600
Behavior Genes
assortment, that is, they are transmit-
ted together from one generation to the
n
e
x
t
,o
rc
o
s
e
g
r
e
g
a
t
e
,a
taf
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equ
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o
higher than chance. Loci that are close
together tend to depart from chance as-
sortment and, within certain limits, the
frequency of recombination, or crossing-
over between loci on paired chromosomes
is proportional to the physical distance be-
tween them. In gene mapping studies, the
genome is measured in units called cen-
timorgans (cM) with 1 cM corresponding
to a pair of loci showing crossing-over,
or recombination, one meiosis in a hun-
dred. The whole genome, averaged across
the sexes (there is more crossing-over in
female than in male meioses) is about
3500 cM long, with 1 cM roughly corre-
sponding to just under a mega base of
DNA (or a million base pairs). Linkage
can be detected over relatively large dis-
tances, 10 cM or more, so that it is possible
to mount a whole genome search using
just a few hundred evenly spaced mark-
ers. The disadvantage of linkage is that
it is capable of detecting only compara-
tively large effects. Linkage is therefore
straightforward in rare, simple Mendelian
neuropsychiatric disorders such as Hunt-
ingdon’s disease or some forms of early-
onset familial Alzheimer’s disease that
show autosomal dominant inheritance.
However, in the case of common, complex
traits, such as schizophrenia or affective
disorders, linkage studies present more of
a challenge.
Parametric linkage analysis
While in stud-
ies of plants or animals under laboratory
conditions it may be possible to arrange
crosses on a large scale and simply count
the numbers of recombinants and nonre-
combinants, studies of humans are more
complicated. The standard statistical ap-
proach to detecting linkage and estimating
recombination is to calculate LOD (log of
the odds) scores. An LOD score is the
common log of the ratio of the proba-
bility that a recombination fraction has a
certain value of less than one half to the
probability that the recombination fraction
equals one half. LOD scores are calculated
fo
rar
ang
eo
fv
a
lu
e
so
fth
er
e
comb
in
a
-
tion fraction from 0 to 0.5 and the value
that gives the maximum LOD is taken as
the most likely value of the recombination
fraction. By convention, an LOD of three
or more (i.e. odds on linkage of 1000 to
1) are accepted as sufFcient support for
linkage and an LOD of – 2 (i.e. odds of 100
to 1 against) is accepted as excluding the
presence of linkage. Unfortunately, LOD
scores were originally intended for sim-
ple traits. Therefore, one of the difFculties
that besets attempts to detect linkage in
psychiatric disorders and other common
diseases is that the mode of transmission
is unknown. That is, the disease does not
usually follow a simple Mendelian pattern
of segregation in families.
T
h
eLODs
c
o
r
ea
p
p
r
o
a
chc
anb
ee
x
-
tended to complex traits by incorporating
penetrance parameters. Penetrance is de-
Fned as the probability that a particular
phenotype will be manifested given a
certain genotype. In Mendelian traits, pen-
etrances are always either 0 or 1. ±or
example, if we consider a trait where there
are two alleles,
A
1
and
A
2
,an
dwh
e
r
e
A
2
is the ‘‘disease’’ allele, there will be
three possible genotypes
A
1
A
1
,
A
1
A
2
,and
A
2
A
2
.I
f
A
2
is recessive, the three geno-
types will show penetrances of 0, 0, and
1 respectively, whereas if
A
2
is domi-
nant, the penetrances will be respectively
0, 1, and 1. Complex traits that depart
from Mendelian patterns can be mod-
eled using a more general single major
locus (SML) approach where penetrances
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