Principles of Plant Genetics and Breeding. George Acquaah

a certain specific gravity, optimum length). In disease resistance breeding, there may not be a significant advantage of selecting for extreme resistance over selecting for less than complete resistance. On the other hand, in breeding nutritional quality, there may be legal guidelines as to threshold expression for toxic substances.

      4.2.17 Early generation testing

      Early generation testing is a selection procedure in which the breeder initiates testing of genetically heterogeneous lines or families in an earlier than normal generation. In Chapter 15, recurrent selection with testers was used to evaluate materials in early generations. A major consideration of the breeder in selecting a particular breeding method is to maximize genetic gain per year. Testing early, if effective, helps to identify and select potential cultivars from superior families in the early phase of the breeding program. The early generation selection method has been favorably compared with other methods such as pedigree selection, single‐seed‐descent, and bulk breeding. The question of how early the test is implemented often arises. Should it be in the F₁‐, F₂‐, or F₃‐derived families? Factors to consider in deciding on the generation in which selection is done include the trait being improved, and the availability of off‐season nurseries to use in producing additional generations per year (in lieu of selecting early).

      4.2.18 Concept of combining ability

      Over the years, plant breeders have sought ways of facilitating plant breeding through efficient selection of parents for a cross, effective and efficient selection within a segregating population, and prediction of response to selection, among other needs. Quantitative assessment of the role of genetics in plant breeding entails the use of statistical genetics approaches to estimate variances and partition them into components as previously discussed. Because variance estimates are neither robust nor accurate, the direct benefits of statistical genetics to the breeder have been limited.

      In 1942, Sprague and Tatum proposed a method of evaluation of inbred lines to be used in corn hybrid production that was free of the genetic assumptions that accompany variance estimates. Called combining ability, the procedure entails the evaluation of a set of crosses among selected parents to ascertain the extent to which variances among crosses are attributable to statistically additive characteristics of the parents, and what could be considered the effect of residual interactions. Crossing each line with several other lines produces an additional measure in the mean performance of each line in all crosses. This mean performance of a line, when expressed as a deviation from the mean of all crosses, gives what Sprague and Tatum called the general combining ability (GCA) of the lines.

      The GCA is calculated as the average of all F₁s having this particular line as one parent, the value being expressed as a deviation from the overall mean of crosses. Each cross has an expected value (the sum of GCAs of its two parental lines). However, each cross may deviate from the expected value to a greater or lesser extent, the deviation being the specific combining ability (SCA) of the two lines in combination. The differences of GCA are due to the additive and additive × additive interactions in the base population. The differences in SCA are attributable to non‐additive genetic variance. Further, the SCA is expected to increase in variance more rapidly as inbreeding in the population reaches high levels. GCA is the average performance of a plant in a cross with different tester lines, while SCA measures the performance of a plant in a specific combination in comparison with other cross combinations.

      The mathematical representation of this relationship for each cross is as follows:

      where X is the general mean and G_A and G_B are the GCA estimates of the parents, and S_AB is the statistically unaccounted for residual or SCA. The types of interactions that can be obtained depend upon the mating scheme used to produce the crosses, the most common being the diallelee mating design (full or partial diallele).

      Plant breeders may use a variety of methods for estimating combining abilities, including the polycross and top‐crossing methods. However, the diallele cross (each line is mated with every other line) developed by B. Griffing in 1956 is perhaps the most commonly used method. The GCA of each line is calculated as follows:

where x represents a specific line. Using the data in Table 4.3, G_A can be calculated as:

Table 4.3 Calculating general and specific combining abilities.

	B	C	D	E	F	G	H	I	J	Total	GCA
A	26	24	29	28	22	21	27	21	28	226	2.98
B		21	35	30	26	22	29	14	19	222	2.45
C			26	21	10	14	13	17	23	169	−4.18
D				25	31	32	28	21	18	245	5.33
E					13	23	15	15	14	184	−2.3
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