Mendelian inheritance: gene interaction and pedigree analysis

In short

Mendelian inheritance explains how discrete hereditary factors (genes) segregate and recombine across generations, giving the predictable ratios Mendel found in *Pisum sativum*. Gene interaction covers the many real cases that deviate from the clean 3:1 and 9:3:3:1 — incomplete dominance, codominance, multiple alleles, epistasis, lethals, modifiers, penetrance — while pedigree analysis applies the same laws backwards, from a family tree to a mode of inheritance and a recurrence risk. It is the single most examined block in B.Sc. Genetics, and is asked in CSIR-UGC NET, GATE BT/XL, ICMR-JRF, DBT-BET and ICAR exams, and in interviews for genetic counselling, clinical laboratory, seed company breeding and bioinformatics variant-curation roles. Indian relevance is direct: high rates of consanguineous marriage in parts of south India raise autosomal recessive disease frequency, and ABO/Rh typing under NBTC blood-bank practice is everyday Mendelian genetics.

Explained

Mendel's laws and the basic crosses

• Mendel's experiments (1856-63, published 1866): seven pairs of contrasting characters in garden pea — seed shape (round/wrinkled), cotyledon colour (yellow/green), flower colour, pod shape, pod colour, flower position, stem height.
• Law of dominance: of a contrasting pair of alleles, one expresses in the F1 heterozygote and masks the other. Not universal (see incomplete dominance).
• Law of segregation (purity of gametes): the two alleles of a gene separate during gamete formation, each gamete receiving one. Physical basis: anaphase I of meiosis. This law is universally true.
• Law of independent assortment: alleles of different genes assort independently of one another. Valid only for genes on different chromosomes, or far apart on the same chromosome (linkage is the exception).
• Monohybrid cross: TT × tt → F1 all Tt (tall) → F2 phenotypic 3 tall : 1 dwarf, genotypic 1 TT : 2 Tt : 1 tt.
• Dihybrid cross: RRYY × rryy → F1 RrYy → F2 9 round-yellow : 3 round-green : 3 wrinkled-yellow : 1 wrinkled-green; 4 phenotypes, 9 genotypes, 16 zygotic combinations.
• Test cross: cross the unknown with the homozygous recessive to reveal its genotype — Tt × tt gives 1:1, TT × tt gives all tall. Used routinely by breeders to detect carriers.
• Back cross: cross F1 back to either parent; a test cross is the special back cross to the recessive parent.
• Reciprocal cross: parents' sexes swapped. Identical results indicate autosomal nuclear inheritance; different results suggest sex linkage or maternal/organelle inheritance.
• Trihybrid and n-hybrid: F2 phenotypic ratio is (3:1)ⁿ expanded; number of gamete types from a heterozygote = 2^n.

