Chapter 24 Pearson Summary

Chapter Twenty-Four: Quantitative Genetics

Section 24.1

1. Difference Between Quantitative and Discontinuous Characteristics

   • Discontinuous Characteristics:

     • Only a few distinct (discrete) phenotypes are present.

   • Quantitative Characteristics:

     • Exhibit continuous variation in phenotype, demonstrating a spectrum of phenotypic expressions.

2. Complex Relation Between Genotype and Phenotype

   • Polygenic Nature:

     • Many genotypes are possible due to multiple genes influencing quantitative characteristics.

   • Influence of Environmental Factors:

     • Environmental factors can further affect phenotype, making the interactions between genotype and phenotype complex.

3. Phenotypes and Polygenic Characteristics

   • Many Possible Genotypes:

     • A high number of genotypes arises because multiple genes are involved.

     • For two alleles at multiple loci, possible genotypes are calculated as $3^n$ (where n = number of loci).

     • For 3 genes: 27 genotypes

     • For 4 genes: 81 genotypes

   • Environmental Influence:
     -Each genotype's phenotype may also change based on environmental conditions, expanding the range of phenotypes further.

Section 24.2

4. Population vs Sample

   • Sample: A subset of the population.

   • Representativeness Requirements:

     • Must be randomly selected

     • Sufficiently large to minimize random differences when compared to the population.

5. Mean and Variance Information

   • Mean: Represents the center of the distribution.

   • Variance: Indicates the spread of the distribution around the mean.

6. Standard Deviation and Variance Relationship

   • Standard Deviation ($s$):

     • Square root of the variance ($ext{Var} = s^2$).

     • Same units as original data.

   • Variance ($ext{Var}$):

     • Expressed in squared units of original data.

7. Correlation Coefficient

   • Association Information:

     • Absolute value indicates the strength of association between two variables.

     • Close to +1/-1: strong association; close to 0: weak association.

   • Important Note: Correlation does not imply causation.

8. Regression

   • Definition: Mathematical relationship between correlated variables.

   • Usage: Predicative tool to estimate one variable based on another.

     • Predict offspring characteristics of a mating without needing genotypic knowledge.

Section 24.3

9. Phenotypic Variance Components

   • $V_G$ – Genotypic variance component.

   • $V_A$ – Additive genetic variance component.

   • $V_D$ – Dominance genetic variance component.

   • $V_I$ – Gene interaction variance component.

   • $V_E$ – Environmental differences variance component.

   • $V_{GE}$ – Interaction of genes and environment variance component.

10. Broad-Sense vs Narrow-Sense Heritability

    • Broad-Sense Heritability ($H^2$):

      • Portion of phenotypic variance due to all genetic variances ($V<em>A + V</em>D + V_I$).

    • Narrow-Sense Heritability ($h^2$):

      • Portion due only to additive genetic variance ($V_A$).

11. Heritability Calculation Methods

    • Elimination of Variance Components:

      • Variance equation: $V<em>P = V</em>G + V<em>E + V</em>{GE}$

      • Set $V<em>{GE} = 0$ or isolate $V</em>G$ or $V_E$ for calculation.

    • Parent-Offspring Regression:

      • Plot parent mean phenotypic values against offspring mean phenotypic values to get the narrow-sense heritability.

    • Comparing Phenotypes by Relatedness:

      • Compare monozygotic versus dizygotic twins.

      • Differences in correlation yield estimates of heritability.

    • Response to Selection:

      • $R = h^2 imes S$, where $S$ is selection differential.

12. Misunderstandings of Heritability

    • Heritability Definition: Portion of variance due to genetic variance, not genotype determination of phenotype.

    • Population-Level Application: Not applicable to individuals.

    • Specific Conditions: Determined for certain populations under specific conditions; not generalizable.

    • Environmental Influence: High heritability can change with environmental shifts.

    • Genotype Differences: High heritability does not indicate population differences stem from genetic differences.

13. QTL Mapping for Polygenic Characteristics

    • Method: Cross two homozygous inbred strains with differing loci, measure quantitative traits, and correlate with molecular markers for QTL determination.

Section 24.4

14. Response to Selection and Heritability

    • $R = h^2 imes S$: Helps predict change in phenotype mean across generations under selection.

15. Response to Selection Plateauing

    • Genetic Variation Depletion:

      • No genetic variation for further response to selection.

    • Natural Selection Factors:

      • Natural selection may counteract artificial selection efforts.

APPLICATION QUESTIONS AND PROBLEMS

Section 24.1

16. Characteristic Classifications

    • a. Kernel color in wheat: Discontinuous; determined by a single locus.

    • b. Body weight in Labrador retrievers: Discontinuous; single locus and two phenotypes.

    • c. Leprosy susceptibility: Quantitative; influenced by multiple genes and environmental factors (continuous trait).

    • d. Number of toes in guinea pigs: Quantitative; determined by multiple loci.

    • e. Number of fingers in humans: Discontinuous; single locus and few distinct phenotypes.

17. Principles of Heredity and Quantitative Characteristics

    • Segregation Principle: Random allele separation into gametes.

    • Independent Assortment: Alleles at one locus separate independently from others (not linked).

    • Application: Principles apply to quantitative characteristics as alleles still assort independently across multiple loci.

18. Genotype Weight Calculations

    • a. F1 Progeny Weight: 10 grams for all Aa Bb.

    • b. F2 Progeny Distribution: Group by uppercase/lowercase alleles for phenotype weight.

      • Outcomes: 16 grams (1/16), 13 grams (4/16), 10 grams (6/16), 7 grams (4/16), 4 grams (1/16).

19. Height Phenotype Expectations in F2 Progeny

    • Expected heights and frequencies from various allele combinations calculated based on given strain heights (12 cm difference) and influence of alleles on phenotype.

