Transcript No Slide Title

Genesis 25:24-26
24 And when her days to be delivered
were fulfilled, behold, there were
twins in her womb.
25 And the first came out red, all over like
an hairy garment; and they called his
name Esau.
26 And after that came his brother out, and
his hand took hold on Esau's heel; and
his name was called Jacob . . .
©2000 Timothy G. Standish
Quantitative
Genetics
Timothy G. Standish, Ph. D.
©2000 Timothy G. Standish
How Could Noah Have Done It?
The diversity of appearance in humans and other
animals is immense
 How could Adam and Eve or Noah and his
family have held in their genomes genes for all
that we see today?
 At least one explanation, that the dark-skinned
races descended from Cain who was marked with
dark pigment (the mark of Cain mentioned in
Gen. 4:15) or Ham as a result of the curse
mentioned in Gen. 9:22-27
 Quantitative or polygenic inheritance offers
much more satisfying answer to this quandary

©2000 Timothy G. Standish
Definitions

Traits examined so far have resulted in
discontinuous phenotypic traits
– Tall or dwarf
– Round or wrinkled
– Red, pink or white

Quantitative inheritance deals with genetic control
of phenotypic traits that vary on a continuous basis:
– Height
– Weight
– Skin color

Many quantitative traits are also influenced by the
environment
©2000 Timothy G. Standish
Nature Vs Nurture
Quantitative genes’ influence on phenotype are at
the crux of the nature/nurture debate
 Socialism emphasizes the environment
 Fascism emphasizes genetics
 Understanding quantitative genetics helps us to
understand the degree to which genetics and the
environment impact phenotype
 Aside from political considerations, quantitative
genetics helps us to understand the potential for
selection to impact productivity in crops and
livestock

©2000 Timothy G. Standish
Additive Alleles
Additive alleles are alleles that change the
phenotype in an additive way
 Example - The more copies of tall alleles a person
has, the greater their potential for growing tall
 Additive alleles behave something like alleles
that result in incomplete dominance
 More CR alleles results in
F2 Generation
redder flowers CR
CW

CR CR CR CR CW
1:
2:
1
CRCR CRCW CWCW
CW CRCW CWCW
©2000 Timothy G. Standish
Additive Alleles
If more than one gene with two alleles that
behave as incompletely dominant alleles are
involved, variability occurs over more of a
continuum
 If two genes with two alleles are involved, X
phenotypes can result

F2
1/4 AA
1/2 Aa
1/4 aa
Additive
alleles
1/4 BB -- 1/16 AABB
4
1/2 Bb -- 2/16 AABb
3
1/4 bb -- 1/16 AAbb
2
1/4 BB -- 2/16 AaBB
3
1/2 Bb -- 4/16 AaBb
2
1/4 bb -- 2/16 Aabb
1
1/4 BB -- 1/16 aaBB
2
1/2 Bb -- 2/16 aaBb
1
1/4 bb -- 1/16 aabb
0
1/16
4/16 = 1/4
6/16 = 3/8
4/16 = 1/4
1/16
©2000 Timothy G. Standish
Additive Alleles

Graphed as a frequency diagram, these results
look like this:
©2000 Timothy G. Standish
Estimating Gene Numbers
The more genes involved in producing a trait, the
more gradations will be observed in that trait
 If two examples of extremes of variation for a trait
are crossed and the F2 progeny are examined, the
proportion exhibiting the extreme variations can be
used to calculate the number of genes involved:
1 = F extreme phenotypes in total offspring
2
4n
 If 1/64th of the offspring of an F2 cross of the kind
described above are the same as the parents, then
1 = 1
N = 3 so there are probably
64 43
about 3 genes involved

©2000 Timothy G. Standish
Economic Implications
Environment
or genetics?
©2000 Timothy G. Standish
Describing Quantitative Traits:
The Mean
Two statistics are commonly used to describe
variation of a quantitative trait in a population
1 The Mean - For a trait that forms a bell-shaped
curve (normal distribution) when a frequency
diagram is plotted, the mean is the most common
size, shape, or whatever is being measured

SXi
X=
n Number of
individual
values
X
D Frequency
Sum of individual
values
D Trait
©2000 Timothy G. Standish
Describing Quantitative Traits:
Standard Deviation
2 Standard Deviation - Describes the amount of
variation from the mean in units of the trait
 Large SD indicates great variability
 68 % of individuals exhibiting the trait will fall
within ±1 SD of the mean, 95.5 % ±2, 99.7 % ±3 SD
 95 % fall within 1.96 SD
-1
+1
s=
n(n - 1)
D Frequency
Number of individuals
Total number of
individuals in sample in each unit measured
nSf(x2) - (Sfx2)
Gradations of
units of
measurement
X
68.3%
D Trait
©2000 Timothy G. Standish
Heritability
Heritability is a measure of how much quantitative
genes influence phenotype
 Two types of heritability can be calculated:
1 Broad-Sense Heritability:
 H2 - Expresses the proportion of phenotypic
variance seen in a sample that is the result of
genetic as opposed to environmental influences
2 Narrow-Sense Heritability:
 h2 - Assesses the potential of selection to change a
specific continuously varying phenotypic trait in a
randomly breeding population

©2000 Timothy G. Standish
1 Broad-Sense Heritability
Proportion of phenotypic variance resulting from
genetic rather than environmental influences
 Components contributing to phenotypic variation
(VP) can be summarized as follows: Genetic and

VP = VE + VG + VGE

Environment
VGE is typically negligible so this formula can be
simplified to: V = V + V
P

Genetics
Environmental
interactions
E
G
As long as this is the case, broad
heritability can be expressed as the
ratio of environmental to genetic
components in phenotypic variation
2
H
VG
=
VP
©2000 Timothy G. Standish
2 Narrow-Sense Heritability
Potential of selection to change a specific
continuously varying phenotypic trait
 Narrow-sense heritability concentrates on VG
which can be subdivided as follows: Interactive or

VG = VA + VD + VI

Additive
VA is typically negligible so this formula can be
simplified to: V = V + V
P

Dominance
epistatic
variance
E
G
As long as this is the case, narrowsense heritability can be expressed ash2
the ratio as follows:
VA
=
VP
©2000 Timothy G. Standish
©2000 Timothy G. Standish