Читать книгу Principles of Plant Genetics and Breeding - George Acquaah - Страница 186

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
F						20	31	17	15	185	−2.18
G							32	14	12	190	−1.55
H								35	38	248	5.7
I									17	171	−3.93
J										184	−2.3
										2024	0

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.