powerpoint-quantitative-genetics.itisppt

©2000 Timothy G. Standish
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 . . .

Timothy G. Standish, Ph. D.
Quantitative
Quantitative
Genetics
Genetics

How Could Noah Have Done It?
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

Definitions
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

Nature Vs Nurture
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

Additive Alleles
Additive Alleles
CR
CW
CR
CR
CW
CW
F2 Generation
2: 1
1:
 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 redder
flowers
CR
CR
CR
CW
CR
CW
CW
CW
CR
CW
CR
CW

Additive Alleles
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
Additive
alleles
4
3
2
3
2
1
2
1
0
F2
1/4 AA
1/2 Aa
1/4 aa
1/4 BB -- 1/16 AABB
1/2 Bb -- 2/16 AABb
1/4 bb -- 1/16 AAbb
1/4 BB -- 2/16 AaBB
1/2 Bb -- 4/16 AaBb
1/4 bb -- 2/16 Aabb
1/4 BB -- 1/16 aaBB
1/2 Bb -- 2/16 aaBb
1/4 bb -- 1/16 aabb
1/16
6/16 = 3/8
1/16
4/16 = 1/4
4/16 = 1/4

Additive Alleles
Additive Alleles
 Graphed as a frequency diagram, these results
look like this:

Estimating Gene Numbers
Estimating Gene Numbers
 If 1/64th of the offspring of an F2 cross of the kind
described above are the same as the parents, then
 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:
4n
1 = F2 extreme phenotypes in total offspring
64
1
43
1
= N = 3 so there are probably
about 3 genes involved

Economic Implications
Economic Implications
Environment
or genetics?

Describing Quantitative Traits:
The Mean
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
=
n
Xi
Sum of individual
values
Number of
individual
values
X
X

Frequency
 Trait

-1 +1
68.3%
=
n(n - 1)
nf(x2
) - (fx2
)
Standard Deviation
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
s
X

Frequency
 Trait
Total number of
individuals in sample
Number of individuals
in each unit measured
Gradations of
units of
measurement

Heritability
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

1 Broad-Sense Heritability
1 Broad-Sense Heritability
 As long as this is the case, broad heritability can be
expressed as the ratio of environmental to genetic
components in phenotypic variation
VP = VE + VG
Genetics
Genetic and
Environmental
interactions
Environment
 Proportion of phenotypic variance resulting from
genetic rather than environmental influences
 Components contributing to phenotypic variation
(VP) can be summarized as follows:
VP = VE + VG + VGE
 VGE is typically negligible so this formula can be
simplified to:
=
VP
VG
H2

2 Narrow-Sense Heritability
2 Narrow-Sense Heritability
 As long as this is the case, narrow-sense heritability
can be expressed as the ratio as follows:
VP = VE + VG
Dominance
Interactive or
epistatic
variance
Additive
 Potential of selection to change a specific
continuously varying phenotypic trait
 Narrow-sense heritability concentrates on VG which
can be subdivided as follows:
VG = VA + VD + VI
 VA is typically negligible so this formula can be
simplified to:
=
VP
VA
h2

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