©2000 Timothy G. Standish
Genesis 25:24-2624 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
Timothy G. Standish, Ph. D.
Quantitative Quantitative GeneticsGenetics
©2000 Timothy G. Standish
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
©2000 Timothy G. Standish
DefinitionsDefinitions 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 NurtureNature 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 AllelesAdditive Alleles
CRCWCRCR CWCW
F2 GenerationF2 Generation
2: 11:
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
CRCR
CRCW
CRCW
CWCW
CR CW
CR
CW
©2000 Timothy G. Standish
Additive AllelesAdditive 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
432321210
F2
1/4 AA
1/2 Aa
1/4 aa
1/4 BB -- 1/16 AABB1/2 Bb -- 2/16 AABb1/4 bb -- 1/16 AAbb1/4 BB -- 2/16 AaBB1/2 Bb -- 4/16 AaBb1/4 bb -- 2/16 Aabb1/4 BB -- 1/16 aaBB1/2 Bb -- 2/16 aaBb1/4 bb -- 1/16 aabb
1/16
6/16 = 3/8
1/16
4/16 = 1/4
4/16 = 1/4
©2000 Timothy G. Standish
Additive AllelesAdditive Alleles Graphed as a frequency diagram, these results
look like this:
©2000 Timothy G. Standish
Estimating Gene NumbersEstimating 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:
4n1 = F2 extreme phenotypes in total offspring
641
43
1= N = 3 so there are probably about 3 genes involved
©2000 Timothy G. Standish
Economic ImplicationsEconomic ImplicationsEnvironment or genetics?
©2000 Timothy G. Standish
Describing Quantitative Traits:Describing Quantitative Traits:The MeanThe 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
=nXi
Sum of individual values
Number of individual values
X
X
Frequency
Trait
©2000 Timothy G. Standish
-1 +1
68.3%=
n(n - 1)nf(x2) - (fx2)
Describing Quantitative Traits:Describing Quantitative Traits:Standard DeviationStandard 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
©2000 Timothy G. Standish
HeritabilityHeritability 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 Heritability1 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
VGH2
©2000 Timothy G. Standish
2 Narrow-Sense Heritability2 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
VAh2
©2000 Timothy G. Standish
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