Deviations from dominance: intra-allelic interactions

• Incomplete (partial) dominance: heterozygote is intermediate. *Antirrhinum majus* (snapdragon) red RR × white rr → pink Rr; F2 1 red : 2 pink : 1 white — phenotypic ratio equals genotypic ratio. Also *Mirabilis jalapa* (4 o'clock plant).
• Codominance: both alleles express fully and separately in the heterozygote — MN blood group (L^M L^N gives both M and N antigens); roan coat in Shorthorn cattle; AB blood group; HbAS sickle-cell trait at the protein level (both HbA and HbS bands on electrophoresis).
• Multiple alleles: more than two alleles of one gene in a population, though any diploid carries only two. Number of genotypes with n alleles = n(n+1)/2.
  • ABO system (gene *ABO*, chromosome 9q34): alleles I^A, I^B, i. I^A and I^B are codominant; both dominant to i. 4 phenotypes, 6 genotypes.
  • Rh system: *RHD*/*RHCE* on chromosome 1; D antigen present (Rh+) is dominant.
  • Coat colour series in rabbits (C > c^ch > c^h > c), eye colour alleles in *Drosophila*.
• Bombay phenotype (O_h): discovered by Bhende and colleagues in Mumbai, 1952 — a homozygous non-functional *FUT1* (H) gene means no H precursor, so an individual genetically I^A or I^B types as O. Classic Indian example and a favourite exam question; it is both a multiple-allele and an epistasis illustration (recessive epistasis of *hh* over *ABO*).
• Lethal alleles: cause death of a genotypic class, distorting ratios.
  • Dominant lethal in homozygous condition: yellow coat in mice (A^Y), creeper fowl, *Manx* cat — Aa × Aa → 2 yellow : 1 agouti (2:1), the AA class dying in utero.
  • Recessive lethal: sickle-cell anaemia, Tay-Sachs, thalassaemia major — carrier × carrier gives 1:2:1 at conception, 2:1 among survivors.
  • Conditional/sub-lethal, semi-lethal: survival depends on environment or reduces viability only partly.
• Pleiotropy: one gene affects several unrelated traits — sickle-cell *HBB* affects RBC shape, pain crises, splenic function, malaria resistance; phenylketonuria affects IQ, pigmentation, urine odour. Mendel's own case: pea flower colour, seed-coat spots and axil pigment are one gene.

Gene interaction between loci: epistasis

Epistasis = one gene (epistatic) masks or modifies the expression of a non-allelic gene (hypostatic). Dihybrid F2 ratios depart from 9:3:3:1 while remaining in sixteenths.

• Why the sixteenths persist: the two loci still assort independently; epistasis changes only how the 16 genotypes are grouped into phenotypes. This is the key conceptual answer in vivas.
• Epistasis vs dominance: dominance is interaction between alleles of the same gene; epistasis is between alleles of different genes.
• Epistasis vs linkage: epistasis alters F2 phenotypic proportions but keeps totals in sixteenths; linkage alters the gamete proportions themselves, giving excess parental types in a test cross.
• Biochemical basis: most epistasis is a metabolic pathway — precursor → intermediate (gene A) → product (gene B). A block upstream masks the downstream step, which is why complementary action gives 9:7.

Modifiers, penetrance, expressivity and polygenes

• Modifying genes: do not produce the trait but alter its degree — spotting in cattle, severity modifiers in thalassaemia.
• Penetrance: proportion of individuals of a given genotype showing the phenotype at all. *Complete* (100%) or *incomplete* — e.g. retinoblastoma *RB1* mutations show ~90% penetrance; polydactyly often incomplete. Non-penetrance causes a pedigree to "skip" without being recessive.
• Expressivity: degree to which the phenotype is expressed in those who show it — variable expressivity in neurofibromatosis type 1 within a single family.
• Phenocopy: environmentally produced trait mimicking a genotype (thalidomide limb defects mimicking phocomelia); it does not transmit.
• Polygenic (quantitative) inheritance: several genes with small, additive effects plus environment — human height, skin colour, grain yield, milk yield. Nilsson-Ehle's wheat kernel colour: two loci → 1:4:6:4:1 (five classes); three loci → 1:6:15:20:15:6:1. Number of F2 classes = 2n+1; proportion of F2 like either extreme parent = (1/4)^n.
• Multiple-factor vs multiple-allele: polygenes are different loci acting on one trait; multiple alleles are many alleles at one locus.
• Mendelian vs non-Mendelian: maternal (cytoplasmic/mitochondrial) inheritance, genomic imprinting (Prader-Willi/Angelman), trinucleotide repeat expansion with anticipation (Huntington, myotonic dystrophy), mosaicism — all give pedigrees that break Mendelian rules.

