Diallel

A Diallel is a mating scheme used by plant breeders and geneticists to test for general and specific combining ability as well as genetic effects behind quantitative traits.^[1]

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In a full diallel, all parents are crossed to make hybrids in all possible combinations. Variations include partial dialleles with and without parents, see Examples. Full dialleles require twice as many crosses and entries in experiments, but allows for testing for maternal effects. If maternal effects are assumed to be negligible, then a partial diallele without reciprocals is effective.

Common analysis methods utilize general linear models to identify heterotic groups^[2], estimate general combining ability (gca)^[3], specific combining ability (SCA)^[3], interactions with testing environments, years, and estimates of additive, dominant, and epistatic genetic effects^[4][5].

Other common mating designs used to study quantitative genetics effects include midparent-offspring regression,generation mean analysis^[6], triple test cross^[7], and the mating schemes proposed by Comstock and Robinson (1948) called by plant breeders NC I nested design, NC II factorial design, and NC III testcross mating designs ^[8].

Examples

Full Diallel^[1]

     a      b      c      d      e   

a  a x a  a x b  a x c  a x d  a x e 

b  b x a  b x b  b x c  b x d  b x e 

c  c x a  c x b  c x c  c x d  c x e

d  d x a  d x b  d x c  d x d  d x e 

e  e x a  e x b  e x c  e x d  e x e 

Partial Diallel with parents, ^[9]

assuming that initial parents are inbred. Otherwise including selfed parents.

     a      b      c      d      e   

a  a x a   

b  b x a  b x b  

c  c x a  c x b  c x c  

d  d x a  d x b  d x c  d x d  

e  e x a  e x b  e x c  e x d  e x e 

Partial Diallel without parents^[9]

     a      b      c      d      e   

a    

b  b x a    

c  c x a  c x b    

d  d x a  d x b  d x c    

e  e x a  e x b  e x c  e x d   

References

1. ^ ^{a b} Hallauer, A. R. and J. B. Miranda Filho. 1988 Quantitative genetics in maize breeding. 2^nd ed. Iowa State University Press, Ames, IO.
2. ^ Griffing, B. 1956. Concept of general and specific combining ability in relation to diallel crossing systems. Australian Journal of Biological Sciences 9: 463-493
3. ^ ^{a b} Gardner, C. O. and S. A. Eberhart. 1966. Analysis and interpretation of the variety cross diallel and related populations. Biometrics 22: 439-452
4. ^ Hayman, B. I. 1954. The analysis of variance of diallel tables. Biometrics 10: 235-244
5. ^ Sprague G. F., and L. A. Tatum. 1942. General vs. specific combining ability in single crosses of corn. J. Am. Soc. Agron. 34: 923-932
6. ^ Hayman, B.I. 1958. The separation of epistatic from additive and dominance variation in generation means. Heredity 12: 371-390
7. ^ Kearsey, M.J. and Jinks, J.L. 1968. A general method of detecting additive, dominance and episstatic variation for metric traits. I. Theory Heredity 23 : 403-409.
8. ^ Comstock, R. E. and H.F. Robinson. 1948. The components of genetic variance in populations of biparental progenies and their use in estimating the average degree of dominance. Biometrics 4:254-266.
9. ^ ^{a b} Kempthorne, O. and R. N. Curnow. 1961. The partial diallel cross. Biometrics 17: 229-250