Estimation of Combining Ability for Yield Traits in Groundnut using Genetic Variance-covariance among Relatives

In any breeding programme, genetic variability is a pre-requisite for developing new cultivars. This variability can be generated by either mutagenesis or through hybridization of different parents, followed by segregation and recombination. The genetic composition (G) of an individual can be expressed as the sum of the average of additive effects (D) or additive effects plus, a deviation due to non-additive effects, i.e., dominance (H) and epistatic interaction (I) (Falconer and Mackay 1996, Bernardo 2002). Hence, the estimation of additive and non-additive effects of an individual (s) is important for further genetic improvement of the desired trait (s) through hybridization as, the mean genotypic value of its progeny is equal to general mean plus the sum of the breeding values of two parents i.e., general combining ability (GCA) and non-additive effects or epistatic interaction due to specific combination of alleles at different loci known as specific combining ability (SCA) (Bernardo 2002). Thus, to generate new genetic variability in recombinant line (s), the genetic divergence and their magnitude of additive effects (GCA) vis-à-vis non-additive effects (SCA) among candidature parent(s) are of utmost importance.
       
In the classical breeding programs, selection for the suitable parental line (s) is made through standard mating designs, example via diallel cross or top cross which partitions the genetic effect of a line into additive and non-additive effects. These additive and non-additive effects are referred to as general and specific combining ability respectively, in these mating designs in plant breeding programs. However, such designs are associated with certain disadvantages like i) Evaluation of the lesser number of parental lines, ii) Assumptions associated with these designs like the absence of epistasis, absence of multiple allelism, random mating, etc. are seldom met, iii) In advanced generations of self-pollinating crops dominance deviation diminishes and only additive ´ additive interaction is fixed in elite genotypes. Thus, these designs cannot be used for estimating the real magnitude of additive effects vis-à-vis epistatic interaction for the desired trait(s).
       
Hybridization in groundnut is very difficult and the success rate is very low, hence, sufficient population size cannot be achieved for proper testing of GCA and SCA across the years or locations in diallel or line × tester fashion of mating of the parent(s). Further, being cleistogamous, advanced generations are purely composed of additive effects and additive × additive gene interactions (epitasis). Since, the models diallel and line ×tester assess suitability of line as a parent based on the overall genetic effect. However, if the given attributes of line are due to the result of interaction between genes (epistasis), then this approach is not ideal as, the performance of the line is more than sum of alleles, leading to an inflated breeding potential for it (Oakey et al., 2006).Thus, the real worth of a genotype(s) as a donor for the further genetic improvement of the desired trait(s) cannot be assessed with precision. But, Oakey et al., (2006) resolved these limitations by partitioning the total genetic effect ‘g’ of lines into additive ‘a’ and non-additive ‘i’ effects by modelling genetic variance-covariance of genotypes in mixed model equation (MME) by incorporating coefficient of parentage (COP) i.e., additive relationship matrix (A) for genetic effects and à matrix for epistatic effects of BLUP analysis, where, à is constructed as (A#A)= à (where # is the element-wise multiplication operator) (Falconer and Mackay 1996). This was useful for the identification of lines with high additive effects and overall high production. Crossa et al., (2006) predicted the breeding values of lines using the additive genetic covariances of relatives, which is the additive relationship matrix A, multiplied by additive genetic variance. Further, the BLUPs of breeding values were obtained using genetic variance-covariance structures constructed as Kronecker product of a structured matrix of genetic variances and covariances for sites and, a matrix of genetic relationship between strains, A. This, was found to efficiently model the genotypic main effects and GE and a low standard error of the BLUPs of breeding values were obtained. But the study did not consider covariances between relatives due to epistatic genetic effects. To overcome this, Burgueño et al., (2007) further extended the factor analytic model proposed by Crossa et al., (2006) to partition GEI into additive ´  environment interaction and additive × additive×environment interaction in wheat for the identification of lines having high additive effects. This was achieved with the incorporation of variance-covariance structures constructed as Kronecker product of a FA model, across sites and additive (A) and additive × additive relationship between lines. The results obtained showed the efficacy of the model for the identification of lines having high additive effects to be used as parents in crossing program as well as have overall high production. In the present investigation, the model given by Burgueñoet_al(2007) for the partitioning of genetic effects into additive (GCA) and non-additive (SCA) effects and their interaction with the environment will be used for the identification of lines having high additive effects, which can be used as parents in crossing programme for germplasm improvement in groundnut.

