Chapter 19 : Inheritance

Inheritance Notes

  • Tutorial 21: Inheritance (JPJC/JC2 H2 Biology, 2025). Covers Mendelian genetics, epistasis, linkage, sex-linked traits, pedigree analysis, polygenic/continuous variation, chi-squared testing in genetics, and applied breeding problems (plants and animals).

  • Explanations, worked examples, and typical exam question formats are summarized with key formulas and ratios in LaTeX.

  • All numerical results, ratios, and probability expressions are included in LaTeX format where shown or useful for study.


1) Basic Gamete Formation and Unlinked Genes

  • When an organism is heterozygous at n unlinked loci (e.g., AaBbCcDd), a gamete receives one allele from each gene locus.

    • For each locus, there is a ½ chance of the gamete containing a specific allele (e.g., a from Aa, b from Bb, c from Cc, d from Dd).

    • For four unlinked loci, the probability of a gamete with genotype abcd is:

    • rac12imesrac12imesrac12imesrac12=rac116.rac{1}{2} imes rac{1}{2} imes rac{1}{2} imes rac{1}{2} = rac{1}{16}.

  • Key takeaway: independence of assortment for unlinked genes leads to multiplicative probabilities across loci.


2) Gene Interaction and Epistasis (examples)

  • Coat pigmentation in dogs (epistasis among pigment genes):

    • Alleles: aW (white) > aS (sable) > ac (copper)

    • White is dominant to sable and copper; sable is dominant to copper.

    • Crosses aWac x aSac yield 4 genotypes and 3 phenotypes (white, sable, copper) in the offspring.

    • Genotype-phenotype mapping (example shown):

    • aW aC aW aS → white

    • aW aS → white

    • aW ac → white

    • aS aC → sable or white depending on dominance relations; the typical outcome in the example yields 4 genotypes and 3 phenotypes overall.

  • Epistasis summary: the effect of one gene (epistatic) masks or modifies the effect of another gene (hypostatic).


3) Sex Determination Systems and Sex-Linked Traits

  • Birds have ZW sex-determination: Males ZZ, Females ZW.

    • If a lethal recessive allele is on the Z chromosome (Za), a cross between a male heterozygote (ZAZa) and a normal female (ZAW) yields certain sex ratios depending on Z-linked lethality.

    • Example logic (simplified): Za on ZZ vs ZAW on ZW yields some offspring where Z with lethal allele loses viability; the remaining viable offspring produce a skewed sex ratio.

  • Red-green color blindness is X-linked recessive in humans.

    • A color-blind man (XbY) has sons who are color blind (XbY) and sons who are not (XBY) depending on the X-bearing sperm; the wife must be a carrier (XBXb) to pass both alleles.

    • If the baby is a girl, the chance she will be color blind is 50% if the mother is a carrier and the father is color-blind (XbY) because daughters inherit one X from each parent.

  • Practical rule: X-linked traits show distinct patterns in pedigrees and often affect males more severely.


4) Pedigrees and Modes of Inheritance

  • Autosomal vs sex-linked patterns (qualitative cues):

    • If affected females have affected sons and affected males do not pass to sons, that suggests X-linked inheritance (sex-linked).

    • If males and females are equally affected, or if affected individuals appear in every generation, autosomal dominant or recessive depending on the pattern.

  • Examples (summarized):

    • Pedigree with a trait where affected males do not pass it to sons indicates a sex-linked trait.

    • If affected parents have affected offspring regardless of the child's sex, an autosomal pattern is implicated.

  • Important caveat: Pedigree patterns give clues, but experimental or lecture-based context is often required to state the mode accurately.


5) Autosomal Dominant/Autosomal Recessive Traits in Pedigrees

  • Problem context: A dominant mutant allele can cause early death if homozygous; if both parents are affected and produce unaffected children, the trait may be recessive or the affected condition may affect viability.

  • In autosomal traits, both sexes are affected with similar frequency, and affected individuals can have unaffected children if they’re carriers in certain contexts.

  • When a pedigree indicates autosomal traits with lethal outcomes, the following interpretation arises:

    • The trait is autosomal because both sexes are affected and transmission is not restricted by sex.

    • Lethality of homozygotes explains absence of certain genotypes in offspring.


6) Epistasis: Types and Phenotypic Ratios

  • Epistasis is gene interaction where one gene masks/modulates the effect of another:

    • Dominant epistasis: a dominant allele at one locus masks the effect of another locus. Example ratio: 12:3:112:3:1 for phenotypes in the F2 when two genes interact (dominant epistasis).

