Gene Lecture 6
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Fundamental Genetics Lecture 6
Quantitative Genetics John Donnie A. Ramos, Ph.D. Dept. of Biological Sciences College of Science University of Santo Tomas
Kinds of Heritable Traits Qualitative Traits with contrasting expressions discontinuous traits mostly controlled by a single gene
Quantitative Traits continuous traits controlled by multiple genes / polygenes (several genes located in different chromosomes but are responsible for a single trait) phenotypes in ranges phenotypes show normal distribution curve (bellshaped curve)
1
Quantitative Trait Examples Height, skin color, intelligence Follows a normal curve
Multiple Factor Hypothesis Several factors or genes can cause the pattern of inheritance in continuous traits Cumulative Quantitative Inheritance of height in tobacco was first studied by Josef Gottlieb Kolreuter
2
Inheritance of Corolla Length Performed by Edward East (1920) Nicotiana longiflora
Characteristics of Quantitative Traits Quantifiable traits ( by measuring, weighing, counting, etc.) Caused by 2 or more gene pairs in different chromosomes Each gene locus may be additive allele (contributiory allele) or non-additive allele (non-contributory allele) Equal effects of each contributory allele Presence of substantial phenotypic variation Analysis of polygenic traits requires the study of large numbers of progeny from a population of organisms.
3
Inheritance of kernel color in wheat Studied by Herman Nilsson-Ehle (1909)
Dark red
Medium red Intermediate red light red
white
Controlled by 2 gene pairs (R1, R2 and their recessive alleles r1 and r2) Genes contributing to redness are called contributory alleles and those that don’t contribute are non-contributory alleles
Inheritance of kernel color in wheat R1R1R2R2
x
r1r1r2r2
R1r1R2r2
x
R1R2
R1r2
r1R2
r1r2
R1R2
R1R1R2R2
R1R1R2r2
R1r1R2R2
R1r1R2r2
R1r2
R1R1R2r2
R1R1r2r2
R1r1R2r2
R1r1r2r2
r1R2
R1r1R2R2
R1R1r2r2
r1r1R2R2
r1r1R2r2
r1r2
R1r1R2r2
R1r1r2r2
r1r1R2r2
r1r1r2r2
1 dark red: 4 medium red :6 intermediate red: 4 light red: 1 white
4
Inheritance of kernel color in wheat Observed phenotypes are caused by the presence or absence of contributory alleles 1 dark red: 4 medium red :6 intermediate red: 4 light red: 1 white 4 contributory alleles 0 Noncontributory Allele
3 contributory alleles 1 Noncontributory Allele
2 contributory alleles 2 Noncontributory Alleles
1 contributory allele 3 Noncontributory Alleles
0 contributory allele 43 Noncontributory Alleles
R1R2
R1r2
r1R2
r1r2
R1R2
R1R1R2R2
R1R1R2r2
R1r1R2R2
R1r1R2r2
R1r2
R1R1R2r2
R1R1r2r2
R1r1R2r2
R1r1r2r2
r1R2
R1r1R2R2
R1R1r2r2
r1r1R2R2
r1r1R2r2
r1r2
R1r1R2r2
R1r1r2r2
r1r1R2r2
r1r1r2r2
Summary: 1 C4 + 4 C3c + 6 C2c2 + 4 Cc3 + 1c4
Calculating the Number of Genes Number of Pairs of Polygenes
Number of Genotypic Classes
Number of Phenotypic Classes
Fraction of F2 similar to Parents
n
3n
2n+1
1/4n
1
3
3
1/4
2
9
5
1/16
3
27
7
1/64
Binomial Distribution: (C+c)n
= 1 C4 + 4 C3c + 6 C2c2 + 4 Cc3 + 1c4
5
Calculating the Number of Genes
Inheritance of skin color in humans Negro
x Mulatto
White x
1/16 Negro: 4/16 Sambo :6/16 Mulatto: 4/16 Quadroon: 1/16 White
Sambo
x
Quadroon
¼ Sambo: 2/4 Mulatto: ¼ Quadroon
Mulatto
x
Quadroon
1/2 Mulatto: 1/2 Quadroon
1/8 Sambo: 3/8 Mulatto: 3/8 Quadroon: 1/8 White
6
Analysis of Polygenes Uses Biostatistics or Biometry Uses: Descriptive summary of sample Satatistical Inference Comparison between populations Statistical Methods: Mean Variance Standard Deviation Standard Error of the Mean
Mean Arithmetic average
_
X =
ΣXi n
Affected by frequency distribution Cannot distinguish between different types of variations
7