Pedigree analysis: symbols, modes and risk

• Symbols: square = male, circle = female, diamond = unknown sex; filled = affected; horizontal line = mating, double horizontal line = consanguineous mating; vertical line to sibship, siblings in birth order left to right; diagonal slash = deceased; a dot inside = carrier; arrow (proband/index case) = the individual through whom the family was found. Generations in Roman numerals (I, II, III), individuals in Arabic numerals.
• Autosomal dominant (AD): every affected has an affected parent (no skipping unless non-penetrance); males and females equally affected; affected × normal → ~50% affected; vertical transmission. Examples: achondroplasia, Huntington disease, Marfan syndrome, familial hypercholesterolaemia, polydactyly, myotonic dystrophy.
• Autosomal recessive (AR): trait skips generations; parents usually unaffected carriers; ~25% of sibs affected; sexes equally affected; consanguinity common in the pedigree. Examples: sickle-cell anaemia, beta-thalassaemia, cystic fibrosis, albinism, PKU, Tay-Sachs, Wilson disease.
• X-linked recessive (XR): mostly males affected; no male-to-male transmission; an affected male's daughters are all carriers; carrier mother → 50% of sons affected; criss-cross inheritance (grandfather to grandson via carrier daughter). Examples: haemophilia A and B, Duchenne muscular dystrophy, red-green colour blindness, G6PD deficiency.
• X-linked dominant (XD): affected father → all daughters affected, no sons; females affected about twice as often and often more mildly (X-inactivation). Examples: hypophosphataemic (vitamin-D-resistant) rickets, incontinentia pigmenti (male-lethal).
• Y-linked (holandric): father to all sons only — e.g. *SRY*-related sex determination, some spermatogenic failure loci.
• Mitochondrial: affected mother transmits to all children; affected father transmits to none; heteroplasmy gives variable severity — MELAS, LHON.
• Working method in an exam: (1) note sexes of affected; (2) check for skipping; (3) check male-to-male transmission; (4) check consanguinity loops; (5) assign the most restrictive consistent mode; (6) assign genotypes to every individual (use A/a notation, '?' where ambiguous); (7) compute the asked risk by multiplying the independent probabilities along the path.
• Carrier frequency shortcut (Hardy-Weinberg): if disease incidence q² is known, q = √(q²) and carrier frequency 2pq ≈ 2q. Useful for population risk questions.
• Indian clinical context: genetic counselling and prenatal diagnosis operate under the Pre-conception and Pre-natal Diagnostic Techniques (PCPNDT) Act, 1994 (as amended) — prenatal diagnosis is permitted for listed genetic/chromosomal indications but disclosure of fetal sex is prohibited; registration of the genetic counselling centre, clinic and laboratory with the Appropriate Authority and Form F records are mandatory. The Medical Termination of Pregnancy Act (as amended in 2021) allows termination up to 24 weeks for specified categories and, with a Medical Board's opinion, beyond that for substantial fetal abnormality. Haemoglobinopathy screening is run under the National Health Mission's programme for prevention and control of haemoglobinopathies (sickle-cell disease elimination is a stated national mission with a 2047 horizon); operational details vary by state, so check the current state guideline before quoting numbers.

Testing goodness of fit — the chi-square test

• Observed ratios in real crosses deviate by sampling error; the chi-square (χ²) test judges whether deviation is chance or a real departure (linkage, epistasis, lethality, differential viability).
• Degrees of freedom = number of phenotypic classes − 1. Critical χ² at p = 0.05: 3.84 (df 1), 5.99 (df 2), 7.81 (df 3), 9.49 (df 4).
• χ² less than the critical value → deviation not significant → the hypothesised ratio is accepted. The test never "proves" the hypothesis; it only fails to reject it.

