Agriculture Reference
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dependent, but the frequency dependence of r 2 is higher than for D ´ . D ´
can achieve the maximum especially if one of the alleles is rare. Thus, r 2
offers advantages for small size populations because its value is not
affected by the frequency of rare alleles (Neale 2008).
The r 2 statistic summarizes both recombination and mutational his-
tory while D ´ measures only recombination history and is only an
accurate statistic for estimating recombination differences. For the
purpose of examining the resolution of association studies, Flint-Garcia
et al. (2003) favors the r 2 statistics, as it is indicative of how markers
might correlate with the QTL of interest, especially if the populations
have undergone a genetic bottleneck. This is important to take into
account for association analysis when rare alleles are frequent in natural
populations.
As implied earlier, AM relies on the rate of LD decay over a physical
distance. There are several factors that in
uence LD but the one with a
central role is recombination, which causes gamete and haplotype
frequencies to change toward their equilibrium values. In order to
calculate how LD is changing in a population, the number of generations
and
recombination fraction should be included in the calculations of
the D value, which is done using the following formula:
Ф
t
D t
D 0
1
Φ
:
Following random mating, in the absence of evolutionary forces and
selection, the decay in LD is 0.5 per generation for unlinked loci.
In addition, LD decay is highly in
uenced by the physical linkage
between loci. For tight linkage and larger values of t
D 0 e Φ t
D t
:
This means that recombination frequency and time act in the same
way, doubling the number of generations halves the recombination
factor. LD decays rapidly in the absence of linkage but persists for
many generations with tight linkage (Mackay and Powell 2006).
In summary, LD is the basic principle of association studies, but in
order to be able to apply a measure of LD to a particular study there are
other considerations to take into account in order to design an optimum
study for the species with which we are working. In this respect, the loci
of interest, the breeding system of the crop, the germplasm being
considered for the crop, and its ploidy levels are very important in
determining the rate of decay across genetic or physical distances in
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