Agriculture Reference
In-Depth Information
reduces to an exponential function (
P
n
), where
n
is the number of loci segregating for the desired
allele and
P
varies by generation of inbreeding
(Table 13.1). Obviously, the reciprocal of DGQ
is the average size of a population that contains
one such desirable genotype. The minimum pop-
ulation size in which one desirable genotype
occurs also changes exponentially (Table 13.2).
Both Tables 13.1 and 13.2 assume independent
segregation of genes (i.e., the loci are more than
50 map units apart) and gene frequency of one-
half. If the genes are linked (i.e., less that 50 map
units apart), the needed population sizes will be
less than predicted (DGQ is higher) for coupling-
phase linkage or greater than predicted (DGQ is
lower) for repulsion-phase linkage.
The geometric changes which occur with
increasing number of loci and decreasing fre-
quency of genotypes with the desirable alleles
upon inbreeding provide a rationale for early-
generation selection, because the proportion
of plants having all of the desirable alleles in
either the homozygous or heterozygous condition
decline upon inbreeding (Shebeski 1967). His-
torically the majority of breeders tend to select for
qualitative traits fi rst and quantitative traits after
a few generations of inbreeding and selection.
Because the frequency of F
2
-derived lines with
the complete complement of desirable alleles
decreases with inbreeding, there are advantages to
selecting for qualitative and quantitative traits
simultaneously in the earliest possible generation.
Based on the increased number of traits and
therefore gene differences that breeders are
working with in the 21st century and on con-
siderations of Tables 13.1 and 13.2, breeding
strategies should emphasize selecting for both
quantitative and qualitative traits simultaneously
in the early generations. Marker-assisted selec-
tion may be used to enrich gene frequencies in
early generations. These concepts will be elabo-
rated further in the section on early-generation
selection and marker-assisted selection.
Mutations
Mutations, or changes in DNA sequence, can be
caused by copying errors during cell division or
by exposure to chemical mutagens, ultraviolet or
ionizing radiation, or viruses. Variation caused by
mutation is nontargeted and may generate novel
Table 13.2
The effect of inbreeding generation and number
of gene differences (or segregating loci) on minimum popula-
tion size.
Minimum Population Size (1/DGQ
a
)
Gene
Differences
DHL
b
or RIL
F
2
F
4
F
6
1
1
2
2
2
2
2
3
4
4
5
4
18
27
32
10
18
315
753
1,024
15
75
5,600
20,653
32,768
20
315
99,437
566,658
1,048,576
Source:
Adapted from DePauw et al. (2007) with kind
permission of Springer Science and Business Media.
a
DGQ, desirable genotype quotient, from Table 13.1.
b
DHL, doubled haploid line; RIL, random inbred line.
Table 13.1
The effect of inbreeding
generation and number of gene
differences (or segregating loci) on the
desirable genotype quotient (DGQ), in
which a desirable genotype has the
preferred allele in either the homozy-
gous or heterozygous condition at a
locus.
Desirable Genotype Quotient (DGQ)
Gene
Differences
DHL or RIL
a
F
2
F
4
F
6
1
0.7500
0.5625
0.5156
0.5000
2
0.5625
0.3164
0.2659
0.2500
5
0.2373
0.0563
0.0364
0.0313
10
0.0563
0.0032
0.0013
0.0010
15
0.0134
0.0002
4.84E
−
05
3.05E
−
05
20
0.0032
1.01E
−
05
1.76E
−
06
9.54E
−
07
Source:
Adapted from DePauw et al. (2007) with kind permission of Springer
Science and Business Media.
a
DHL, doubled haploid line; RIL, random inbred line.