20. Tomato Weight Analysis

    • Conclusion: At least six loci likely involved in weight variation, using the expected distribution based on test results of 2000 F2 variations.

21. Backcross Progeny Variability

    • Backcross shown to have greater genetic variability than F1 due to the genetic diversity derived from meiosis between heterozygous parents.

22. Mendel's Pea Plant Height

    • If height was quantitative, Mendel’s results would differ, complicating conclusions on inheritance principles (dominance, segregation).

Section 24.2

23. Guinea Pig Digits Frequency Distribution

    • 2: 0, 3: 5, 4: 15, 5: 5, 6: 1; indicating total of 25.

24. Weight Calculation in Students

    • Mean: 67.6 kg, Variance calculated; SD calculated as $s = \sqrt{224.9} = 15$ kg.

25. Tadpole Size and Metamorphosis Time Correlation

    • Inverse correlation suggests larger tadpoles metamorphose quicker.

26. Mosquito Fish Correlation Calculation

    • Correlation coefficient calculated from covariance and the formula to derive the relationship between weight, length (r=0.95).

27. Mother-Daughter Heights Correlation

    • a. Correlation coefficient calculated; result signifies strong relationship.

    • b. Estimated height of daughter based on mother's height through regression calculations, yielding 67.8 inches.

28. Tail Length Variance Components

    • a. Narrow-sense heritability calculated as $0.5/1.3 = 0.38$.

    • b. Broad-sense heritability calculated as $0.9/1.3 = 0.69$.

29. Additive Genetic Variance Calculation in Rabbits

    • VA determined as $0.4(0.8) = 0.32$.

30. Phenotypic Variance Among Groups

    • a. Group A likely highest variance due to genetic diversity.

    • b. No, environmental variance will differ among the groups, reducing generalizability.

31. Heritability Effects of Variance Components

    • a. Increase in dominance variance decreases narrow-sense heritability.

    • b. Broad-sense heritability will increase due to total genetic component increase.

    • c. Increase in environmental variance decreases narrow-sense heritability, as it increases total phenotypic variance.

    • d. Broad-sense heritability decreases due to increase in total phenotypic variance with heightened environmental variance.

32. Heritability of Flower Color

    • Estimated heritability = 0; no genetic variance present since all plants are homozygous.

Section 24.3

33. Broad-Sense Heritability of Bluebonnets

    • a. Heritability = $15/20 = 0.75$.

    • b. Inaccuracy likely due to differential environmental conditions affecting varied genetic populations.

34. Monozygotic vs Dizygotic Twins

    • Assumption may be violated due to monozygotic twins sharing a more similar environment than dizygotic counterparts; leading to biased heritability estimates.

35. Phenotypic Variation in Shell Breadth

    • Narrow-sense heritability equals the proportion due to additive genetic variance inferred to be 0.7.

36. Height Conclusion Among Southwestern University Students

    • Only reasonable conclusion is (d); heritability applies only to variance, not individuals or absolute height.

37. Regression Coefficient for Offspring-Parent Relationship

    • Estimated narrow-sense heritability as regression coefficient = 0.8.

38. Highest Heritability Line in Figure

    • The line with $b = 1$ represents the highest heritability, indicating greatest regression of offspring phenotype on parent phenotype.

39. Heritability Differences in Natural vs Laboratory Populations of D. buzzati

    • Differences due to phenotypic variance affected by environmental factors in natural populations rather than genetic variance in laboratory settings.

40. Mr. Jones’ Farm Case Study

    • Salesman is correct; heritability does not indicate societal response to environmental changes affecting phenotype.

41. QTL Mapping Comparison with Genome-Wide Studies

    • QTL mapping involves pedigree analysis in distinct crosses, while genome-wide studies assess associations in a population of unrelated individuals, both utilize genetic markers.

42. Wing Length Increase Calculations in Cockroaches

    • a. Selection differential $S = 10 - 4 = 6 cm$; expected response $R = 0.6 imes 6 = 3.6 cm$.

    • b. Progeny average wing length = $4 cm + 3.6 cm = 7.6 cm$.

43. Best Responding Cattle Characteristic to Selection

    • Tenderness has highest narrow-sense heritability resulting due to low variance compared to others in response to selection.

44. Narrow-Sense Heritability Calculation for Sheep Wool Production

    • $h^2 = R/S = 6/8 = 0.75$ correspondingly derived from response and selection differential differences.

45. Strawberry Weight Prediction

    • R = 1.5 g; progeny predicted weights would harbor a weight of 3.5 g.

46. Response to Selection in Corn Strain

    • Indicating ongoing response showcases present genetic variation; not plateauing yet.

47. Genetic Influence on Drosophila Traits

    • Increased wing length inversely affects head width, indicating complexities of traits relational to genetic correlations.

48. Heritability Expectation of Domestic vs Wild Pigs

    • Wild boars likely have higher heritability due to less domestication and more genetic variance compared to selective environments of domestic pigs.

49. Fitness and Response to Selection

    • Equal fitness among all genotypes implies no phenotypic variance due to environmental variation, leading to zero response on selection.

CHALLENGE QUESTIONS

50. Bipolar Disorder Inheritance Indication

    • Suggests potential influence of X-linked inheritance due to sibling patterns observed in affected individuals, with emphasis on male connections.

51. Musical Ability Heritability Design

    • Proposed longitudinal study with monozygotic twins reared apart against dizygotic twins to derive quantitative heritability through correlation comparisons.

52. Eisen's Litter Weight Study

    • Levels off likely from opposing selection rather than total loss of genetic variance. Immediate response to reversed selection showcasing still-present genetic variance.