IMAT Biology · Formula sheet

Genetics and Inheritance formulas

13 formulas, 7 reference tables and 22 common traps for IMAT Biology Genetics and Inheritance, grouped by subtopic.

Genes, Alleles, Mendel's Laws and Mutations

Gene, allele, genotype and phenotype: the core vocabulary

Term	Meaning	Example
Gene	A DNA sequence coding for a product, at a fixed locus	The gene for pea plant height
Allele	One alternative form of a gene	$T$ (tall) and $t$ (dwarf)
Genotype	The two alleles an individual carries	$TT$ , $Tt$ or $tt$
Phenotype	The trait that is seen or measured	Tall or dwarf
Homozygous	Both alleles the same	$TT$ or $tt$
Heterozygous	Two different alleles	$Tt$ , which is tall
Dominant allele	Expressed even when only one copy is present	$T$ in a $Tt$ plant In a heterozygote, only the dominant allele is certain to show in the phenotype.
Recessive allele	Expressed only when two copies are present	$t$ , seen only in $tt$

By convention the dominant allele takes a capital letter and the recessive allele the same letter in lower case.

Mendel's laws and the chromosomal theory of inheritance

Law or idea	What it says	Explained in meiosis by
Segregation	Each gamete gets one allele of each gene	Homologous chromosomes separating in anaphase I
Independent assortment	Alleles of different genes are sorted into gametes independently	Random orientation of homologous pairs at the equator in metaphase I
Dominance	The dominant allele masks the recessive one in a heterozygote	Not a meiosis event: it is about gene expression
Chromosomal theory	Genes are carried on chromosomes	Chromosomes and alleles both come in pairs and both segregate in meiosis

Independent assortment fails for genes close together on the same chromosome: they are linked.

Mutations: changes in the genetic information, and sickle-cell anaemia

Type	What changes	Typical effect
Silent substitution	One base, but the codon still codes the same amino acid	No change in the protein
Missense substitution	One base, giving a different amino acid	One amino acid changed (sickle-cell haemoglobin)
Nonsense substitution	One base, giving a stop codon	A shortened, usually useless protein
Frameshift	One or two bases inserted or deleted	Every amino acid after the change can be different
Chromosome mutation	Chromosome structure or number	Many genes affected (e.g. trisomy 21)

Common traps

Genes are shared; alleles differ

All humans carry the same genes (a gene for eye colour, a gene for blood group). What differs between two people, even siblings, is which alleles of those genes they carry. Options that say siblings or twins have "different genes" are wrong; "different alleles" is right for non-identical twins.

Dominant does not mean common or stronger

Dominance only describes what shows in a heterozygote. A dominant allele can be rare in a population (the allele for Huntington's disease is dominant and rare), and a recessive allele can be very common.

Natural selection is not one of Mendel's laws

A statement such as "individuals with useful traits survive and reproduce more" is Darwin's natural selection. Mendel's laws are segregation, independent assortment and dominance. Exam lists of statements often mix the two.

Sickle-cell haemoglobin still carries oxygen

HbS differs from normal haemoglobin by one amino acid in each

\beta

chain, which changes its structure. It still binds and transports oxygen. The problem is that deoxygenated HbS forms long fibres that bend red cells into sickles, which block capillaries and are destroyed early.

Punnett Squares, Probability, Test Crosses and Dihybrid Crosses

Learn this subtopic in the notes

Monohybrid crosses and the Punnett square

Cross of two heterozygotes

Aa \times Aa \rightarrow \tfrac{1}{4}\,AA + \tfrac{1}{2}\,Aa + \tfrac{1}{4}\,aa

$A$ dominant allele
$a$ recessive allele

Probability rules for crosses: multiply for AND, add for OR

Product and sum rules

P(A \cap B) = P(A)\,P(B) \qquad P(A \cup B) = P(A) + P(B)

$P(A \cap B)$ probability that A and B both happen (independent events)
$P(A \cup B)$ probability that A or B happens (events that exclude each other)

The test cross: revealing an unknown genotype

Test cross outcomes

AA \times aa \rightarrow \text{all } Aa \qquad Aa \times aa \rightarrow \tfrac12\,Aa + \tfrac12\,aa

$aa$ the homozygous recessive tester

Dihybrid crosses: the 9 : 3 : 3 : 1 ratio and the branch method

Branch method for independent genes

P(\text{combined}) = P(\text{gene 1 outcome}) \times P(\text{gene 2 outcome}) \times \dots

$\tfrac34, \tfrac14$ dominant and recessive phenotype from $Aa \times Aa$
$\tfrac12, \tfrac12$ dominant and recessive phenotype from $Aa \times aa$

Common traps

A 3 : 1 ratio is a probability, not a rule for each family

Two carriers with four children will not always have exactly one affected child. Each child independently has a

\tfrac14

chance. The ratio appears only in large numbers of offspring.

Earlier children do not change the odds

If two carriers already have an affected child, the next child still has exactly a

\tfrac14

chance of being affected. Each fertilisation is a new, independent event. Options that lower or raise the chance because of previous children are wrong.

