Green leaves are used as a vegetable, fully developed green pods are used in vegetable dishes, rice and pilaw and some are roasted with salt. Chickpeas serve as energy and protein source as animal feed [3].Chickpea and other pulse crops are stapled foods in many countries and play an enhanced role in the diets of vegetarians around the world. Since chickpea is one of the most important pulse crops in Bangladesh, hence extensive research efforts are necessary for its improvement.

The main objective of chickpea research is to grow high yield and for that effective breeding plan is necessary. To formulate an efficient breeding programme for developing high yielding variety, it is essential to understand the mode of inheritance of the genes, the magnitude of gene effects and their mode of action [12].Thus, it is important to identify and estimate non-allelic interactions which could otherwise inflate the measures of additive and dominance components. To find the nature of gene action of quantitative traits, various mating designs have been developed. The mating designs such as generation mean analysis, triple test cross and biparental cross provides information about all the three components of variance viz., additive, dominance and epistatic. Generation mean analysis is based on first order statistics. Estimates based on first order statistics are statistically more robust and reliable than those based on second degree statistics [45].Generation mean analysis provides the opportunity first to detect the presence or absence of epistasis by scaling test and when present, it measures them appropriately. It also determines the components of heterosis in terms of gene effects and some other statistics. Therefore, present investigation have been done to getting the genetic information about the parameters of mean effects, additive, dominance, additive × additive and dominance × dominance gene interaction and thereby helps in formulating the guidelines for handling the segregating material in the subsequent generations by the exploitation of fixable component.

2 Materials and methods

2.1 Ethics and consent to participate

The plant materials used in this study were complied with the research guideline as per the protocols of Rajshahi University, Bangladesh. These plant materials were cultivated and collected from Bangladesh Agriculture Research Institute (BARI), Gazipur, Dhaka, Bangladesh.

2.2 Collection of materials

Five chickpea genotypes viz., BARI chola-1 (G-1), BARI chola-3 (G-3), BARI chola-4 (G-4), BARI chola-7 (G-7) and BARI chola-8 (G-8) were collected form Regional Agricultural Research Station (RARS), Ishurdi, Pabna, Bangladesh for this experiment. Among the genotypes, G-1, G-3, G-4 and G-7 were desi and only G-8 was kabuli type of chickpea. Five different single crosses viz. cross-1(G-8 × G-3), cross-2 (G-8 × G-1), cross-3 (G-8 × G-4), cross-4 (G-4 × G-8) and cross-5 (G-8 × G-7) have been done for raising F1, F2 and F3generations.

2.3 Design of the experimental field

Experiment has been conducted following randomized complete block design. The seeds of different generations along with their parents were sown in the research filed of Rajshahi University of Bangladesh considering randomized complete block design. Different rows with five hills were considered for both individual lines and generations. Seeds of the parents and generations were sown randomly in different plots. The gap between replications, plots, rows and hills were 120 cm, 80 cm, 45 cm and 45 cm, respectively.

2.4 Collection of data

As per Deb and Khaleque [7], the data of thirteen quantitative characters such as date of first flower (DFF), plant height at first flower (PHFF), number of primary branches at first flower (NPBFF), number of secondary branches at first flower (NSBFF), date of maximum flower (DMF), plant height at maximum flower (PHMF), number of primary branches at maximum flower (NPBMF), number of secondary branches at maximum flower (NSBMF), plant weight at harvest (PWH), number of pods per plant (NPd/P), pod weight per plant (PdW/P), number of seeds per plant (NS/P) and seed weight per plant (SW/P)were collected on an individual plant basis.

2.5 Biometrical analysis

The collected data were analyzed following biometrical technique as suggested by Mather [34] based on the mathematical model of Fisher et al. [15] and those of Lush [30], Cavalli [5], Warner [49], Hayman and Mather [19] and Mather and Jinks [35]. The techniques that have been used are described in the following sub-heads:

i. Mather's scaling test

Mather [34] and Hayman and Mather [19] gave four tests for scale effects. In this investigation, only two scales C and D were used as:

\({\text{C}}\,{ = }\,{4}\overline{{{\text{F}}_{1} }} \, - \,2\overline{{{\text{F}}_{1} }} \, - \overline{{{\text{P}}_{1} }} \, - \,\overline{{{\text{P}}_{2} }}\) and \({\text{D}}\,{ = }\,{4}\overline{{{\text{F}}_{3} }} \, - \,2\overline{{{\text{F}}_{2} }} \, - \,\overline{{{\text{P}}_{1} }} \, - \,\overline{{{\text{P}}_{2} }}\).