Variance Used to estimate the variation present in large populations Represents the average squared deviation of the measurements from the mean Example: important in determining the influence of environment on the phenotype of a polygene
_
s2 =
Σ(Xi - X )2 n-1
Other Statistical tests Standard Deviation Used to determine the sample variation around the mean (using original units of measurement) Square root of the variance
s =
s2
Standard Error of Mean Used to estimate how much the means of other similar samples drawn from the same population might vary Measures the accuracy of sample mean _
SX =
s n
8
Analysis of Quantitative Character 18 oz tomato
Mean of F1
_
X =
ΣXi n
x
=
6 oz tomato
626 52
= 12.04 oz
Mean of F2
_
X =
ΣXi n
=
872 72
= 12.11 oz
Analysis of Quantitative Character
Standard deviation = 1.13
= 2.06
Interpretation
= 12.11±2.06
= 12.04±1.13 (nearly identical weight)
(more variable weights)
9
Heritability Determines the impact of heredity versus environment on a phenotype Broad-sense heritability Measures degree of phenotypic variance Phenotypic variance is the sum of environmental vaiance, genetic veriance, and the interaction between the two. Narrow-Sense heritability Measure of potential response to selection Useful in assessing selection potential in randomly breeding animal or plant populations Artificial Selection –selecting specific group Twin studies in humans
Artificial selection in corn
10
Twin studies in humans
Mapping Quantitative Trait Loci
DDT resistance is polygenic
11
Test Yourself Inheritance of the main internode length (I) in a hypothetical plant involves quantitative inheritance. The average internode length of plant variety A is 3.2 inches. A second variety (variety B) belonging to the same species has an average internode length of 2.10 inches. Crossing these two varieties of plants produced an F1 of a third variety (Variety C) with an average internode length of 2.65 inches. Selfing of variety C produced an F2 of 25 % similar to variety A; 50 % similar to variety C and 25 % similar to variety B. 1. How many polygene pairs are involved in the inheritance of the internode length? 2. What is the approximate contribution (in inches) of each polygene? 3. How many contributory alleles are found in variety A? 4. How many contributory alleles are found in variety B? 5. How many contributory alleles are found in variety C? 6. Give the genotype of variety A 7. Give the genotype of variety B 8. Give the genotype of variety C
12
Quantitative Genetics John Donnie A. Ramos, Ph.D. Dept. of Biological Sciences College of Science University of Santo Tomas
Kinds of Heritable Traits Qualitative Traits with contrasting expressions discontinuous traits mostly controlled by a single gene
Quantitative Traits continuous traits controlled by multiple genes / polygenes (several genes located in different chromosomes but are responsible for a single trait) phenotypes in ranges phenotypes show normal distribution curve (bellshaped curve)
1
Quantitative Trait Examples Height, skin color, intelligence Follows a normal curve
Multiple Factor Hypothesis Several factors or genes can cause the pattern of inheritance in continuous traits Cumulative Quantitative Inheritance of height in tobacco was first studied by Josef Gottlieb Kolreuter
2
Inheritance of Corolla Length Performed by Edward East (1920) Nicotiana longiflora
Characteristics of Quantitative Traits Quantifiable traits ( by measuring, weighing, counting, etc.) Caused by 2 or more gene pairs in different chromosomes Each gene locus may be additive allele (contributiory allele) or non-additive allele (non-contributory allele) Equal effects of each contributory allele Presence of substantial phenotypic variation Analysis of polygenic traits requires the study of large numbers of progeny from a population of organisms.
