Literature Review 33
Griffing's method of analysis of diallel cross data involve general and specific combining abilities. Combining abilities can be interpreted as additive, dominance and various types of epistasis; therefore the predominant types of genetic variances can be determined_
The genetic variances between the crosses is partitioned into two components: variance of general combining ability (ifgca) which contains additive variance and additive x additive type of epistasis, and variance of specific combining ability (ifsca) which contains dominance variance as we!! as all other types of epistasis. The relation between ifgca and if.ca with genetic components was defined by Griffing (1956b) and Kempthorn (1 955) in terms of additive and non-additive variances.
The estimates of genetic components of variations and epistasis are derived from covariance of full-sib and half-sib families as follows:
where:
cov"·' = [( 1 +F)/4 )u', +[ ( ( 1 +F)/4 )2)u 'AA+[( (1 +F)/4 )2 ]a' AAA+ ..
c o v , 5 : [ ( 1 + F ) / 2 ] u\ + [ ( ( 1 + F ) / 2 ) 2 ] u',+ [ ( ( 1 + F ) /2 ) 2] u2AA+ [(( 1 +F)/2)2]u2,0+[((1+F)I2)']a' 00 + . .
if A : additive genetic variance of random mating, non-inbred (i.e. panmictic) if AA : additive x additive type of epistasis
if AAA: additive x additive x additive type of epistasis if 0 : dominance x genetic variance of panmictic if AD : additive x dominance type of epistasis if 00 : dominance x dominance type of epistasis
The variance components in terms of the covariances between relatives are· ifgca ::: COVH_S_
ifsca ::: COVF 5_-2COVHs
The braadsense and narrowsense heritabilities can be estimated using the ifgca and c?-sca as follows:
Literature Review 34
There are several advantages of the combining ability analysis (Griffing, 1 956a; 1 956b) over the diallel analysis as used by Mather and Jinks (1982), since the combining ability variances estimate a simple and reliable genetic situation and a genetic model in the presence of epistasis. On the other hand, the diallel analysis of Mather and Jinks (1 977) in which the absence of epistasis is one of the basic assumptions, is not necessary in Griffing's diallel analysis. In this case, there is no limitation on the number of al!eles and the analysis can be used for any number of alleles per locus and any number of loci.
2.2.6 Heritability
The heritability of any character is a measure of the relative importance of heredity. Therefore, heritability may be considered as the usefulness of a character under selection. A character can be hereditary in the sense of being determined by 1) total genotype, and 2) average transmission from the parent to the offspring. The genotype versus environment meaning leads to the first definition of heritability known as descriptive heritability. Descriptive heritability is equal to the ratio of the all of the genotypic variance if G (additive, dominance and epistasis) to the phenotypic variance c!P and is commonly symbolised by h265. The later meaning leads to the second definition of heritability known as narrowsense heritability and is equal to the ratio of additive genetic variance cl A to the phenotypic variance of individuals in the population, and is commonly symbolised h2 NS (e.g. Nyquist, 1 991 ). In plant breeding, characters with a high narrowsense heritability are of particular interest, since characters with higher narrowsense heritability have higher genetic advance (.fiG) under selection (see Section 2.2.7), and also may be evaluated more readily in field trials. When narrowsense heritability is high, more reliance can be placed on mass selection, and when heritability is low, more emphasis must be placed on progeny, sib or family selection (Nyquist, 1991).
The broadsense heritability is generally of little interest in plant breeding except in clonal or hybrid cultivars. All of the genotypic variance in some population is accounted for not just the additive variance. Example include a population with different genotype structure (mixture of homozygotes and
Literature Rev;ew 35 heterozygotes), asexua!!y propagated species with high heterozygosity (i.e. fruit and forest trees), and apomictically propagated species. To obtain an unbiased broadsense heritability in self�fertilising species, Nyquist (1991) recommended using an F 2 population derived from a cross between parents within a random mating population.
1t is possible that by changing the environment, the genotypic and additive effects change. We can assume that, in the presence of genotype x environment interactions, changes in environment could result in changes i n phenotype. The environment could be defined as either microenvironment, e g temperature, light, level of nutrition etc., or macro-environment, e.g. area (location), growing season, year etc.
In plants, the observed variance is the variance of phenotypic values of individuals within a population. The family heritability in plants is the observed phenotypic variance among family means. In fact, family heritability is the ratio of the among family additive genetic value component to the phenotypic variance among family means. For within family heritability, the observed variance is the phenotypic variance among individuals within the families. If individuals in a plant species can be measured, heritability on an individual basis can be calculated. In some cases e.g. dry mass of some plants, heritability can not be measured on an individual basis.
To estimate heritability, Pederson ( 1 972) evaluated and compared four mating designs, the partial diallel cross, the full diallel cross, and the North Carolina designs I and 1!. The if A• if 0 and if w were measured and a true genotype x environment interaction was assumed to be absent. Of these four designs, the partial diallel design was the most preferred, followed by the North Carolina design 11, the complete diallel and then the North Carolina design ! .
To estimate the heritability and standard error of heritability, Gordon e t af. (1 972) used 2 cross-classified models. The first mode! consisted of block, environment, genotype, and genotype x environment interaction. The second model consisted of year, site, site x block interaction, block within environment, genotype, genotype x site interaction, genotype x year interaction and genotype x site x year interaction. Gordon et al. (1 972) also estimated all of the variance components and standard errors of heritabilities. In another study, Gordon (1979) estimated heritability and standard errors ofheritabilitles for perennial crops. Pesek
Literature Review