Key points

• Allele - alternative form of a gene at one locus; locus - its physical position on the chromosome.
• Genotype vs phenotype - genetic constitution vs observable expression; phenotype = genotype + environment.
• Homozygous/heterozygous/hemizygous - identical alleles / different alleles / a single copy (X-linked genes in males).
• Law of segregation - universally valid; independent assortment - valid only for unlinked genes.
• Test cross - cross with homozygous recessive; the only reliable way to expose a heterozygote.
• Incomplete dominance - 1:2:1 in F2, phenotypic = genotypic ratio, heterozygote intermediate.
• Codominance - both alleles expressed, heterozygote shows both products (AB blood group, MN, roan).
• Multiple alleles - n alleles give n(n+1)/2 genotypes; ABO gives 6 genotypes, 4 phenotypes.
• Bombay phenotype - *hh* blocks H antigen, so an I^A/I^B individual types as O; reported from Mumbai in 1952.
• Epistasis - inter-gene masking; ratios 9:7, 9:3:4, 12:3:1, 13:3, 15:1, 9:6:1 — all still in sixteenths.
• Complementary genes (9:7) - two dominants needed together; the biochemical pathway explanation.
• Lethal genes - distort ratios; homozygous dominant lethal gives 2:1 instead of 3:1.
• Pleiotropy - one gene, many traits (sickle cell, PKU); opposite of polygeny.
• Penetrance vs expressivity - whether the phenotype appears at all vs how strongly it appears.
• Polygenic inheritance - 2n+1 F2 classes; extreme parental class = (1/4)ⁿ of F2.
• Pedigree rules - AR skips and loves consanguinity; AD is vertical; XR has no male-to-male transmission; XD affected father gives all daughters affected; mitochondrial is maternal only.
• Chi-square - tests goodness of fit; df = classes − 1; reject the ratio if χ² exceeds 3.84 (df 1) at p = 0.05.
• PCPNDT Act, 1994 - governs prenatal diagnosis in India; sex disclosure is prohibited.

Formulas and examples

Example 1 — Dihybrid cross with chi-square. A pea cross RrYy × RrYy gives 556 seeds: 315 round-yellow, 108 round-green, 101 wrinkled-yellow, 32 wrinkled-green. Test the 9:3:3:1 hypothesis.

• Expected: 556 × 9/16 = 312.75; × 3/16 = 104.25 (each); × 1/16 = 34.75.
• Deviations: +2.25, +3.75, −3.25, −2.75.
• χ² terms: 2.25²/312.75 = 5.0625/312.75 = 0.0162; 3.75²/104.25 = 14.0625/104.25 = 0.1349; 3.25²/104.25 = 10.5625/104.25 = 0.1013; 2.75²/34.75 = 7.5625/34.75 = 0.2176.
• χ² = 0.0162 + 0.1349 + 0.1013 + 0.2176 = 0.47; df = 4 − 1 = 3; critical value 7.81.
• 0.47 < 7.81 → deviation is not significant; the data fit 9:3:3:1. (These are Mendel's own figures.)

Example 2 — Lethal gene, 2:1 ratio. Yellow mice (A^Y a) are crossed together and 180 live pups are born.

• Zygotic ratio 1 A^YAY : 2 A^Ya : 1 aa, but A^YAY dies before birth.
• Survivors = 3/4 of zygotes, in the ratio 2 yellow : 1 agouti → yellow = 180 × 2/3 = 120, agouti = 180 × 1/3 = 60.
• Total zygotes conceived = 180 × 4/3 = 240, so 60 embryos died.

Example 3 — ABO and the Bombay phenotype. A woman of blood group O marries a group AB man; their first child is group O. Is it possible, and what are the possibilities for the next child?

• Normal ABO: I^A I^B × ii → children are I^A i (A) or I^B i (B) in 1:1 — a group O child is impossible.
• Explanation: the mother is Bombay phenotype, genotype say I^A i hh (or I^B i hh) — she lacks H antigen and types as O.
• If she is I^A i hh and the father is I^A I^B HH, children are all H h (H antigen present) and ABO genotypes I^A I^A, I^A I^B, I^A i, I^B i in 1:1:1:1 → phenotypes A : AB : A : B = 2 A : 1 AB : 1 B, i.e. 50% A, 25% AB, 25% B, with no further O.
• Lesson for a blood bank: a Bombay-phenotype patient's serum contains anti-H and reacts with ordinary O cells, so only Bombay-phenotype blood can be transfused — India maintains rare-donor registries for this.