The test of significance was done with the use of respective standard errors (S.E.) of the scales.

ii. Test of potence

It could be done by comparing F1 and F2 means and is calculated by the following formula:

$$ \begin{gathered} \overline{{{\text{F}}_{1} }} \, = \,{\text{m}}\, + \,\left[ {\text{h}} \right] \hfill \\ \frac{{ - \overline{{{\text{F}}_{2} }} \, = \,{\text{m}}\, + \, - {\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 2}}\right.\kern-0pt} \!\lower0.7ex\hbox{$2$}}\,\left[ {\text{h}} \right]}}{{\overline{{{\text{F}}_{1} }} \, - \,\overline{{{\text{F}}_{2} }} \, = \,{\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 2}}\right.\kern-0pt} \!\lower0.7ex\hbox{$2$}}\,\left[ {\text{h}} \right]}} \hfill \\ \end{gathered} $$

Test of significance by “t” test as \({\text{t}}\, = \,\frac{{{\text{Estimated}}\,{\text{value}}\,{\text{of}}\,\overline{{{\text{F}}_{1} }} \, - \,\overline{{{\text{F}}_{2} }} }}{{{\text{Standard}}\,{\text{error}}\,{\text{of}}\,{\text{mean}}}}\).

iii. Joint scaling test

Joint scaling test was done based on 2 and 3-parameter model proposed by Cavalli [5] as follows:

Generation

Mean

Weight

Coefficients of parameters

m

[d]

[h]

P1

  

1

1

0

P2

  

1

−1

0

F1

  

1

0

1

F2

  

1

0

½

F3

  

1

0

¼

Where, ‘m’ measures mean, [d] and [h] measures the additive and dominance gene effects, respectively which need to be estimated. The expected mean values of all generations were calculated using matrix knowledge.

iv. Study of gene action

Hayman’s [18] five parameter model is used to estimation of various genetic components to know the gene action as follows:

$$ \begin{gathered} {\text{m}}\,{ = }\,\overline{{{\text{F}}_{2} }} \hfill \\ {\text{d}}\, = \,{\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 2}}\right.\kern-0pt} \!\lower0.7ex\hbox{$2$}}\overline{{{\text{P}}_{1} }} \, - \,{\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 2}}\right.\kern-0pt} \!\lower0.7ex\hbox{$2$}}\overline{{{\text{P}}_{2} }} \hfill \\ {\text{h}}\,{ = }\,{\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 6}}\right.\kern-0pt} \!\lower0.7ex\hbox{$6$}}\left( {4\,\overline{{{\text{F}}_{1} }} \, + \,12\,\overline{{{\text{F}}_{2} }} \, - \,16\,\overline{{{\text{F}}_{3} }} } \right) \hfill \\ {\text{i}}\,{ = }\,\overline{{{\text{P}}_{1} }} \, - \,\overline{{{\text{P}}_{2} }} \, + \,\left( {{\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 2}}\right.\kern-0pt} \!\lower0.7ex\hbox{$2$}}} \right)\left( {\overline{{{\text{P}}_{1} }} \, - \,\overline{{{\text{P}}_{2} }} \, + \,{\text{h}}} \right)\, - \,{\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 4}}\right.\kern-0pt} \!\lower0.7ex\hbox{$4$}}\,{\text{l}} \hfill \\ {\text{l}}\,{ = }\,{\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 3}}\right.\kern-0pt} \!\lower0.7ex\hbox{$3$}}\,\left( {16\,\overline{{{\text{F}}_{3} }} \, - \,24\,\overline{{{\text{F}}_{2} }} \, + \,8\,\overline{{{\text{F}}_{1} }} } \right) \hfill \\ \end{gathered} $$

Test of significance of each of the parameters have been done by ‘t’ test.