    • Recessive epistasis: recessive alleles at one locus mask another gene’s effect. Classic example yields a 9:3:4 ratio.

    • Duplicate recessive epistasis: both gene pairs need at least one dominant allele to express phenotype; homozygous recessive at either locus leads to a recessive phenotype. Often yields a 9:7 ratio.

    • Duplicate dominant epistasis: dominant alleles at either gene give a phenotype; only double recessive yields alternate phenotype, commonly 15:1.

  • Example cross discussions in material show several epistasis patterns, with explicit genotype-phenotype maps and resulting F2 phenotypes.


7) Dihybrid and Polygenic Inheritance in Plants and Animals

  • Dihybrid crosses (AaBb x AaBb) for two unlinked genes typically yield a 9:3:3:1 phenotypic ratio in the F2 (for complete dominance and independent assortment).

  • In some cases, trait interactions produce more complex ratios (epistasis), e.g., 12:3:1 (dominant epistasis) or 9:7 (duplicate/recessive/dominant interactions).

  • Polygenic/continuous variation concept:

    • Continuous variation arises from the additive effects of many genes (polygenes) and is strongly influenced by the environment.

    • Discontinuous variation arises from one or a few genes with clear-cut phenotypes and is less influenced by the environment (exceptions exist).

  • Practical example (coffee leaf length graph): continuous variation is environment-influenced; the graph shows a gradient rather than discrete categories.


8) Chi-Squared Tests in Genetics

  • Purpose: determine whether observed offspring phenotypes/genotypes differ significantly from expected Mendelian ratios.

  • Formula: χ2=(O<em>iE</em>i)2E<em>i\boxed{ \, \, \chi^2 = \sum \frac{(O<em>i - E</em>i)^2}{E<em>i} \, \, } where Oi are observed counts and E_i are expected counts under a hypothesis (e.g., 9:3:3:1).

  • Decision rule: compare computed chi-squared value to critical value for given degrees of freedom (df). If chi-squared < critical value, fail to reject the null hypothesis (no significant difference).

  • Example outcomes in the notes show several chi-squared calculations:

    • F2 dihybrid 9:3:3:1 example yielded


    • chi-squared value = 2.52.5 with p-value > 0.05 at appropriate df, leading to no significant deviation.

    • For a 12:3:1 test (dominant epistasis), chi-squared like result: 2.882.88 vs a critical value of 5.995.99 (p = 0.05); conclusion: not significantly different; supports dominant epistasis as explanation.

    • For a 9:7 epistasis scenario, chi-squared value 1.60 with critical 3.841 at p = 0.05; conclusion: data consistent with epistasis as explanation.

  • Practical tips:

    • Always state df (degrees of freedom) when interpreting chi-squared values.

    • Use chi-squared to test for fit to expected Mendelian ratios and to compare observed to expected under hypotheses like epistasis or linkage.


9) Linkage, Recombination, and Mapping Genes

  • Linkage: genes on the same chromosome tend to be inherited together (non-independent assortment) unless crossing over occurs.

  • Parental types vs recombinant types in a test cross: higher frequency of parental gametes indicates linkage; recombinant gametes arise from crossing over.

  • Measures:

    • Recombination frequency (RF) = (number of recombinant offspring / total offspring) × 100%. RF provides map units (centiMorgans, cM) distance between genes.

  • Classic problem types: two linked genes with a dihybrid parent produce a majority of parental phenotypes and a minority of recombinants in the offspring; chi-squared can test whether observed proportions fit expected linkage patterns.

  • Example (Drosophila/ linked gene cross): test crosses yield 8:8:1:1 phenotypic ratios under certain linkage configurations; analysis requires identifying parental and recombinant combinations and using chi-squared to support linkage vs independent assortment.


10) Polygenic Traits and Environmental Influence (Continued)

  • Fast Plants (Brassica): demonstrates rapid generation time and utility in teaching polygenic traits and selection.

    • Observed F2 phenotypes after two crosses included: purple stems with green leaves, purple stems with yellow leaves, white stems with green leaves, white stems with yellow leaves.

    • Expected dihybrid ratio under independent assortment would be 9:3:3:1 for two unlinked genes.

    • Observed counts led to chi-squared testing to see if deviation from expectation is due to chance.