3
Inheritance of kernel color in wheat Studied by Herman Nilsson-Ehle (1909)
Dark red
Medium red Intermediate red light red
white
Controlled by 2 gene pairs (R1, R2 and their recessive alleles r1 and r2) Genes contributing to redness are called contributory alleles and those that don’t contribute are non-contributory alleles
Inheritance of kernel color in wheat R1R1R2R2
x
r1r1r2r2
R1r1R2r2
x
R1R2
R1r2
r1R2
r1r2
R1R2
R1R1R2R2
R1R1R2r2
R1r1R2R2
R1r1R2r2
R1r2
R1R1R2r2
R1R1r2r2
R1r1R2r2
R1r1r2r2
r1R2
R1r1R2R2
R1R1r2r2
r1r1R2R2
r1r1R2r2
r1r2
R1r1R2r2
R1r1r2r2
r1r1R2r2
r1r1r2r2
1 dark red: 4 medium red :6 intermediate red: 4 light red: 1 white
4
Inheritance of kernel color in wheat Observed phenotypes are caused by the presence or absence of contributory alleles 1 dark red: 4 medium red :6 intermediate red: 4 light red: 1 white 4 contributory alleles 0 Noncontributory Allele
3 contributory alleles 1 Noncontributory Allele
2 contributory alleles 2 Noncontributory Alleles
1 contributory allele 3 Noncontributory Alleles
0 contributory allele 43 Noncontributory Alleles
R1R2
R1r2
r1R2
r1r2
R1R2
R1R1R2R2
R1R1R2r2
R1r1R2R2
R1r1R2r2
R1r2
R1R1R2r2
R1R1r2r2
R1r1R2r2
R1r1r2r2
r1R2
R1r1R2R2
R1R1r2r2
r1r1R2R2
r1r1R2r2
r1r2
R1r1R2r2
R1r1r2r2
r1r1R2r2
r1r1r2r2
Summary: 1 C4 + 4 C3c + 6 C2c2 + 4 Cc3 + 1c4
Calculating the Number of Genes Number of Pairs of Polygenes
Number of Genotypic Classes
Number of Phenotypic Classes
Fraction of F2 similar to Parents
n
3n
2n+1
1/4n
1
3
3
1/4
2
9
5
1/16
3
27
7
1/64
Binomial Distribution: (C+c)n
= 1 C4 + 4 C3c + 6 C2c2 + 4 Cc3 + 1c4
5
Calculating the Number of Genes
Inheritance of skin color in humans Negro
x Mulatto
White x
1/16 Negro: 4/16 Sambo :6/16 Mulatto: 4/16 Quadroon: 1/16 White
Sambo
x
Quadroon
¼ Sambo: 2/4 Mulatto: ¼ Quadroon
Mulatto
x
Quadroon
1/2 Mulatto: 1/2 Quadroon
1/8 Sambo: 3/8 Mulatto: 3/8 Quadroon: 1/8 White
6
Analysis of Polygenes Uses Biostatistics or Biometry Uses: Descriptive summary of sample Satatistical Inference Comparison between populations Statistical Methods: Mean Variance Standard Deviation Standard Error of the Mean
Mean Arithmetic average
_
X =
ΣXi n
Affected by frequency distribution Cannot distinguish between different types of variations
7
Variance Used to estimate the variation present in large populations Represents the average squared deviation of the measurements from the mean Example: important in determining the influence of environment on the phenotype of a polygene
_
s2 =
Σ(Xi - X )2 n-1
Other Statistical tests Standard Deviation Used to determine the sample variation around the mean (using original units of measurement) Square root of the variance
s =
s2
Standard Error of Mean Used to estimate how much the means of other similar samples drawn from the same population might vary Measures the accuracy of sample mean _
SX =
s n
8
Analysis of Quantitative Character 18 oz tomato
Mean of F1
_
X =
ΣXi n
x
=
6 oz tomato
626 52
= 12.04 oz
Mean of F2
_
X =
ΣXi n
=
872 72
= 12.11 oz
Analysis of Quantitative Character
Standard deviation = 1.13
= 2.06
Interpretation
= 12.11±2.06
= 12.04±1.13 (nearly identical weight)
(more variable weights)
9
Heritability Determines the impact of heredity versus environment on a phenotype Broad-sense heritability Measures degree of phenotypic variance Phenotypic variance is the sum of environmental vaiance, genetic veriance, and the interaction between the two. Narrow-Sense heritability Measure of potential response to selection Useful in assessing selection potential in randomly breeding animal or plant populations Artificial Selection –selecting specific group Twin studies in humans
Artificial selection in corn
10
Twin studies in humans
Mapping Quantitative Trait Loci
DDT resistance is polygenic
11
Test Yourself Inheritance of the main internode length (I) in a hypothetical plant involves quantitative inheritance. The average internode length of plant variety A is 3.2 inches. A second variety (variety B) belonging to the same species has an average internode length of 2.10 inches. Crossing these two varieties of plants produced an F1 of a third variety (Variety C) with an average internode length of 2.65 inches. Selfing of variety C produced an F2 of 25 % similar to variety A; 50 % similar to variety C and 25 % similar to variety B. 1. How many polygene pairs are involved in the inheritance of the internode length? 2. What is the approximate contribution (in inches) of each polygene? 3. How many contributory alleles are found in variety A? 4. How many contributory alleles are found in variety B? 5. How many contributory alleles are found in variety C? 6. Give the genotype of variety A 7. Give the genotype of variety B 8. Give the genotype of variety C
12
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