Transcript Quantitative Genetics

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
Genetics
Environmental
interactions
VGE is typically negligible so this formula can be
simplified to: V = V + V
P
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
Dominance
epistatic
variance
VA is typically negligible so this formula can be
simplified to: V = V + V
P
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