19.Genetic Analysis of Quantitative Traits

19.Genetic Analysis of Quantitative Traits

Introduction

Quantitative traits are phenotypic characteristics that show continuous variation and are typically influenced by multiple genes and environmental factors. Unlike single-gene traits, which display discrete categories, quantitative traits form a spectrum of phenotypes. This chapter explores the genetic and statistical principles underlying quantitative trait inheritance.

19.1 Quantitative Traits Display Continuous Phenotypic Variation

Discontinuous vs. Continuous Variation

• Discontinuous variation: Phenotypes of single-gene traits fall into distinct categories (e.g., Mendelian 3:1 ratio in F2).

• Continuous variation: Polygenic and multifactorial traits show a range of values without clear boundaries between categories.

Genetic Potential

• Traits like human height are influenced by multiple genes and environmental factors (e.g., nutrition).

• Parents transmit a "genetic potential" to offspring, which may be realized depending on environmental influences.

Major Gene Effects

• Polygenic traits result from multiple genes, each with varying influence.

• Major genes (e.g., OCA2 for eye color) have strong effects; modifier genes have lesser effects.

Additive Gene Effects

• Additive genes: Each allele contributes incrementally to the phenotype.

• Some traits have equal additive effects from each gene; others have distinct contributions.

Multiple-Gene Hypothesis

• Proposed in the early 1900s to explain continuous variation by segregation of multiple genes.

• Nilsson-Ehle used this to describe wheat kernel color, controlled by two genes (A and B).

Explaining Kernel Color in Wheat

• Alleles A1 and B1 each add one unit of color; A2 and B2 add none.

• More "1" alleles result in darker color; all "2" alleles result in the lightest color.

Figure 19.1: Polygenic Inheritance of Wheat Kernel Color

Illustrates the distribution of kernel color in F2 generation from a dihybrid cross, showing five phenotypic classes.

Additive Genes and Continuous Variation

• Increasing the number of additive genes increases the number of phenotypic categories.

• With two genes: five classes; with three genes: seven classes.

Figure 19.2: Three-Gene Additive Model

Shows seven phenotypic classes for kernel color when three additive genes are involved.

Calculating Phenotypic Categories

• Number of categories: $2n + 1$, where n = number of genes.

• Example: Three genes → $2(3) + 1 = 7$ categories.

Figure 19.3: Phenotype Distributions with Additive Genes

Demonstrates how increasing gene number smooths the phenotypic distribution.

Table 19.1: The Effect of Multiple Contributing Genes on Phenotypic Variation

Number of Genes	Number of Phenotype Categories	Frequency of Most Extreme Phenotypes
1	3	1/4
2	5	1/16
3	7	1/64
4	9	1/256
5	11	1/1024
6	13	1/4096
7	15	1/16,384
8	17	1/65,536
9	19	1/262,144
10	21	1/1,048,576

Allele Segregation in Quantitative Trait Production

• Edward East (1916) studied corolla length in Nicotiana longiflora (tobacco).

• Crossed pure lines (short and long corolla); F1 was intermediate; F2 showed a wide range.

Experimental Results and Conclusions

• F2 generation showed continuous variation, not matching parental extremes.

• Conclusion: Multiple genes and environmental factors influence quantitative traits.

Effects of Environmental Factors

• Genetic and nongenetic factors both contribute to phenotypic variation.

• Gene-environment interaction increases the range of possible phenotypes.

Figure 19.5: The Effect of Gene-Environment Interaction

Shows how increasing gene-environment interaction broadens phenotypic distributions.

Threshold Traits

• Some traits, though polygenic, are expressed in discrete categories (e.g., affected/unaffected).

• Threshold traits are common in medical genetics (e.g., disease susceptibility).

Figure 19.6: Threshold Traits

Illustrates the concept of genetic liability and the threshold for expressing a trait.

Genetic Liability

• Genetic liability: The risk of expressing an affected phenotype, determined by the sum of risk alleles.

• First-degree relatives of affected individuals have higher liability due to shared genetics.

Figure 19.7: Polygenic Model for a Threshold Trait

Shows distribution of liability alleles and the threshold for trait expression.

Nongenetic Factors

• Environmental and developmental factors can influence whether individuals near the threshold express the trait.

19.2 Quantitative Trait Analysis Is Statistical

Statistical Foundations

• R.A. Fisher (1918) showed that quantitative traits result from additive effects of multiple genes.

• Statistical methods are essential for analyzing quantitative traits and gene-environment interactions.

Statistical Description of Phenotypic Variation

• First step: Construct a frequency distribution for the trait in a random sample.

• Distribution shows the proportion of individuals at each measured value or category.

Figure 19.8a: Adult Height Frequency Table

Height (cm)	Number	Frequency (%)
155–157	4	0.4
158–160	8	0.8
161–163	26	2.6
164–166	58	5.8
167–169	92	9.2
170–172	148	14.8
173–175	186	18.6
176–178	181	18.1
179–181	148	14.8
182–184	92	9.2
185–187	53	5.3
188–190	22	2.2
191–193	8	0.8
194–196	4	0.4
197–199	1	0.1

Figure 19.8b: Adult Height by Sex

Height (in)	Females (n)	Males (n)
60	1	0
61	1	0
62	5	0
63	7	0
64	12	0
65	18	0
66	16	0
67	8	0
68	1	0
69	0	3
70	0	3
Total	68	70
Average (x̄)	64.5 in	70.2 in
Standard deviation (s)	±2.7 in	±3.2 in
Variance (s2)	7.29 in2	10.24 in2

Measures of Central Tendency

• Mean (x̄): Sum of all values divided by the number of individuals.

• Mode: Most common value.

• Median: Middle value in the distribution.

Variance and Standard Deviation

• Variance (s2): Measures spread around the mean.

$s^2 = \sum (x_i - \bar{x})^2 / df$

• Standard deviation (s): Square root of variance, in the same units as the trait.

$s = \sqrt{s^2}$

Partitioning Phenotypic Variance

• Phenotypic variance ($V_P$) can be divided into:

  • Genetic variance ($V_G$): Due to genotype differences.

  • Environmental variance ($V_E$): Due to environmental differences.

• In inbred populations, $V_G = 0$; in controlled environments, $V_E = 0$ (rare in nature).

Summary

• Quantitative traits are influenced by multiple genes and environmental factors, resulting in continuous phenotypic variation.

• Statistical methods are essential for analyzing and interpreting quantitative trait data.

• Partitioning variance helps distinguish genetic from environmental contributions to trait variation.