Evaluación de la propuesta de intervención

The term diallel cross is used to describe a mating design in which a set of p _{fixed lines are chosen as male and female parents. Crosses are made}

between these parents in all possible combinations. There are maximum of {i possible crosses, which can be divided into three groups: (1) the p _{selfings of}

parental lines themselves; (2) p(p- 1)/2 _{F1s; (3)} p(p- 1)/2 _{reciprocal F1s.}

From early 1 940's techniques involving diallel crosses have been invented and used to investigate quantitative inheritance problems. This design probably has been used more. frequently than any other design to estimate general and specific combining ability. Genetic interpretation and analysis are _\ presented fn numerous papers. Griffing (1 956 a & _{b), Hayman and Jinks}

(Hayman, 1 954b; 1 957; 1 958; Jinks, 1 954) and Kempthorne (1 956) presented different approaches in diallel crossing method. Since then a number of workers have used these approaches to investigate quantitative genetic parameters in plant populations. Illustrations of and improvements to the theory have also been made. Mather and Jinks (1 982) developed an analysis of diallel cross data based on the variance and covariance estimates of a sample of parents and their F1s following work done by Hayman (1954b). The most important feature of their method is regressing of wr on vr _(covariance

and variances of parental arrays respectively) by which an average degree of dominance and genetical diversity arrong parents can be estimated. The graph based on the ratio W/Vr is linear and its slope does not depart significantly from one if additive dominance model describe the data,

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otherwise, in the presence of non-allelic interactions (epistasis), the linear relationship does-not exist.

Depending on the material under investigation and postulated underlying mechanism and methods of estimation there are two view points for diallel analysis. As mentioned by Hayman (1954b) the interest may lie in a particular set of parental lines (fixed effect model) or it may lie in a base population from which these lines were unbiasedly sampled. Kempthorne and Hayman and Jinks have based their methods on different models. Hayman (1 954b; 1 957; 1958), Jinks (1954; 1 956), and Gardner and Eberhart (1 966) attempted to investigate the genetics of the difference between a set of inbred lines whereas Kempthorne (1956) developed a model which was adapted to random mating populations. Griffing (1 956b) amalgamated both of those approaches. He was one of the first plant breeders who introduced and utilized general and specific combining ability in terms of population genetics. The analysis of Griffing (1956a) is less demanding in terms of its genetical assumptions. Kempthorne's (1 956) model allows a complete orthogonal partitioning of the total epistatic variance.

, ' As was pointed out by Sprague (1966) and Christie and Shattuck I

{1 992), in general any model developed for the estimation of genetic variances involves a series of biological assumptions. These vary somewhat with the model but the more common restrictions are:

1 - normal diploid behaviour at meiosis.

2- no reciprocal (maternal or cytoplasmic) effects. 3- no multiple alleles.

4- _{linkage equilibrium.}

5- no selection {random sample from a population). 6- no epistasis {no non-allelic interaction).

Hayman and Jinks developed some ideas on this theory in the 1960s in a series of papers (mainly in Jinks and Hayman, 1 953; Jinks, 1954; Hayman, 1 954a), in which they were mainly concerned about a particular set

CHAPTER 1WO 31 of inbred lines. Although their method and its assumptions have been criticized by several authors {Gilbert, 1 958; Baker, 1 978) and some of the assumptions have been regarded as unrealistic {Baker, 1 978), it has been widely used to investigate quantitative genetic aspects of metric characters. One of the features of the Hayman and Jinks method is the presentation of epistasis based on graphical analysis, in which the values related to Vr {the variance of all of the offspring of the rth parent) are plotted against Wr { the covariance between those offspring and their nonrecurrent parents). This graph made it possible to study the relative dominance and epistasis properties of the parents used.

Kempthorne {1 956) developed a model for analysis of the diallel crosses. His genetic interpretation was in terms of genetic variances and covariances in a random mating population. Therefore, he has mentioned the fact that his analysis is useful only when it is going to be used to make inferences about a base random mating population.

Griffing {1956b) has introduced four models depending upon whether or not the inbred lines and/or the reciprocal F/s are included:

1 - all p2 _{combinations are included}

2- inbreds and one set of F /s are included 3- F/s and reciprocal F/s are included

4- _{only one set of F1's are included.}

Usually the experimental data are used to estimate genetic statistics of the population from which the parents were sampled, this being random effect model. A fixed effect model exists also, in which parent lines are considered to be a fixed set of lines and the results are not going to be extended to a further reference population.-

Based on the paper written by Fisher {1918) and Kempthorne {1956), Griffing {1 956a) developed his analysis. He has derived his model which represents the genotypic value in terms of additive and non-additive genetic ett.ects. His final model symbolically was written as:

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Gritting (1 956a) also defined general combining ability as a function of additive genetic effects and specific combining ability as a function of dominance genetic effects. Gritting (1 956b) has further elaborated his idea. He presented the model for the qJh _{observation in a randomized-blocks design as}

follows:

in which u is the population mean effect Vq _{is the effect for the} qth _genotype,

bk is the ,!h block effect, (bv)qk is the interaction between the qth genotype and

the ,!h _{block, and} eqld _{is the environmental effect peculiar to the} qJh _individual.

The variety effects for those diallel crossing methods in which reciprocal F/s are not included, are considered in terms of general.and specific combining ability effects,

and the same effect for those diallel crossing methods in which reciprocal F1 's are included were:

vq = g1 + gi + sif +rif

The major disadvantage of diallel methods of analysis is the limitation of usage of parents in crossing scheme. This would subject the .estimates of variance components to large sampling errors. In the other words estimates of variance components could not be significant estimates of population parameters unless the number of parents exceeds ten. Otherwise, a fixed model is recommended (Hayn:an, 1 963).

Diallel cross between inbred plants can be used for measuring general combining ability in the development of open pollinated or synthetic· cultivars

'cHAPTER 1WO ₃₃

(Baker, 1 978). l_{t also can make useful information for measuring hybrid}

performances or in assessing prediction of the potential of hybrid breeding programme. In fixed models of diallel crosses, genetic interpretation of the results should be attempted only when the parents of the diallel cross are homozygous. In cross pollinated crops such as maize, this needs a laborious and time-consuming process. Self-incompatibility in plants such as red clover makes things more complicated. Because of these limitations most of the applications of diallel cross in cross pollinated plants is confined to estimating general and specific combining ability means and effects.