Principles of Plant Genetics and Breeding. George Acquaah

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      The others may be calculated as for line A. The next step is to calculate the expected value of each cross. Using the cross CD as an example, the expected value is calculated as follows:

      SCA is calculated as follows:

      This is done for each combination and a plot of observed values versus expected values plotted. Because the values of SCA are subject to sampling error, the points on the plot do not lie on the diagonal. The distance from each point to the diagonal represents the SCA plus sampling error of the cross. Additional error would occur if the lines used in the cross are not highly inbred (error due to the sampling of genotypes from the lines).

      Combining ability calculations are statistically robust, being based on first degree statistics (totals, means). No genetic assumptions are made about individuals. The concept is applicable to both self‐pollinated and cross‐pollinated species, for identifying desirable cross combinations of inbred lines to include in a hybrid program or for developing synthetic cultivars. It is used to predict the performance of hybrid populations of cross‐pollinated species, usually via a test cross or polycross. It should be pointed out that combining ability calculations are properly applied only in the context in which they were calculated. This is because GCA values are relative and depend upon the mean of the chosen parent materials in the crosses.

      A typical ANOVA for combining ability analysis is as follows:

Source	df	SS	MS	EMS
GCA	p −1	SG	MG	σ2E + σ2SCA + σ2GCA
SCA	p(p − 1)/2	SS	MS	σ2E + σ2SCA
Error	m	SE	ME	σ2E

      The method used of a combining ability analysis depends on available data:

      The method depends on available data:

       Parents + F1 or F2 and reciprocal crosses (i.e. p2 combination).

       Parents + F1 or F2, without reciprocals (i.e. ½ p(p + 1 combinations).

       F1 + F2 + reciprocals, without parents and reciprocals (i.e. ½ p(p−1) combination.

       Only F1 generations without parents, reciprocals (i.e. ½ p(p−1) combinations.

      4.2.19 Mating designs

      Artificial crossing or mating is a common activity in plant breeding programs for generating various levels of relatedness among the progenies that are produced. Mating in breeding has two primary purposes:

      1 To generate information for the breeder to understand the genetic control or behavior of the trait of interest.

      2 To generate a base population to initiate a breeding program.

      The breeder influences the outcome of a mating by the choice of parents, the control over the frequency each parent is involved in mating, and the number of offspring per mating, among other ways. A mating may be as simple as a cross between two parents, to the more complex diallele mating.

       Hybrid crosses

      These are reviewed here to give the student a basis for comparison with the random mating schemes to be presented.

       Single cross = A × B → F1 (AB)

       3‐way cross = (A × B) → F1 × C → (ABC)

       Backcross = (A × B) → F1 × A → (BC1)

       Double cross = (A × B) → FAB; (C × D) → FCD; FAB × FCD → (ABCD)

      These crosses are relatively easy to genetically analyze. The breeder exercises significant control over the mating structure.

       Mating designs for random mating populations

      The term mating design is usually applied to schemes used by breeders and geneticists to impose random mating for a specific purpose. To use these designs, certain assumptions are made by the breeder:

       The materials in the population have