The diallel cross refers to a set of all possible matings between several genotypes (Hayman, 1954a; 1954b). The genotypes may be individuals, clones, homozygous varieties, etc. The diallel analysis helps to obtain information on the genetic systems governing the inheritance of attributes to be improved, and hence may help in predicting the performance in subsequent generations by assessing the potential of different crosses in F1 and F2 (Dickson, 1967; Dabholkar, 1992). Like other mating designs, diallel mating is a frequently used design for estimating the additive and dominance genetic (polygenic) effects involved in quantitative traits observed in the half- and full-sib progenies generated in plant breeding programmes. The diallel design has additional benefits in that the analysis applies to all the
crosses involved and permits the estimation of parameters for additive, dominance and environmental effects, and allows recognition of non-allelic interactions (Hayman, 1954a;
1954b; Griffing, 1956; Jinks, 1956; Matther and Jinks, 1982; Christie and Shattuck, 1992). In addition, this technique enables the breeder to combine desirable genes that are found in two or more genotypes (Dabholkar, 1992).
There are four basic designs and analysis for the diallel mating design (Christie and Shattuck, 1992), and they include
1. Analysis of general and specific combining ability or Griffing’s analysis (Griffing, 1956);
2. Analysis of array variances and covariance’s or Hayman and Jinks analysis (Jinks and Hayman, 1953; Hayman, 1954b, Jinks, 1954; 1956);
3. Analysis of additive and dominance effects, also referred to as Gardner and Eberhart’s analysis (Gardner and Eberhart, 1966; Eberhart and Gardner, 1966) and;
4. Partial diallel analysis (Gilbert, 1958; Kempthorne and Curnow, 1961).
The present study used Griffing’s analysis to determine the combining ability of varieties and characterise the nature and extent of gene action (Christie and Shattuck, 1992). This analysis requires no genetic assumptions (Wright, 1985), and has been shown to convey reliable information on the combining potential of parents (Nienhuis and Singh, 1986).
This design provides breeders with useful genetic information,such as general combining ability (GCA) and specific combiningability (SCA), to help them devise appropriate breeding andselection strategies (Zhang et al., 2001). The GCA and SCA effects help to locate the parents and crosses that will be responsible in bringing about a particular type of gene action (Dabholkar, 1992). General combining ability refers to the mean performance of a line in all its crosses, and is expressed as a deviation from the mean of all crosses (Falconer and Mackay, 1996). It is the average value of all F1s having this line as one parent, the value being expressed as a deviation from the overall mean of crosses. Any particular cross has an expected value which is the sum of the general combining abilities of its two parental varieties. However, the cross may deviate from this value to a greater or lesser extent. This deviation is called the SCA of the two varieties in combination (Falconer and Mackay, 1996).
Differences in GCA have been attributed to additive, additive x additive and higher order interactions of additive genetic effects in the base population, while differences in SCA have been attributed to non-additive genetic variance (Baker, 1978).
Resistance to FRR has been observed to be additive in nature being governed by 3-7 largely dominant genes with major additive effects (Bravo et al., 1969), two to three recessive genes (Azzam, 1958), two genes with recessive duplicate action (McRostie, 1921) or with dominant and recessive epistasis (Smith and Houston, 1960). However, Hassan et al. (1971) reported a shift from additive gene action to partial dominance with length of exposure to the pathogen. Similarly, Wallace and Wilkinson (1966) reported that resistance was dominant, while others simply reported that resistance to FRR was complex (Wallace and Wilkinson, 1965). These findings show a lot of inconsistency, which is probably due to the different sources of resistance that were used as well as the fungal isolates, environmental conditions, and the methods of testing and evaluation in these studies. This study reports further on the inheritance of resistance to FRR in improved populations being developed for Africa.
Heritability (h2) is a statistical tool used to evaluate the genetic control of traits determined by many loci and can be used to effectively plan strategies for incorporating characters into new cultivars (Falconer and Mackay, 1996). Breeders are interested in heritability for the simple reason that characters with higher values can be improved more rapidly with less intensive evaluation than those with lower heritability. However, heritability estimated is unique to the population being studied and the environmental conditions to which individuals have been subjected (Falconer, 1989; Dabholkar, 1992). Populations which are genetically uniform, such as inbred varieties, are expected to show lower heritability than genetically diverse populations. When heritability is high, more reliance can be placed on mass selection, and when it is low, more emphasis is placed on progeny, sib, or family selection.
The heritability is used to estimate the improvement due to selection. The ratio of the genotypic variance (VG) to phenotypic variance (VP) expresses the extent to which individual phenotypes are determined by the genotypes, and is referred to as heritability in the broad sense (H2), or the degree of determination. Broad sense heritability estimates include additive (VA), dominance (VD) and epistatic (VI) sources of genetic variation. The ratio VA/VP expresses the extent to which the phenotypes are determined by the genes transmitted from the parents, and is termed as heritability in the narrow sense (h2). It determines the degree of resemblance between relatives and is therefore of greatest importance in breeding programmes (Falconer and Mackay, 1996). Heritability is a reflection of only the additive sources of variation. Environmental variance (VE) forms part of
phenotypic variance and affects the magnitude of heritability; when it is high heritability is low and when it is low heritability is high.
Hassan et al. (1971) reported broad sense heritability (H2) of resistance to FSP of up to 64.3% under greenhouse conditions, and up to 79.7% under field conditions, and narrow sense heritability (h2) of up to 44.3% in inter-genepool crosses. Schneider et al. (2001) reported an even higher h2 of resistance to FSP of up to 71% in F4-derived families developed within the same genepool, while Román-Avilès and Kelly (2005) reported h2 up to 51% in inbred backcross line populations (IBL). The moderate to high heritability estimates suggest that resistance to FRR could be improved by selection.