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Genetics: Analysis and Principles
Robert J. Brooker
CHAPTER 25
QUANTITATIVE GENETICS
25.1 QUANTITATIVE TRAITS

A quantitative trait is any trait that varies measurably in a
given species
Quantitative Traits Exhibit a
Continuum of Phenotypic Variation

Quantitative traits show a continuum of
variation within a group of individuals

Quantitative traits do not naturally fall into a
small number of discrete categories
Quantitative traits can be described by using a
frequency distribution
The trait is divided arbitrarily into a number of
discrete phenotypic categories
Figure 25.1 Normal distribution of a quantitative trait
25.2 POLYGENIC INHERITANCE

Most quantitative traits are polygenic and exhibit a
continuum of phenotypic variation

Polygenic inheritance refers to the transmission of
traits that are governed by two or more genes

The locations on chromosomes that affect the
outcome of quantitative traits are called quantitative
trait loci (QTLs)

QTLs may contain many genes

Some or all of which may affect quantitative traits
Polygenic Inheritance and
Environmental Factors

The first demonstration that continuous variation is
related to polygenic inheritance occurred in 1909

The Swedish geneticist Herman Nilsson-Ehle studied the
inheritance of red pigment in the hull of wheat Triticum
aestivum

Nilsson-Ehle performed the following cross
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P
F1
F2
True-breeding red X true-breeding white
Intermediate red
Great variation in redness:


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As shown in Figure 24.3b, Nilsson-Ehle discovered that
the colors fell into a 1:4:6:4:1 ratio
He concluded that this species is diploid for two different
genes that control hull color


White, light red, intermediate red, medium red, dark red
Each gene exists in two alleles: red or white
He hypothesized that these two loci must contribute
additively to the color of hull
Figure 25.3


Many polygenic traits are difficult or
impossible to categorize into several discrete
genotypic categories
This is especially true when


1. The number of genes controlling the trait
increases
2. The influence of the environment increases
Effect of # of genes
• If there is no
environmental effect,
the number of
contributing genes
can be estimated by
either:
– the number of
phenotypic classes
or
– by the fraction of the
total population of an
extreme phenotype
class
The basic model for quantitative traits

P=G + E

P = phenotypic value for the trait of one individual
(plant or animal).

G = the effect of the genes carried by the individual
(genotypic value).

E = the effect of the environmental factors on the
phenotype of the animal.
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Genotypic Value





Genotypic value is the overall effect of all the genes
carried by the individual on its phenotype. It includes:
Additive effects of genes (A): the sum of individual
effects (average effects) of alleles.
Dominance effects of genes (D): interaction between
alleles at the same gene
Epistatic effects (I): interaction between alleles on
different genes
G = A + D + I P = A+ D + I + E
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Heritability
• Heritability in the broad sense (H2): is the proportion of the phenotypic
variance that is due to all genetic effects ( additive, dominance and epistasis):
VG VA  VD  VI
H  
VP
VP
2
It measures the strength of the relationship between the phenotypic values of the
individuals and their genotypic values.
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Heritability in the narrow sense (h2): is
the proportion of the phenotypic variance
that is due to additive genetic effects only.
VA
h 
VP
2
It measures two things:
1. The degree to which the offspring resemble their parents
in the phenotype for a trait.
2. The strength of the relationship between the phenotypic
values and the additive genetic effects (the relationship
between P and A).
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
1.
2.
3.
Notes:
Heritability is a measure on a population of
individuals in a given environment for a given
character. It is NOT measured on one
individual.
Heritability can be estimated for each
quantitative trait.
It varies from population to another and from
environment to another for the same traits.
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Importance of heritability




Heritability is very important in selection (in
genetic improvement)
It determines if phenotypic selection would be
efficient or not:
Small heritability: phenotypic selection is not
efficient (low accuracy of selection).
High heritability: phenotypic selection is efficient
(high accuracy of selection)
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
Realized heritability

The most common way to estimate narrow sense
heritability in a starting population
R
2
hN =
S

Where




Here
R = XO – X
S = XP – X

So
hN2 =
XO – X
XP – X
R is the response in the offspring
S is the selection differential in the parents
Where

X is the mean of the starting population
XO is the mean of the offspring

XP is the mean of the parents


Example:

An experiment is begun with a population of fruit flies in
which the average bristle number for both genders is 37.5.


The parents chosen from this population had an average bristle
number of 40
The offspring of the next generation had an average bristle number
of 38.7
hN2 =
hN2 =
XO – X
XP – X
38.7 – 37.5
40 – 37.5
=
1.2
2.5
= 0.48
Thus, 48% of the
phenotypic
variation is due to
additive alleles
Example 1

The narrow-sense heritability for potato
weight in a starting population of
potatoes is 0.42, and the mean weight
is 1.4 lb. If a breeder crosses two
strains with average potato weights of
1.9 and 2.1 lb, respectively, what is the
predicted average weight of potatoes in
the offspring?

Example 2. A farmer wants to increase the
average body weight in a herd of cattle. She
begins with a herd having a mean weight of
595 kg and chooses individuals to breed that
have a mean weight of 625 kg. Twenty
offspring were obtained, having the following
weights in kilograms: 612, 587, 604, 589,
615, 641, 575, 611, 610, 598, 589, 620, 617,
577, 609, 633, 588, 599, 601, and 611.
Calculate the realized heritability for body
weight in this herd.