In present study a set of 40 advanced breeding lines (ABL) at F₉ generation developed through pedigree breeding methos, comprising full sibs and half -sibs were used (Table 1).  The lines were sown at three locations viz., Farm area of Oilseeds section, Department of Plant Breeding and Genetics, Punjab Agricultural University, Ludhiana, Regional Research Station, Kapurthala, Krishi Vigyan Kendra, Kheri during spring (first fortnight of March 2019) and kharif (mid May 2019). The test genotypes were planted in the alpha lattice design with three replications each. A plot of three rows of three-meter-length were sown for each genotype with row-to-row and plant-to-plant spacing of 30 cm and 15 cm, respectively in each replication at each location. Table 2 represents mean yield of these genotypes at given locations during respective seasons.




       
The data for yield was recorded for each ABL and was analyzed for the estimation of genetic variance-covariance for environment using the modeldeveloped by Oakey et al., (2006) and Burgueñoet_al(2007) in Microsoft excel 2017. Information from relatives through COP i.e.,
among half and full-sib lines was estimated as:


Where,
Individual X and Y are full sibs (FS) or half sibs (HS) if they both have same parents A and B or have one common parent.
The variance-covariance matrix of additive genetic effect was obtained from COP multiplied by the population additive genetic variance,Mixed model equations (MME) combining the genetic main effects and genetic × environment interaction effects for fitting the data from g genotypes, (i=1,2,... ...,g), s site (j=1,2,... ...,s) and r replicated (in each site) using the à and A matrices (both of dimensions g × g) can be written as:

 
 
Where,
X, Z_r, Z_g and Z_ge are the design matrices for fixed effects of sites, random effects of replicates within sites, genotype(s) ge, respectively. Vector b denotes the fixed effects of sites and vectors. r, a, i, ie and E contain random effects of replicates within sites, additive, additive × additive, additive× environment interaction, additive × additive× environment interaction and residuals respectively and are assumed to be random and normally distributed with zero mean vectors and variance-covariance matrices R, G_a, G_i, G_ae, G_ie and N, respectively, such that:
 
Variance-covariance matrices R and N are assumed to have a simple variance component structure, as defined for MME.
Assuming independence between vectors a and i, partitioning of total genetic effect g has normal distribution with mean zero and variance-covariance G_g= G_a + G_i, where the variance-covariance matrix of the additive, (G_a) and additive × additive main effects, (Gi), are modelled asand .
The unstructured variance-covariances are transformed to heterogeneity of within environment genetic variance (CSH model), in which case å_g1 or å_ge has structure: Similarly, other matrices Z_geie, Z_gi and Z_ge were also obtained.
The solution for the vector of fixed site effects, b and vector of random effects of replicates within sites r ; additive a ; additive×additive i ; additive × environment (G_ae) _ae and additive × additive × environment (G_ie) interaction ie were obtained following Henderson (1975).

 
 
The genetic gain-based heritability (narrow sense) for individual genotypes was estimated as per method given by Oakey et al., (2006).

Combining ability refers to the relative ability of a genotype to transfer the desirable performance to its crosses. It is one of the powerful tools available to estimate the combining ability effects and in the selection of desirable parents and crosses for exploiting heterosis (Sarker et al., 2002; Muhammad et al., 2007). Since, the potential for being a good donor is primarily attributed by additive effects or breeding value, it is important to separate these effects from epistatic genetic effects. The partitioning of genotypic values into its components i.e., additive, additive × additive and their interaction with environment calculated as per the model given by Burgueño et al., (2007) are depicted in Table 3. Groundnut being a self-pollinated crop, so here the non-additive effects i.e., G_i and G_ie reflect epistatic interactions, as inbreeding largely eliminated dominance effects (Oakey et al., 2006). From Table 3, line Mallika has low genotypic value but shows highest G_a value. Similarly, line CGL-27 has quite low genotypic value, but the second highest G_a value, vice-versa is the case with line CGL-23. These results, hence, indicate lines having high breeding values does not have high commercial value (Burgueño et al., 2007). Secondly, although lines Mallika and CGL-27 show high G_a value but also show moderate to high G_ae values. Hence, subdivision of environments is needed for exploiting this interaction of these lines in specific environments to maximize the overall genetic gains. These observations are in agreement with the findings of Burgueño et al., (2007). Lines CGL-36 and CGL-11 although have low G_a value than Mallika and GL-27 but show negative value for G_ae (Table 3). Here, cross can be attempted between lines with overall high genetic effects, for example CGL-11 having both overall high genotypic value and Ga with negative Gae (Table 3) and CGL-36 with overall high additive effects and negative G_ae, i.e., crossing good×good to maximize overall genetic gains (Burgueño et al., 2007).

Overall high genetic value of a line may not be an indicator of its breeding potential, as genetic value is contributed by both additive and non-additive effects. Hence, partitioning of these effects into its components and their interaction with environment is necessary to assess reliable potential of lines for their suitability as parents.

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