Example 4 — Pedigree risk, autosomal recessive. A phenotypically normal couple have an albino child. What is the chance their next child is (a) albino, (b) a normal carrier, (c) that two of their next three children are albino?

• Both parents must be Aa (each had to give an 'a'). Offspring: 1 AA : 2 Aa : 1 aa.
• (a) P(albino) = 1/4 = 0.25.
• (b) P(carrier) = 2/4 = 1/2; but P(carrier *given* normal appearance) = (2/4)/(3/4) = 2/3.
• (c) Binomial with N = 3, r = 2, p = 1/4, q = 3/4: [3!/(2!1!)] × (1/4)² × (3/4) = 3 × 0.0625 × 0.75 = 0.1406 ≈ 14.1%.

Example 5 — X-linked recessive, carrier risk. A woman's maternal uncle has haemophilia A; her mother and grandmother are normal and no one else is affected. What is the chance her son is a haemophiliac?

• The affected uncle's mother (the grandmother) must be a carrier, X^H X^h.
• P(the woman's mother is a carrier) = 1/2.
• P(the woman inherited X^h | mother carrier) = 1/2 → P(woman is a carrier) = 1/2 × 1/2 = 1/4.
• P(her son is affected) = 1/4 × 1/2 = 1/8 = 12.5%.
• If a factor VIII assay or molecular carrier test clears her mother, the risk falls to near zero — this is how counselling uses laboratory data to collapse pedigree probabilities.

Example 6 — Epistasis identification. An F2 from a sweet-pea cross gives 272 purple and 208 white flowers (total 480). Which interaction?

• Test 9:7 → expected purple = 480 × 9/16 = 270, white = 480 × 7/16 = 210.
• χ² = (272−270)²/270 + (208−210)²/210 = 4/270 + 4/210 = 0.0148 + 0.0190 = 0.034; df = 1, critical 3.84 → fits.
• Conclusion: complementary (duplicate recessive) epistasis — both dominant C and P are required for pigment; CCpp × ccPP gives a purple F1 and 9:7 in F2.

Where it is used

• Clinical genetics and counselling: recurrence-risk calculation, carrier screening and prenatal/newborn diagnosis at centres such as AIIMS, PGIMER, CMC Vellore, SGPGI, NIMHANS and private labs (Medgenome, Lal PathLabs, Metropolis, Strand) — all operating within the PCPNDT Act framework.
• Blood banking and transfusion medicine: ABO/Rh grouping, antibody screening, rare-donor registries for Bombay phenotype; practice governed by Drugs and Cosmetics licensing and NBTC/state blood transfusion council guidelines, with NABH/NABL accreditation of labs.
• Plant and animal breeding: test crosses to detect carriers, epistasis in flower/grain colour, polygenic selection for yield — ICAR institutes (IARI, IIRR, IIHR), NDRI for cattle, and seed companies (Nuziveedu, Rasi, Mahyco, Bayer, Syngenta, Kaveri).
• Haemoglobinopathy control programmes: sickle-cell and thalassaemia carrier screening in Gujarat, Maharashtra, Madhya Pradesh, Odisha and the tribal districts; counselling of carrier couples is pure autosomal recessive arithmetic.
• Bioinformatics and variant curation: ACMG/AMP-style variant classification needs segregation evidence from pedigrees, de-novo status, penetrance estimates and mode of inheritance — roles at Medgenome, Strand Life Sciences, Mapmygenome, Eurofins, and in NIBMG/DBT research projects.
• Forensic and disputed-parentage work: ABO exclusion logic (now superseded by STR profiling) and Mendelian exclusion principles used by state Forensic Science Laboratories and CDFD Hyderabad.