v. Analysis of components of variation

Based on the additive-dominance model variances of different generations under study can be written following Mather and Jinks [36] as:

$$ {\text{VF2}}\,{ = }\,\frac{1}{2}{\text{D}}\,{ + }\,\frac{1}{4}{\text{H}}\,{ + }\,{\text{E,}}\,\overline{{\text{V}}} {\text{F3}}\,{ = }\,\frac{1}{4}{\text{D}}\,{ + }\,\frac{1}{8}{\text{H}}\,{\text{ + E and}}\,{\text{V}}_{{\overline{{\text{F}}} 3}} \,{ = }\,\frac{1}{2}{\text{D + }}\frac{1}{16}{\text{H + E}}_{{2}} \, $$

where, VF2 = variance of F2 family, \(\overline{{\text{V}}}\) F3 = mean variance of F3 families and \({\text{V}}_{{{\overline{\text{F}}\text{3}}}}\) = variance of F3 family means.

vi. Degree of dominance

The average degree of dominance over all loci was determined by the square root of the ratio between H and D [34].

$$ {\text{Degree}}\,{\text{of}}\,{\text{dominance}}\, = \,\sqrt{\frac{H}{D}} $$

where, D = additive component of variation and H = dominance component of variation.

vii. Effective factors (K1)

The number of effective factors was estimated using the formula of Mather [33] as follows:

$$ {\text{K}}_{1} \, = \,\frac{{\frac{1}{4}\left( {\overline{{{\text{P}}_{1} }} \, - \,\overline{{{\text{P}}_{2} }} } \right)}}{{\text{D}}} $$

where, D = least square estimate of component of genetic variation.

viii. Heritability

Heritability was calculated in two different ways following Mather [34].

a) Broad sense heritability (h2b) calculated as follows:

$$ {\text{h}}^{{2}} {\text{b = (}}\frac{1}{2}{\text{D + }}\frac{1}{4}{\text{H) / (}}\frac{1}{2}{\text{D + }}\frac{1}{4}{\text{H + E)}} $$

b) Narrow sense heritability (h2n) calculated as follows:

$$ {\text{h}}^{{2}} {\text{n = }}\frac{1}{2}{\text{D / (}}\frac{1}{2}{\text{D + }}\frac{1}{4}{\text{H + E)}} $$

where, D, H and E are the estimates of components of variation.

ix. Genetic advance (GA) was calculated by the formula as suggested by Lush [30]

$$ {\text{GA}}\, = \,{\text{K}}\, \times \,\sigma_{{\text{P}}} \, \times \,{\text{h}}^{{2}}_{{\text{b}}} {\text{or h}}^{{2}}_{{\text{n}}} $$

where, K = the selection differential [30] and σP = standard deviation of F2 variance.

x. Genetic advance as percentage of mean (GA %) was measured by the following formula:

$$ {\text{GA}}\% \, = \,\frac{{{\text{GA}}}}{{\overline{{\text{X}}} }}\, \times \,100 $$

where,\(\overline{{\text{X}}}\) = grand mean for a respective character.

xi. Heterosis was calculated using the following formula:

$$ {\text{Heterosis over mid}} - {\text{parent }}\left( {{\text{MP}}} \right)\, = \,\frac{{\overline{{F_{1} }} \, - \,MP}}{MP} $$
$$ {\text{Heterosis over better}} - {\text{parent }}\left( {{\text{BP}}} \right)\, = \,\frac{{\overline{{F_{1} }} \, = \,BP}}{BP} $$

t = estimated value of the parameter/standard error of the parameter.

xii. Inbreeding depression (ID) was estimated as follows:

$$ {\text{Inbreeding depression }} = \,\frac{{\overline{{{\text{F}}_{1} }} \, - \,\overline{{{\text{F}}_{2} }} }}{{\overline{{{\text{F}}_{1} }} }} $$

t = estimated value of the parameter / standard error of the parameter.

3 Results and discussion

3.1 Results

A first order statistics based biometrical technique was applied to determine the nature and magnitude of gene action in the expression of quantitative traits. Generation mean analysis provides measurement of these effects very efficiently.