"An affected boy" is not "a boy who is affected"

"The next child is an affected boy" multiplies by

\tfrac12

for the sex. "If the next child is a boy, is he affected?" does not, because the sex is already given. Read which one the question asks before multiplying.

Sixteen boxes are not sixteen genotypes

The

AaBb \times AaBb

square has 16 boxes, but several boxes share a genotype: there are 9 genotypes and, with complete dominance, 4 phenotypes. Answers of 16 count boxes, not genotypes or phenotypes.

9 : 3 : 3 : 1 needs both conditions

The ratio appears only when both parents are heterozygous for both genes AND the genes assort independently. Linked genes, or a parent homozygous for one gene, give a different ratio.

Incomplete Dominance, Codominance, Blood Groups and Polygenes

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Incomplete dominance and codominance

Heterozygote cross without dominance

C^R C^W \times C^R C^W \rightarrow 1\ \text{red} : 2\ \text{intermediate} : 1\ \text{white}

$C^R, C^W$ two alleles, neither dominant (superscripts are used instead of capital and small letters)

Polygenic inheritance and continuous variation

Phenotype classes for n additive genes

\text{classes} = 2n + 1

$n$ number of genes, each with one contributing and one non-contributing allele

Multiple alleles: the ABO and Rh blood groups

Blood group	Genotypes	Antigen on red cells	Antibodies in plasma
A	$I^A I^A$ or $I^A i$	A	Anti-B
B	$I^B I^B$ or $I^B i$	B	Anti-A
AB	$I^A I^B$	A and B	Neither anti-A nor anti-B
O	$i\,i$	Neither A nor B	Anti-A and anti-B
Rh negative	$dd$	No D antigen	Anti-D only after exposure to D

Rh positive is

DD

Dd

, with the D antigen and no anti-D.

Common traps

Incomplete dominance is not blending inheritance

A pink snapdragon looks like a blend, but its alleles stay separate: two pink parents produce red and white offspring again. Blending inheritance (the idea that parental traits mix irreversibly) was disproved by Mendel's work.

An AB parent cannot have a group O child

A group AB parent passes on either

I^A

I^B

, never

i

, so every child has at least one antigen. A family with an AB parent and an O child points to a wrong parentage claim (or a rare mutation), not to normal inheritance.

Antibodies are against the antigens you lack

Group A people have anti-B, not anti-A. Mixing these up reverses every transfusion answer. Group O red cells can go to all ABO groups because they carry no A or B antigen; group AB people can receive all groups because their plasma has neither antibody.

Sex Chromosomes, the SRY Gene and X-linked Inheritance

Learn this subtopic in the notes

X-linked recessive inheritance: haemophilia, colour blindness, Duchenne

Carrier mother and unaffected father

X^H X^h \times X^H Y \rightarrow \tfrac14 X^H X^H + \tfrac14 X^H X^h + \tfrac14 X^H Y + \tfrac14 X^h Y

$X^h$ X chromosome carrying the recessive allele
$Y$ Y chromosome, carrying no allele of this gene

X-linked dominant and Y-linked inheritance

Affected father, X-linked dominant

X^R Y \times X^r X^r \rightarrow \text{daughters all } X^R X^r,\ \text{sons all } X^r Y

$X^R$ X carrying the dominant allele that causes the condition
$X^r$ X carrying the normal recessive allele

Sex determination in humans: XX, XY and the SRY gene

Situation	Sex that develops	Reason
XX	Female	No SRY gene
XY	Male	SRY on the Y starts testis development
XX with SRY moved onto one X	Male	SRY is present, even without a Y
XY with SRY lost or not working	Female	No working SRY
XXY	Male	One Y with SRY is enough

SRY can move onto an X by an abnormal crossover in the father's meiosis, giving an X-bearing sperm that makes a male.

Common traps

It is SRY, not the Y chromosome as a whole, that makes a male

An XX person carrying SRY on one X develops as a male, and an XY person without a working SRY develops as a female. Statements that tie maleness only to "having a Y" miss this.

A father never passes an X-linked allele to his son

Sons receive their father's Y. So an affected son of an unaffected father got the allele from his mother, and an affected father cannot have an affected son through his own X. Any option tracing an X-linked allele from father to son is wrong.

"Half the sons" is not "a quarter of the children"

For a carrier mother and a normal father,

\tfrac12

of the sons are affected, but only

\tfrac14

of all children are affected sons. Women are affected far less often than men, never more often, for a recessive X-linked allele.

An X-linked allele in a boy came from his mother

Whether the X-linked allele is dominant or recessive, a boy's only X came from his mother. If he has an X-linked dominant condition, his mother must carry the allele, and since it is dominant she is affected too. His father is irrelevant to it.