  • The discussion highlights the value of model organisms with rapid generation times, enabling quick cycles of crossing and selection for desired traits.


11) Plant and Animal Genetics: Worked Examples and Key Takeaways

  • Maize (corn) dihybrid crosses (texture and color) illustrate classic dihybrid inheritance with a 9:3:3:1 expectation under normal dihybrid cross.

    • Observed F2 results can be analyzed for linkage or epistasis by mapping phenotypes to genotypes and applying chi-squared tests.

  • Labrador coat color (two unlinked genes with epistasis) illustrates how dominant and recessive alleles in separate loci interact to produce multiple phenotypes (yellow, black, brown) with specific genotype requirements.

  • Dihybrid and test-cross problems in Drosophila demonstrate X-linked inheritance and the usefulness of test crosses to reveal linkage and gene order.

  • In many examples, the correct answer requires:

    • Identifying whether genes are linked or unlinked

    • Recognizing epistasis patterns (dominant, recessive, duplicate)

    • Translating between genotype and phenotype in multi-gene interactions

    • Applying chi-squared tests to support or refute hypotheses about linkage and interaction


12) Quick Reference: Common Ratios and Concepts

  • Independent assortment (unlinked genes):

    • Dihybrid cross (AaBb) yields F2 phenotype ratio 9:3:3:19:3:3:1 under complete dominance.

  • Epistasis patterns and typical ratios:

    • Dominant epistasis: 12:3:112:3:1

    • Recessive epistasis: 9:3:49:3:4

    • Duplicate recessive epistasis: 9:79:7

    • Duplicate dominant epistasis: 15:115:1

  • Sex-linked inheritance: males & females can show different patterns; X-linked recessive traits frequently affect males more due to having a single X chromosome.

  • Polygenic traits: continuous variation caused by multiple genes plus environmental factors; example: leaf length in hybrid coffee plants and plant height in peas.

  • Linkage and recombination: RF between genes determines map distance; lower RF → closer linkage; higher RF → farther apart.

  • Chi-squared basics: extdf=ext(numberofphenotypicclasses)1ext{df} = ext{(number of phenotypic classes)} - 1; compare to critical values to decide significance.


13) Selected Problem Variants (Summary of Key Points from Transcript)

  • Page 1: Unlinked four loci: abcd probability in gametes = rac116rac{1}{16}.

  • Page 2: Hair-color gene alleles in dogs: 4 genotypes, 3 phenotypes; white dominant to sable and copper; sable dominant to copper; cross yields specific genotype-phenotype mapping.

  • Page 3: Sex determination in birds (ZW); lethal Z-linked allele calculations; color blindness X-linked inheritance and 50% female risk if baby is a girl when the mother is a carrier.

  • Page 4-6: Pedigree interpretation for autosomal vs sex-linked; autosomal dominant vs recessive evidence; hypophosphatemia pedigree indicates autosomal recessive pattern; I-1 and I-2 genotypes discussed.

  • Page 7-8: Epistasis in mice coat color; epistatic interactions for pigment (dd morphs lead to white); codominance/epistasis in plant coloration; cotyledon color examples.

  • Page 9-11: Drosophila and coffee leaf data; chi-squared calculations; interpretation of continuous vs discontinuous variation; concept of epistasis in maize and labrador retrievers.

  • Page 12-13: Labrador coat color cross: two genes (E/e and B/b) with epistasis; dihybrid cross; progeny phenotypes with ratios; epistasis explanation.

  • Page 14-15: Maize dihybrid results and chi-squared test; F2 phenotypic ratio; concluding normal dihybrid inheritance in a chi-squared context.

  • Page 16-18: Morgan’s crosses for X-linked eye color in Drosophila; creation of cross tables; male/female progeny expectations; instructions for completing cross tables.

  • Page 19-20: Honey bees behavior controlled by genes A/a and B/b; offspring phenotypes under different parental genotypes; selection to fix traits in workers; diet/environment in bees for queen vs worker development.

  • Page 21-22: Fast Plants (Brassica) data; chi-squared interpretation; discussion of continuous vs discontinuous variation and selection implications; epistasis in F2 (
    9:3:4 example).

  • Page 23-25: Mice and epistasis problems; inheritance of fur color and cross outcomes, including test crosses and ratios.

  • Page 26-27: Tobacco corolla tube length (continuous variation); discussion of polygenic inheritance and experimental design; chi-squared interpretation.