3.1.1 Mather's scaling test

Mather's scaling test was done to see whether additive-dominance model was adequate or not. Estimated values of scales C and D are presented in Table 1. Table showed that in cross-1, all studied traits were significant for at least one of the scale. Regarding cross-2, all the traits except PWH were significant for at least one of the scale tests. In cross-3, at least one of the scales was found to be significant for all the characters except NSBFF, PHMF and NSBMF. In cross-4, except NPBMF at least one of the scales was significant for all the traits. Regarding cross-5, scale C was noted as significant for DFF, PHFF, NSBFF, NSBMF, PWH, NS/P and SW/P and scale D was significant for all traits except DFF and PWH.

Table 1 Estimated values of scales (C and D), potence, parameters (\({\hat{\text{m}}}\), \({\hat{\text{d}}}\) and \({\hat{\text{h}}}\)) and χ2for thirteen characters of five crosses in chickpea
Full size table

3.1.2 Test of potence

The values of potence of studied traits are given in Table 1. Potence was significant for all the characters except DFF, NPd/P and NS/P in cross-1. In cross-2, all the characters showed significant potence except PHFF and NPBFF. Regarding cross-3, except NPBFF, DMF and PHMF all traits exhibited significant potence. In cross-4, potence was significant for all the traits except DFF and PdW/P. All the characters except PHFF showed significant potence in cross-5. These results reflect to some extent in calculation of dominance ratio.

3.1.3 Joint scaling test

The obtained values of joint scaling test (χ2) values are shown in Table 1. Most of the studied traits of different crosses exhibited significant χ2 values. Table 1 showed that all the traits showed significant χ2 values in cross-1. Except PWH, NPd/P and NS/P all the traits showed significant χ2 values in cross-2. All the characters showed significant χ2 values except NSBFF and NSBMF in cross-3. In cross-4, all traits exhibited significant χ2 values except NPBMF and regarding cross-5 none of the traits showed non-significant χ2 values.

3.1.4 Gene action

For gene action, values of five parameters viz., m, [d], [h], [i] and [l] are estimated according to Hayman [18] and presented in Table 2.The mean effect ‘m’ was significant and positive for all the crosses and characters. In cross-1, traits viz., DFF, PHFF, DMF, PHMF, NPBMF, NSBMF, PWH, NPd/P and NS/P were found to be significant in respect of additive effect [d] on the other hand, DFF, PHFF, NPBFF, DMF, NPBMF, NSBMF, NPd/P, PdW/P, NS/P and SW/P were found to be significant in case of dominance effect [h]. The additive × additive interaction [i] exhibited significant value for DFF, DMF, PHMF, NPBMF, NSBMF, NPd/P, PdW/P, NS/P and SW/P while, dominance × dominance gene interaction [l] showed significant value for DFF, DMF, PHMF, NSBMF, NPd/P, PdW/P, NS/P and SW/P. Regarding cross-2, [d] found to be significant for NSBFF, PHMF, NSBMF, NPd/P and NS/P and [h] for DFF, PHFF, NPBFF, NSBFF, DMF, PHMF, NPBMF and NPd/P. Additive × additive [i] gene action had significant effect on NPBFF, NSBFF, DMF and NS/P whereas, dominance × dominance [l] gene effect played significant role on DFF, PHFF, NPBFF, NSBFF, DMF and PdW/P. In cross-3, [d] had significant effect on NPBMF, NSBMF, NPd/P and NS/P while [h] had significant effect on PHFF, NPBFF, NSBFF, DMF, PWH and PdW/P. The non-allelic parameter [i] was significant for PHFF, DMF, NPBMF, PWH, NPd/P, PdW/P, NS/P and SW/P while, [l] was significant for DFF, PHFF, DMF, NPBMF, PWH, NPd/P, PdW/P, NS/P and SW/P. In cross-4, the fixable heritable effect i.e. [d] was significant for NPBMF, NSBMF, NPd/P and NS/P while, un-fixable heritable effect i.e. [h] was significant for most of the characters except DFF, NSBFF and NSBMF. The estimated [i] for most of the traits found to be significant on the other hand, [l] expressed significant only for PHFF, NSBFF, DMF, PHMF and NSBMF. In cross-5, [d] noted as significant for NPBMF, NSBMF, PWH, NPd/P, PdW/P, NS/P and SW/P whereas, [h] exhibited significant for most of the traits except DFF, PHMF and NSBMF. Fixable gene interaction [i] had significant effect for most of the traits except DFF, NSBFF and PHMF, while, un-fixable gene interaction [l] had the significant effect for most of the traits except NPBFF, NSBFF, PHMF and NPBMF. All types of gene interactions viz., m, [d], [h], [i] and [l] were significant for DFF, DMF, NSBMF, NPd/P and NS/P in coss-1; for NSBFF in cross-2 and for PWH, NPd/P, PdW/P, NS/P and SW/P in cross-5.

