Agriculture Reference
In-Depth Information
Table 2.1.
Data for linkage disequilibrium (LD) calculations from
Falconer and Mackay (1996) for alleles at loci A and B.
A
A
1
A
2
p
A
q
A
B
B
1
p
B
p
A
p
B
r
q
A
p
B
t
B
2
q
B
p
A
q
B
s
q
A
p
B
u
equilibrium, both groups will have the same frequencies (Falconer and
Mackay 1996):
D
ru
st
D
p
A
p
B
q
A
q
B
p
A
q
B
q
A
p
B
:
As we can see,
D
value depends on the allele frequencies of the
population and a
D
value of 1 can only be achieved if
p
A
q
A
=
p
B
q
B
.
Therefore, a new statistic, standardized
D
or
D
´
(aka
D
prime), was
developed (Lewontin 1964).
D
´
D
=
D
max
;
where
D
max
=min (
p
A
*
p
B
,
q
A
*
q
B
)if
D
<
0 and min (
p
A
*
q
B
,
q
A
*
p
B
)if
0 (Neale 2008).
D
´
value reaches 1 when at least one of the gamete
combinations (A
1
B
1
,A
1
B
2
,A
2
B
1
, and A
2
B
2
) frequency is 0. These values
of
D
´
D
>
ect why this LD estimate is used to have an idea of the
recombination rate between a pair of loci. But when
D
´
= 1, this does
not guarantee the absence of recombination due to issues of (i) dealing
with hidden recombination such as when two haplotypes recombine
and generate an already existing haplotype or (ii) when rare alleles are
common in a population (Neale 2008).
The other major LD statistic is
r
2
proposed by Hill and Robertson
(1968), which is another form of
D
:
re
r
2
D
2
=
p
A
*
q
B
*
q
A
*
p
B
:
The value of
r
2
also ranges between 0 and 1 and it provides a good
predictive power for recombination between two loci. When
r
2
=1,
this is referred to as complete linkage. Both statistics are frequency
