Biology Reference
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trait (such as measured Ascaris burden), we term it a quantitative trait
nucleotide (QTN) variant. The effect of a functional variant on the
phenotype can be quantified by the QTN-specific variance that is given by
s q ¼ 2pð1 pÞa 2 , where p is the minor allele frequency of the QTN and
a
is one-half the difference between phenotypic means of the two
homozygotes. Biologically, we expect
to be determined by biophysical
molecular properties of the QTL and to be relatively constant across
populations. The term 2p(1
a
p) is also known as the expected heterozy-
gosity of the underlying genotype and measures the variance of a trait
that is scored as the number of minor alleles in the diploid genotype. The
relative genetic signal intensity for this QTN is given by the QTN-specific
heritability h q ¼ s q =s P
s P
is the total variance of the phenotype.
The relative genetic signal for a quantitative trait locus (QTL) is deter-
mined by the sum of the QTN-specific heritabilities (although these must
be corrected for possible linkage disequilibrium among variant sites) in
the immediate region of the QTL and thus will be influenced by all of
the relevant functional variants in the region. In algebraic form, the
QTL-specific heritability is
, where
P 2p i 1 p i a i
s P
X h qi
h 2 Q ¼
¼
where the summation is over the functional variants in the regions of
the QTL. Similarly, the total heritability of the phenotype is given by the
sum of all of the QTL-specific heritabilities over the whole genome or
h 2
¼ P h 2 Qi .
ASSESSIN G HERITABILITY IN HUMAN PE DIGREES
At this point, we can employ variance decomposition theory to derive
a model that allows for the infection-related phenotypic variance to be
decomposed into components that are due to host genetic factors and
random environmental factors. For n host individuals, the n
n pheno-
U
typic covariance matrix (
) is given by the following variance component
model:
U ¼ð2Fh 2 þ Ie 2 Þs p
(12.2)
where 2
is twice the kinship matrix (i.e. the coefficient of relationship
matrix) among individuals which is derived from the host pedigree
structure, and
F
is the identity matrix (with ones on its diagonal and
zeros elsewhere). The identity matrix simply conveys the assumed
structure of the remaining environmental (which also includes all model
error components) component in which everyone experiences a unique
I
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