Table 2 Estimated values of gene effects (m, [d], [h], [i] and [l]) of parents, F1, F2 and F3generations for thirteen characters of five crosses in chickpea
Full size table

Two types of epistasis observed in this investigation. Those in which [h] and [l] have the same sign it will refer to as complementary type and those in which [h] and [l] have opposite sign it will refer to as duplicate type. From Table 2 complementary epistasis was observed for NPBFF, NSBFF and PHMF in cross-1; for PHMF, NPBMF, NSBMF, PWH, NPd/P, PdW/P, NS/P and SW/P in cross-2; for NPBMF, NSBMF and NPd/P in cross-3; for NSBFF in cross-4 and for NSBFF, PHMF, NPBMF and PWH in cross-5. Among these traits, only PWH in cross-5 showed significant value of [h] and [l]. Due to positive sign of [h] and [l] all the above traits in the respective crosses showed complementary epistasis between dominant increaser. On the other hand, duplicate type of epistasis was noted for DFF, PHFF, DMF, NPBMF, NSBMF, PWH, NPd/P, PdW/P, NS/P and SW/P in cross-1; for DFF, PHFF, NPBFF, NSBFF and DMF in cross-2; for DFF, PHFF, NPBFF, NSBFF, DMF, PHMF, PWH, PdW/P, NS/P and SW/P in cross-3; for DFF, PHFF, NPBFF, DMF, PHMF, NPBMF, NSBMF, PWH, NPd/P, PdW/P, NS/P and SW/P in cross-4 and for DFF, PHFF, NPBFF, DMF, NSBMF, NPd/P, PdW/P, NS/P and SW/P in cross-5. Among these traits, due to negative sign of [h] and positive sign of [l] the characters viz., DMF and NSBMF in cross-1; DMF in cross-2; DMF, PWH, PdW/P, NS/P and SW/P in cross-3; DFF, DMF, PHMF and NSBMF in cross-4 and DMF and NSBMF in cross-5 shown duplicate epistasis between dominant increaser while rest of the traits shown duplicate epistasis between dominant decreaser. Again the traits viz., DFF, DMF, NSBMF, NPd/P, PdW/P, NS/P and SW/P in cross-1; DFF, PHFF, NPBFF, NSBFF and DMF in cross-2; PHFF, DMF, PWH and PdW/P in cross-3; PHFF, DMF and PHMF in cross-4 and PHFF, DMF, NPd/P, PdW/P, NS/P and SW/P in cross-5 shown significant value of [h] and [l].

3.1.5 Components of variation

The estimated values of D, H and E are presented in Table 3. Perusal the Table 3, it was noted that additive component exhibited positive value in 61 cases and negative in 4 cases. On the other hand, dominance component expressed positive value in 8 cases and negative in 57 cases. Both components D and H exhibited positive values in 5 cases in all the crosses.

Table 3 Estimated values of component of variation (D, H and E), degree of dominance (√H/D) and effective factor (K1) for thirteen characters of five crosses in chickpea
Full size table

3.1.6 Degree of dominance

The degrees of dominance (√H/D) as measured from the estimate of components of variation are shown in Table 3. The values of √H/D for most of the characters in studied crosses showed over dominance. Partial dominance was noted for PWH in cross-1 and NSBMF, NPd/P, NS/P and SW/P in cross-4. The highest dominance ratio found for PWH in cross-5 with negative sign.