  • Page 28-29: Drosophila test crosses with linkage and recombination; explanation of parental vs recombinant outcomes; mapping and cross diagrams.

  • Page 30-31: Dihybrid and independent assortment explanation via pea genetics (R/r and A/a); scenario where two loci independently assort to produce a 9:3:3:1 ratio; height in peas and the effect of the T/t allele on gibberellin synthesis; heterozygous Tt shows same phenotype as TT due to functional enzyme production.

  • Page 32-33: ABO blood typing system with IA, IB, i alleles; Rh factor genetics (Rh+ and Rh-); independence of ABO and Rh loci; di- and tri-allelic inheritance; cross examples with Type A Rh+ x Type B Rh+ yielding type O Rh- offspring under certain scenarios; genetic-diagram practice.

  • Page 34-35: Epistasis in pea flowers (9:7 ratio for duplicate recessive epistasis); F2 phenotypes and linking genotype to phenotype; chi-squared interpretation for epistasis; discussion of pea plant strengths for genetic studies.

  • Page 36-38: Tobacco continuous variation; locus definition; test cross data for linkage; definition of linkage; use of test crosses to deduce linkage vs independent assortment.

  • Page 39-41: Drosophila gene mapping with test crosses; multiple tables showing parental vs recombinant gametes and phenotypes; steps to determine gene order and map distances via recombinant frequency.

  • Page 42-45: Fruiting flies cross data; chi-squared test utility; vestigial wing and ebony body as a mutational event; recessive mutations and why they are less likely to be found in natural populations.

  • Page 46-50: Haemophilia in Queen Victoria’s family; genetic pedigree exercises; epistasis and X-linked inheritance in human pedigrees; chicken comb genetics and Bateson/Punnett demonstration of gene interaction (epistasis in comb types); walnut vs rose vs pea vs single combs; mapping and cross diagrams; two- and multi-gene interaction demonstrations.


14) Practical Takeaways for Exam Preparation

  • Always identify whether genes are unlinked or linked when interpreting ratios and crosses.

  • Map gene interactions by writing down genotype-to-phenotype relationships, then derive expected phenotypic ratios for F2 under the given interaction (dominant/recessive/duplicate epistasis).

  • Use chi-squared tests to assess fit to expected Mendelian ratios and to justify conclusions about linkage and epistasis.

  • For sex-linked traits, remember that males are XY and females XX in many organisms (e.g., Drosophila), and cross outcomes often show different patterns for sons vs daughters.

  • Distinguish continuous vs discontinuous variation. Continuous variation indicates polygenic inheritance with environmental influence; discontinuous variation suggests monogenic or oligogenic controls.

  • For plant/j breeding problems (maize, peas, tobacco, fast plants), map genotypes to phenotypes carefully, and consider linkage, epistasis, and environmental effects when interpreting data.

  • Practice constructing and interpreting Punnett squares, dihybrid/tri-hybrid crosses, test crosses, and pedigree analyses as standard exam patterns.


Appendix: Notation Quick-Reference

  • Alleles: uppercase for dominant (e.g., A, B, E, R) and lowercase for recessive (a, b, e, r).

  • Epistasis notation conventions in explanations often label dominant epistatic allele as E (or A) and recessive epistatic allele as e (or a), with hypostatic alleles for the visible trait as e.g., B/b or R/r depending on the example.

  • Common genotype-phenotype mappings in epistasis problems:

    • Recessive epistasis: aa masks whether B/b is present (e.g., 9:3:4).

    • Dominant epistasis: presence of A- masks B/b effects (e.g., 12:3:1).

    • Duplicate recessive epistasis: aa or bb yields the same phenotype; often 9:7.

    • Duplicate dominant epistasis: A- or B- each can produce the same phenotype; only aabb yields another phenotype (often 15:1).

  • Quick problem-solving reminders:

    • If a problem involves linked genes, first identify parental types and recombinants, then decide whether to apply a linkage-based ratio or a 9:3:3:1 expectation.

    • In sex-linked problems, draw X and Y chromosomes explicitly, and track paternal and maternal alleles across generations.

    • In chi-squared problems, list observed and expected counts for all phenotype/genotype classes, compute chi-squared, and compare with the appropriate critical value for the given df.

If you’d like, I can tailor these notes to a specific sub-topic (e.g., epistasis, linkage, or chi-squared calculations) and expand the corresponding sections with more worked examples and step-by-step solutions.