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Mating designs in plant breeding

The application areas for mating designs are the selection of genotypes as variety parents in breeding of hybrid varieties and synthetic varieties and the estimation of genetic variance components for optimizing the design of breeding programs. The requirements for factoral and diallel designs are

  • - each female must be able to be mated with several males (no incompatibilities, synchronize the time of flowering, the number of ears in maize is limited!)
  • - genetically identical (mother) plants are available (clones, inbred lines, double haploid lines) if the number of female inflorescences per plant is limited.
  • - hybrid mechanism (mechanical, CMS)

Within a partial dialell each parent is crossed with 3 clones, but the 3 clones are different per parent. Within this design the number of genotypes is reduced. The result is SCA can only be estimated for the crosses conducted. The SCA is of interest as each cross may deviate from the expected value (GCA). The GCA can be calculated but is then based on different testers per parent. Differences in GCA are due to additive and additive by additive interaction in the base population.

A) Factorial / North Carolina II design in breeding of maize hybrids (Comstock and Robinson 1952)

The factorial design is the most important in practical plant breeding programs for selection for testcross performance. It can be used also for pre-selection of interpool 3W and 4W hybrids.
The factorial design is used for selecting (parents of) interpool hybrids. In a factorial lines from pool A are crossed to lines of pool B. I.e. in maize it is common to use flint lines as fathers and dent lines as mothers.

Within a partial factorial each parent is crossed with 3 lines, but the 3 lines are different per parent. Within this design the number of genotypes is reduced. The result is SCA can only be estimated for the crosses conducted. The GCA can be calculated but is then based on different testers per parent.

Estimation of GCA and SCA

For calculating the general (GCA) and specific combining ability (SCA) the mother plants are tested with the same set of testers. The tester can be lines (inbred tester), populations (broad based tester) or hybrids. According to the performance the best hybrids are selected.
Y= μ + GCAi +GCAj + SCAij; is the father, j is the mother plant

The expected value of a cross with a specific male (or female) can be calculated as:
Yi = mean (Y) + GCA1; Y is the yield of all crosses, GCA1 is the GCA of male 1
GCA1= mean (Yi) – mean (Y); Yi is the yield of all crosses with male 1

The expected SCA can be calculated as:
SCA12= Y12 – GCA1 –GCA2 – mean(Y); Y12 is the yield of the cross between father 1 and mother 2

 Prediction of three and four way hybrids after Jenkins 1934

The factorial is used to predict 3-/4-way hybrids.
Three way cross (I1 x I2) x I3 ~ (O13 + O23)/2
Four way cross: (I1 x I2) x (I3 x I4) ~ (O13 + O14 + O23 + O24)/4

Three way crosses are for example applied within CMS breeding to retain the fertility of the hybrids. The three- and four way hybrids are predicted with single cross hybrids of the respective parents. I.e. k=10 mothers, l=10 fathers lead to a factorial of 100. 2025 hybrids need to be evaluated to select a good 4-way hybrid. Instead the 100 data points are used to predict 2025.

Estimation of heterosis

If data from homozygous parents is available heterosis can be estimated as

  • Midparent heterosis: h= yO – (yP1 + yP2)/2; O is the offspring yield and P1 and P2 are the yields of the two parents.
  • Better parent heterosis: h= yO – max(yP1, yP2)

 B) Diallel

The diallel can be used for preselection of parents of intrapool 3W and 4W hybrids and synthetic varieties.

The diallel design is used for selecting parents of synthetic varieties or selecting hybrid parents when no heterotic pattern (like flint and dent pool in maize) are available. Within the diallel a certain number of clones from the same pool are crossed to each other. Thus the closes are used as mother and father plants (reciprocal cross). As a result the number of produced synthetics can be large. If there are no maternal effects (i.e. CMS), the reciprocal cross is not needed. As such only half of the crosses are conducted.

Y=F-1/n(F-S)
F is the mean of the crosses F, S is the mean of all selfed crosses S.

 Estimation of GCA and SCA (method 4, after Griffing 1956; without reciprocal)

Yij= mean (Y) + GCAi + GCAj + SCAij; s.o.
GCAi= mean [ (Yi)/ (k-2) ] – [ (Y/ (k(k-2)/2) ]; Yi is the sum of the yields with male I, Y is the sum of the yield of all crosses conducted, k is the number of clones used.
SCAij= mean (Yij) – [ (Yi + Yj) / (k-2) ] + [ 2Y/ ((k-1)(k-2)) ]

c) North Carolina I design or Hierarchical design (Comstock and Robinson 1952)

Each male is crossed to a different set of females. As such the females are nested within males. Each cross generates one family. The females are grown within isolation plots surrounded by the pollinating male. Full sibs with the same mother and father plants are within families; half sibs with the same mother or father are across families.

With the hierarchical design the additive and dominance variance can be estimated.  

Literature:
Comstock, R.E., and H.F. Robinson. 1952. Estimation of average dominance of genes. In. Heterosis, Iowa State College Press, Ames, 494-516.
Griffing, B. 1956. Concept of general and specific combining ability in relation to diallel crossing systems. Austr. J. Biol. Sci. 9, 463-493.
Jenkins, M.T. 1934. Methods of estimating the performance of double crosses in corn. Journal of the American Society of Agronomy. 26: 199–204.

November 14th, 2010
Topic: Crop Science, Plant breeding Tags: None

4 Responses to “Mating designs in plant breeding”

  1. Variance components and Estimation of genetic covariance between relatives | cropscience.ch Says:

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  3. Line development and hybrid evaluation (example maize) | cropscience.ch Says:

    [...] GCA via topcross test. The general combining ability (GCA) is estimated by crossing the inbred lines to one common tester (an advanced inbred line of the opposite heterotic pool). The GCA is determined by comparing the performance of each progeny, assuming that the only di erence between the progenies can be attributed to di erent inbred parents. Breeders tend to test more inbreds than to increase the number of test parents, which can reduce the cost of seed production, by convergence, called convergent improvement. The performance of 3-way or 4-way hybrids is predicted rather than tested in the fi eld. [...]

  4. Estimation of general combining ability (GCA) and prediction of hybrid performance | cropscience.ch Says:

    [...] There are different mating designs for creating hybrids. see other post [...]

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