3.1.7 Effective factors

Number of effective factors (K1) is presented in Table 3. It was noted from this table that the value of K1 was less than one for all the characters and crosses. Among the characters and crosses of this work, the highest value of K1 was recorded as 0.8334 for NPd/P in cross-1 and the lowest value of K1 was noted as -0.4131 for NS/P in cross-4.

3.1.8 Heritability

Heritability estimates both in broad sense (h2b) and narrow sense (h2n) based on the components of variation and the result shown in Table 4. The highest broad sense heritability (-7.884160) was noted for PdW/P in cross-2 but with negative sign which is due to the negative value of H component. However, in some cases values of h2bwere low. Again, the estimates of narrow sense heritability was also found to be high for most the characters in different crosses. Regarding narrow sense heritability the traits viz., NPd/P and PdW/P in cross-1; NSBMF in cross-3; PWH, NPd/P, PdW/P and NS/P in cross-4 and DFF, PWH, NPd/P, PdW/P, NS/P and SW/P in cross-5 found to be low. Narrow sense heritability found to be higher than broad sense heritability for most of the cases. Again, in some cases viz., PWH in cross-1; NPd/P and NS/P in cross-4 and DFF, NPd/P, PdW/P, NS/P and SW/P in cross-5 the values of broad sense heritability was higher than narrow sense heritability.

Table 4 Estimated values of heritability \(\left( {{\text{h}}^{2}_{{\text{b}}} ,\,{\text{h}}^{2}_{{\text{n}}} } \right)\), genetic advanced (GAb, GAn) and genetic advanced as percentage of mean (GA%b, GA%n) for thirteen characters of five crosses in chickpea
Full size table

3.1.9 Genetic advance

The results of broad and narrow sense genetic advance are presented in Table 4.The highest value of broad sense genetic advance (GAb) was noted as 99.946720 for PWH in cross-1, as −345.017113 for NPd/P in cross-2, as −128.425972 for NS/P in cross-3, as −34.848625 for NS/P in cross-4 and as -172.696431 for PWH in cross-5. The highest value of narrow sense genetic advance (GAn) was recorded as 195.393401 for NS/P in cross-1, as 513.994412 for PdW/P in cross-2, as 287.327577 for NS/P in cross-3, as 115.845801 for PHFF in cross-4 and as 95.047541 for NS/P in cross-5.

3.1.10 Genetic advance as percentage of mean

Estimated values of broad and narrow sense genetic advance as percentage of mean (GA%) are presented in Table 4. Most of the characters in the crosses GA% in broad and narrow senses were found to be high. The highest GA% in broad sense was noted as −142.748512 for SW/P in cross-1, as −485.982151 for PdW/P in cross-2, as −175.003624 for NPd/P in cross-3, as −117.216325 for SW/P in cross-4 and as 178.902630 for SW/P in cross-5. The highest GA% in narrow sense was noted as 358.312300 for NPBFF in cross-1, as 2497.776145 for PdW/P in cross-2, as 633.617221 for NSBFF in cross-3, as 462.206153 for NSBFF in cross-4 and as 381.902611 for NPBMF in cross-5.

3.1.11 Heterosis

Both mid-parent (MP) and better-parent (BP) heterosis were estimated and are presented in Table 5. MP heterosis was found to be significant for NPBFF and NPBMF in cross-1; NPBFF, NSBFF and NPBMF in cross-2; NPBMF and NS/P in cross-3; NPBFF, NSBFF and NPBMF in cross-4 and NPBFF, NSBFF and NPBMF in cross-5. On the other hand, BP heterosis was found to be significant for NPBFF and NPBMF in cross-2; NPBFF, NSBFF and NPBMF in cross-4 and NPBFF and NPBMF in cross-5.

Table 5 Estimated values of mid-parent (MP) and better-parent (BP) heterosis for thirteen characters of five crosses in chickpea
Full size table

3.1.12 Inbreeding depression

Inbreeding depression (ID) was calculated and is presented in Table 6. Non-significant inbreeding depression was observed for all characters and crosses. Among the characters and crosses, negative inbreeding depression was recorded in 14 cases and positive inbreeding depression noted in 51 cases.

