Indirect selection 1

Genotype-environment interactions could

be

of primary importance in a spaced plants situation in a breeder's nursery, in comparison with the normally

imposed

growing conditions for the plants in a pure or mixed species sward.

The

difference in spacing makes the reference population of environments quite different and so the estimations of genotypic values (Comstock and Moll,

1963).

Traditionally, the breeder selects the plants in a spaced plant environment and the agronomist tests them under sward conditions, not surprisingly revealing many inconsistencies (Ahlgren,

1944;

Ahlgren

et aI., 1945;

Lazenby and Rogers,

1962;

Van Dijk and Winkelhorst,

1978).

The same trait in two different environments can

be

considered two different traits

(Falconer,

1952;

Van Vleck,

1964;

Searle,

1965;

McWilliam and Latter,

1 970;

Wiggans

et

aI. ,

1980;

Fernando

et aI., 1984;

Rattunde

et aI. ,

199 1 ;

Van Sanford

et ai.,

1993).

The objective is to select in one environment to obtain a better result in another. This could be the case when the selection in one of the environments is difficult, but the decision should

be

based in the solution of the following formula suggested by Lerner and Cmden

( 1 948).

(2. 10)

where CLlGAB is the correlated genetic advance in environment

B

when selection is done in environment

A,

LlGB is the genetic advance in environment B, iA is the intensity of selection in

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1 7

environment

A,

iB is the intensity of selection in environment B , hA is the square root of the heritability of the character in environment

A,

hB is the square root of the heritability of the character in environment B and rA(AB) is the genetic correlation that measures the degree of association between the genetic variations of the character in environments

A

and B.

The

rA(AB) is not likely to be known because

A

and B are environments and not characters, but rp(AB) (phenotypic correlation between the same character in the two environments) may be known.

(2. 1 1)

where rE(AB) is the environmental correlation between

A

and B (the same as rp with

all

one cultivar), eA is the complement of the square root of heritability of

A

(eA

= 1

-h�, and ea is

the complement of the square root of heritability of B (ea

= 1

-

hB). Then:

CtiGAB

tiGB

(2. 12)

If the ratio is greater than 1 ,

there is more genetic advance if selection is done in

A

to improve B than to select directly in B (Baker,

1986; 1 994).

2.2.6 MULTIPLE SELECTION

Smith

(1936)

suggested for the first

time

a method of multiple selection worked out in a logical and systematic manner. The value of plants is expressed as a linear function of

their

characters and by the use of "discriminant functions" developed by Fisher (Fisher,

1 936),

it is possible to derive the best available guide to the genetic value of each line.

Smith's index was extended by Hazel

(1943)

to the case when each individual has a true breeding value and the correlation of its genetic value with the observed phenotypic

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1 8

expression is known. The main contnbution of Hazel's paper was the definition o f a method to estimate the variances and covariances required (Lin,

1978).

Some considerations follow:

(a) the phenotypic value

(Pi)

is partitioned into two components, a genotypic value (Gi) defined as the average over all possible environments, and an environmental contnbution <Bi), i.e. the model is:

(2. 13)

(b)

only additive (average allele) effects are part of the genotypic value in the model.

(c) with attnbutes being i =

1, 2, ... ,In,

the genotypic importance is H =

L

atGi. where at are

constants defined by the breeder. H is also partitioned linearly.

The solution to find the selection index is the linear function

I

=

L�Pi

which

correlates best with the index H. The solving fonnula to find

the

b's is:

Pb = Ga

(2. 14)

where

P

is the matrix of phenotypic variances and covariances,

G

is the matrix of genotypic variances and covariances and

a

is the vector of economic values or weights (Tallis,

1962;

Lin, 1978;

Humphreys,

1995).

The solution

(b

=

p-1Ga)

of the simultaneous equations is obtained by Gaussian elimination (Humphreys,

1995).

A

restricted index developed by Kempthome and Nordskog

( 1 959)

is used when not only the best progress in H is important, but also when some Gi should remain constant or unchanged. The mathematical solution was developed by the authors and consists of a simultaneous solution subject to the condition that the covariance between the index and the linear function of genotypes is zero for the character involved to prevent any genetic change.

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1 9

The Smith-Hazel index selection was named "estimated index" by

Williams ( 1962)

because the coefficients of the index are calculated using estimated parameters of the population. The author pointed out that the theoretical accuracy of the index may fail when the estimates are subject to large variation.

The indexes might be divided into three different groups according to their use:

Type

1 -

Type 2 - Type

3 -

to improve several characters at a time.

to improve one character with assistance from other characters.

to improve complex characters. The traits considered in the index may not include the one of interest, as in characters that are not directly

measurable. Such an index can be referred to as an indirect selection index. Binet

(1965, loco cit.

Lin,

1978)

combined measurable traits to obtain genetic gains in another character not included in the index.

Cunningham ( 1969) suggested a method to decide which traits should be included in the index by dropping each trait in sequence. The reduction in rIH (correlation between

I and

H)

is the parameter used to consider the importance of each trait since genetic progress is proportional to this correlation. The disadvantage of this method is that it requires

the

calculation of a reduced index for each variable to be evaluated, plus the full rank index.

Response to multitrait selection could be predicted by extending the univariate individual selection response Equation

(2.5)

to several traits:

r

= yIGs where yl and

G

means the same as for Equation

(2. 14)

and

r

is a vector of selection responses and s is a vector of selection differentials for measured traits (Humphreys,

1995).

Other methods like "tandem" and "independent culling levels" are also

used

to select plants considering several attnbutes or environments. The tandem method is to select for each character (or the same character in different environments) at a

time until

each is considered improved. The method of independent culling levels or multiple goals allows the breeder to

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2 0

define a certain critical level for each character (or the same character ill different enviromnents) and only the plants better for all of them are selected.

Several authors compared the efficiency of these three ways of multiple selection. The method of total score (selection index) is the most efficient, followed by independent culling levels (Bennett and Swiger, 1980) and finally by the tandem method (Hazel and Lush, 1942; Young, 196 1 ; Finney, 1962).

Index selection is always better than tandem selection for all combinations of parameters simulated (pesek and Baker, 1969a; 1969b). The efficiency of tandem selection is

increased by selecting first the most important traits, and the efficiency of index selection is

increased by calculating the coefficients more frequently (pesek and Baker, 1969; Villanueva and Kennedy, 1993).

Elgin

et al.

(1970) compared several multiple-trait selection methods in an alfalfa trial.

The independent culling levels followed the estimated index in efficiency and the least efficient was the tandem method (Elgin

et al. ,

1970; Eagles and Frey, 1974).

From the information given by the authors mentioned above,

the

estimated selection index is the best but certain limitations have to be considered:

(a) parameters change due to selection; for example, the genetic variance becomes smaller in each successive cycle of selection and the optimum index changes.

(b)

true parameters are never known; the estimated parameters from samples are more accurate when the sample is big, but when it is small the estimates of theoretical gains could be biased.

Humphreys (1995) using selection index, compared the multivariate response with the observed response after one generation of selection among half-sib families in six populations of Perennial ryegrass, and concluded that this multivariate approach can be used to predict

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2 1

breeding progress and to identify key traits and populations in which breeding objectives were

most likely to be achieved.

In document Quantitative genetics of sheep preference in red clover (Trifolium pratense L ) under spaced plant and sward conditions : a thesis presented in partial fulfilment of the requirements for the degree of Doctor of Philosophy (Ph D ) in Pasture Breeding, Depa (Page 49-54)