Linkage, Gene Maps, Variation and Non-disjunction

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Linked genes and recombination frequency

Recombination frequency

RF = \frac{\text{number of recombinant offspring}}{\text{total offspring}} \times 100\%

$RF$ recombination frequency (crossover value), in %

Building a gene map from crossover values

Distances add along a chromosome

d(A,B) = d(A,C) + d(C,B) \quad \text{when C lies between A and B}

$d$ map distance, in map units (= % recombination)

Meiosis and fertilisation as sources of genetic variation

Chromosome combinations from independent assortment

\text{gametes} = 2^{n} \qquad \text{zygotes} = 2^{n} \times 2^{n}

$n$ haploid chromosome number (number of homologous pairs)

Non-disjunction and aneuploidy: Down, Turner and Klinefelter syndromes

Condition	Karyotype	Sex	Main features
Down syndrome (trisomy 21)	47, +21	Either	Learning disability, typical facial features, heart defects
Turner syndrome	45, X	Female	Short stature, ovaries do not work, usually infertile
Klinefelter syndrome	47, XXY	Male	Small testes, usually infertile, sometimes breast growth
Triple X	47, XXX	Female	Often no obvious signs; may be tall
XYY	47, XYY	Male	Often no obvious signs; may be tall

An embryo missing a whole autosome almost never survives to birth; 45, X is the only monosomy commonly seen in live births.

Common traps

Crossing over happens inside one parent's meiosis

Crossing over is between the two homologous chromosomes of one person, during prophase I as that person makes gametes. It is never between a chromosome from the sperm and one from the egg at fertilisation, and it does not happen in the zygote's mitotic divisions.

Variation between siblings is made before fertilisation

The differences between a brother and a sister come from each parent's meiosis (random orientation in metaphase I, crossing over in prophase I) and from which sperm meets which egg. Nothing in the zygote's own mitotic divisions reshuffles alleles.

Klinefelter is male, Turner is female

Sex follows the presence of the Y (with SRY), not the number of X chromosomes. XXY is male despite two X chromosomes; X with no second sex chromosome is female.

Pedigree Analysis and Allele Frequencies

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Probabilities from a pedigree, including the two-thirds rule

Chance of an affected child from uncertain carriers

P(\text{affected child}) = P_1 \times P_2 \times \tfrac14

$P_1, P_2$ probability that each parent is a carrier
$\tfrac14$ chance two carriers have an affected child

Allele frequencies and the Hardy-Weinberg principle

Hardy-Weinberg equations

p + q = 1 \qquad p^2 + 2pq + q^2 = 1

$p$ frequency of the dominant allele $A$
$q$ frequency of the recessive allele $a$
$2pq$ frequency of heterozygotes (carriers)

Reading a pedigree: symbols and the five inheritance patterns

Pattern	Typical clues	Proof or key rule
Autosomal recessive	Skips generations; both sexes equally	Two unaffected parents have an affected child
Autosomal dominant	Appears in every generation; both sexes equally	Two affected parents have an unaffected child
X-linked recessive	Mostly males; passed through unaffected carrier mothers	An affected woman's father and all her sons are affected
X-linked dominant	More females than males affected	An affected man has all daughters and no sons affected
Y-linked	Males only	Passed from father to every son

Common traps

An affected boy with unaffected parents fits several patterns

An affected son of two unaffected parents fits autosomal recessive (both parents carriers), X-linked recessive (carrier mother) and a new mutation. It does not fit any dominant pattern, because a dominant allele inherited from a parent would show in that parent.

An unaffected sibling of an affected person is a carrier with 2/3, not 1/2

Of the four equally likely children of two carriers, one is

aa

. If we know the child is unaffected, that box is gone; of the three left (

AA

Aa

aA

), two are carriers. Using

\tfrac12

\tfrac14

here gives one of the wrong options.

Count alleles, not individuals

The frequency of

A

is not the share of people with an

A

. Each

AA

person contributes two copies, each

Aa

one, and the total is twice the number of people. Dividing by the number of people, or counting

AA

once, gives a wrong option.

Genetics and Inheritance formulas

Genes, Alleles, Mendel's Laws and Mutations

Gene, allele, genotype and phenotype: the core vocabulary

Mendel's laws and the chromosomal theory of inheritance

Mutations: changes in the genetic information, and sickle-cell anaemia

Common traps

Punnett Squares, Probability, Test Crosses and Dihybrid Crosses

Monohybrid crosses and the Punnett square

Probability rules for crosses: multiply for AND, add for OR

The test cross: revealing an unknown genotype

Dihybrid crosses: the 9 : 3 : 3 : 1 ratio and the branch method

Common traps

Incomplete Dominance, Codominance, Blood Groups and Polygenes

Incomplete dominance and codominance

Polygenic inheritance and continuous variation

Multiple alleles: the ABO and Rh blood groups

Common traps

Sex Chromosomes, the SRY Gene and X-linked Inheritance

X-linked recessive inheritance: haemophilia, colour blindness, Duchenne

X-linked dominant and Y-linked inheritance

Sex determination in humans: XX, XY and the SRY gene

Common traps

Linkage, Gene Maps, Variation and Non-disjunction

Linked genes and recombination frequency

Building a gene map from crossover values

Meiosis and fertilisation as sources of genetic variation

Non-disjunction and aneuploidy: Down, Turner and Klinefelter syndromes

Common traps

Pedigree Analysis and Allele Frequencies

Probabilities from a pedigree, including the two-thirds rule

Allele frequencies and the Hardy-Weinberg principle

Reading a pedigree: symbols and the five inheritance patterns

Common traps

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