Table 6 Estimated values of inbreeding depression (ID) for thirteen characters of five crosses in chickpea
Full size table

4 Discussion

Genetic information regarding the nature, relative magnitude and type of gene action following a proper genetic model is very important for successful breeding research. Thus, both additive and non-additive components of genetic variations along with their allied parameters are of immense use for plant breeders under different situations.

To find out the presence or absence of non-allelic interaction, Mather’s [34] scaling test was done. At least one of the scale found to be significant for all the studied characters in all the crosses except PWH in cross-2; NSBFF, PHMF and NSBMF in cros-3 and NPBMF in cross-4. Significant of any one of the scale indicating that additive-dominance model is inadequate to explain the variation in the studied characters. Similar observations were reported by Rahman and Saad [41] in Vigna sesquipedalis, Singh et al. [46] in mung bean and Deb and Khaleque [7] in chickpea. Potence found to be significant in maximum cases. Non-significance potence indicating no difference between F1 and F2 and there will be no dominance and vice-versa indicating dominance may be ambi-directional [17].

Mather’s scaling test can detect adequacy of additive-dominance model but not so effective. An elaborated procedure which is an effective combination of a whole set of scaling tests into one was suggested by Cavalli [5] named ‘joint scaling test’. Non-significant χ2 values observed for PWH, NPd/P and NS/P in cross-2; NSBFF and NSBMF in cross-3 and NPBMF in cross-4 in this investigation which indicated that the additive-dominance model is adequate to explain the relationship among the generations and hence additive and dominant genes are responsible in the inheritance of these characters and crosses. Samad et al. [43] and Nahar et al. [37] in black gram also got the non-significant χ2values for different characters and crosses. On the other hand, most of the traits exhibited significant χ2 values indicated that the additive-dominance model is inadequate. This result corroborate with the findings of Deb and Khaleque [7] in chickpea, Devi and Sood [8] in bell pepper and Kumar et al. [28] in sweet sorghum. Inadequacy of the model indicated that except the additive and dominance gene effects, non-allelic interaction and linkage may be a part to the inheritance of these characters.

The presence of non-allelic gene interactions was confirmed due to the inadequacy of additive-dominance model, then data were further analyzed employing five parameters viz. m, [d], [h], [i] and [l] model. These genetic parameters provide information about the gene action involved for a particular trait. Estimates of genetic effects for the five parameters model indicated that mean effect ‘m’ of each cross was significant. Both additive [d] and dominance [h] effects showed significant and non-significant values in different characters and crosses. Higher magnitude of dominance than additive in most of the cases indicated the greater role of dominance effect in the inheritance of these traits. Some of the characters exhibited both significant additive and dominance gene action in all the studied crosses. Among the interaction effects, additive × additive [i] and dominance × dominance [l] effects were also found to be significant for most of the characters. Makne [31], Venkateswarlu et al. [48] and Jivani et al. [22] in groundnut observed the involvement of both additive and non-additive gene action for different traits. The significance of additive and dominance effects was reported by Manoharan and Thangavelu [32] in groundnut. Shoba et al. [44] observed the significance of [d], [h], [i], [l] and duplicate effect of different traits in different crosses in groundnut, Ezhilarasi and Thangavel [9] reported the significance of [d], [h], [i], [l] and duplicate effect of plant height in different crosses in bhendi. Both complementary and duplicate types of epistasis are observed in this work. Duplicate type of epistasis badly affects the crop improvement and generally hinders the pace of progress in selection and hence, a higher magnitude of dominance and dominance × dominance type of interaction effects would not be expected. It also indicated that selection should be delayed after several generations of selection (single seed descent) until a high level of gene fixation is attained. Khattak et al. [24] found duplicate type of non-allelic interactions in mung bean and in lentil by Khodambashi et al. [25]. Kumar and Prakash [27] and Kiani et al. [26] found the complementary type of gene interaction in their materials.