Interview questions

• Q: Which of Mendel's laws is universally true and which has exceptions? A: Segregation is universal because it follows meiotic anaphase I; independent assortment fails for linked genes on the same chromosome, and dominance fails in incomplete dominance and codominance.
• Q: Why did Mendel succeed when earlier hybridisers did not? A: He chose a self-pollinating plant with true-breeding lines and sharply contrasting discrete characters, followed one or two traits at a time over several generations, and counted large numbers, analysing them mathematically.
• Q: Difference between incomplete dominance and codominance? A: In incomplete dominance the heterozygote is a blended intermediate because the single functional allele makes insufficient product; in codominance both allelic products are made and detectable separately, as in AB blood group.
• Q: What is the difference between dominance and epistasis? A: Dominance is interaction between alleles at the same locus; epistasis is one locus masking the expression of a different locus.
• Q: Why do epistatic F2 ratios still add up to 16? A: The two loci still assort independently, so the 16 genotypic combinations remain; epistasis only regroups them into fewer phenotypic classes.
• Q: A cross gives a 9:7 F2. What does it tell you? A: Complementary or duplicate-recessive epistasis — dominant alleles of both genes are needed for the phenotype, so all nine double-dominant classes are one phenotype and the remaining seven look alike.
• Q: How can a child of blood group O be born to an AB parent? A: If the other parent is Bombay phenotype (*hh*), lacking the H precursor; the child can also be O-typing Bombay, or an extremely rare cis-AB or chimerism can explain it.
• Q: Why does a dominant lethal allele give a 2:1 ratio instead of 3:1? A: The homozygous dominant class dies before scoring, leaving the heterozygotes and homozygous recessives in a 2:1 ratio among survivors.
• Q: A pedigree shows an affected father and all his daughters affected but no son affected. Which mode? A: X-linked dominant — the father passes his only X to every daughter and his Y to every son.
• Q: Why is consanguinity a clue to autosomal recessive inheritance? A: Related parents are more likely to share a rare recessive allele inherited from a common ancestor, raising the chance of a homozygous affected child.
• Q: A dominant trait appears to skip a generation. Explain without abandoning dominance. A: Incomplete penetrance (or very mild expressivity, or germline mosaicism) — the carrier is genotypically affected but shows no detectable phenotype.
• Q: Difference between pleiotropy and polygenic inheritance? A: Pleiotropy is one gene affecting many traits; polygenic inheritance is many genes each contributing a small additive effect to one trait.
• Q: How do you decide whether a deviation from 3:1 is significant? A: Apply a chi-square test on observed and expected counts with df = classes − 1; for df = 1 a χ² above 3.84 rejects the ratio at p = 0.05.
• Q: What does the proband arrow mean in a pedigree? A: It marks the index case — the affected individual through whom the family came to clinical attention, and the starting point for the family history.

Common mistakes

• Using percentages or ratios instead of actual counts in the chi-square formula, and taking df as the number of classes rather than classes − 1.
• Confusing a test cross (with the homozygous recessive) with a back cross (with either parent) or with an F1 self-cross.
• Writing the F2 of incomplete dominance as 3:1 — it is 1:2:1, with phenotypic equal to genotypic ratio.
• Quoting the carrier risk of a phenotypically normal sib of an affected child as 1/2 instead of 2/3 (the 1/4 affected class is excluded by observation).
• Treating epistasis as linkage: both distort ratios, but epistasis keeps the total in sixteenths whereas linkage produces excess parental classes in a test cross.
• Claiming male-to-male transmission for an X-linked trait, or forgetting that an affected male's daughters are all obligate carriers in X-linked recessive disease.
• Mixing up pleiotropy with polygeny, and multiple alleles (one locus) with multiple factors (several loci).
• Forgetting that each child is an independent event — three normal children do not reduce the risk for the fourth below 1/4.

Related topics

Chromosomes, linkage and gene mapping · Cytogenetics and chromosomal disorders · Population genetics and Hardy-Weinberg equilibrium · Molecular basis of inheritance and gene expression · Human molecular genetics and genetic counselling · Quantitative genetics and plant breeding