Additive component of variation (D) expressed positive value in all the crosses for all the characters except NPd/P, NS/P and SW/P in cross-4 and NPd/P in cross-5 where it was negative. Considerable amount of D indicated that additive component of variation was important in the present investigation. Similar results were reported by Adeniji et al. [2] in West African okra, Farshadfar et al. [14] and Deb and Khaleque [7] in chickpea. On the other hand, dominance component (H) exhibited negative value in all the crosses for all the characters except PWH in cross-1; NPd/P and NS/P in cross-4 and DFF, NPd/P, PdW/P, NS/P and SW/P in cross-5. These results corroborate with the findings of Samad et al. [43] and Nahar et al. [37] in black gram. Negative estimation of component of variation, however might arise from genotype × environment interaction [20] and sampling errors [34].

Degree of dominance (√H/D) for most of the characters in studied crosses showed over dominance. Nahar et al. [37] in black gram recorded over dominance for all the traits in their materials. Similar results were also obtained by Farshadfar et al. [14] and Deb and Khaleque [7] in chickpea and Samad et al. [43] in black gram. The negative sign of √H/D indicated dominance towards decreasing parents.

As Mather [33] effective factors (K1) is the smallest unit of hereditary material. It may be a closely linked gene, or at the lower unit a single gene. In this study, the values of K1 were low for all the characters and crosses under study. Haque et al. [17] obtained similar result in black gram.

Heritability estimates both in broad (h2b) and narrow (h2n) senses were found to be high in majority cases. However, in some cases these values were low. Adeniji et al. [2] reported high broad sense heritability in their study. Farshadfar et al. [14] reported high broad sense heritability in chickpea. On the other hand, Novoselovic et al. [38] reported high narrow sense heritability in wheat. Khodambashi et al.[25] reported high value of narrow sense heritability for pods per plant, seeds per plant and seeds per pod suggesting that selection of these three yield components is likely be helpful to gain more yield.

Genetic advances (GA) in broad and narrow senses were high in maximum cases indicated that improvement of these characters is possible through selection. Farshadfar et al. [13] found low to moderate GA in their materials. Deb and Khaleque [7] recorded low to high GA both in broad and narrow sense in chickpea, whereas Samad et al. [43] and Nahar et al. [37] reported low GA in blackgram. Traits containing high h2n with high GA values are always good breeding materials.

Most of the characters in all studied crosses genetic advance as percentage of mean (GA %) in broad and narrow senses were high. However, heritability estimates along with the genetic gain is usually more useful than heritability values alone in predicting the resultant effect from selecting the best individuals as was indicated by Johnson et al. [23] in soybean and Swarup and Chaugale [47] in sorghum. The high heritability and high genetic gain are the indication of additive gene effects [39]. Deb and Khaleque [7] in chickpea reported high GA% for different characters in studied crosses.

Mid-parent and better-parent heterosis found to be significant in few cases. These characters in those crosses could be used for commercial utilization as hybrid vigour. Abdullah et al. [1] observed significant MPH and BPH in wheat. Iqbal and Nadeem [21] and Reddy [42] reported significant MPH in their study. Devi and Sood [8] observed significant BPH in bell pepper.

Inbreeding depression is important in the evolution of outcrossing mating systems and, because intercrossing inbred strains improves yield (heterosis), which is important in crop breeding, the genetic basis of these effects has been debated since the early twentieth century [6]. Non-significant inbreeding depression (ID) values were observed for all the characters and crosses indicating absent inbreeding depression in this material. In this work, negative ID observed in 14 cases, whereas, positive ID exhibited in 51 cases. Gutierrez and Singh [16] in bush bean recorded non-significant ID values for most of the characters and crosses. Positive ID revealed that the value of progenies in the F2 generation in comparison with F1 reduced, while negative ID indicated the increase of F2 in relation to F1 progenies.

5 Conclusions

It may summarize that both scaling and joint scaling tests indicated the presence of epistasis in maximum cases except PWH in cross-2, NSBFF and NSBMF in cross-3 and NPBMF in cross-4 and hence these traits might be considered for the development of potential genotypes in chickpea. Regarding gene action, five parameters model revealed the importance of additive, dominance and epistasis gene interactions for the studied traits in majority cases. The role of duplicate epistasis was found to important in majority cases. The dominance components of variation and epistasis could be exploited for the development of hybrids. Therefore, present investigation indicated that further breeding experiments could be done considering two lines of research, first for the development of pure lines and second for the utilization of hybrid vigour commercially.