Qualitative population geneticsOutline of lecture:

I. Definition

II. Assumptions – genetic equilibrium

III. Hardy-Weinberg rule

IV. Importance of gene- and genotype frequency

V. Chi2-test (control of H-W proportions)

VI. Genic variation statistics

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• 8. Principles and laws of Mendelian genetics

• 9. Exceptions in Mendelian genetics: allelic polymorphism, pleiotropy,

epistasis, superdominance, X-linked inheritance

• 10. Exceptions in Mendelian genetics: linkage, crossing over and

uniparental inheritance (genomic imprinting, maternal-mtDNA)

• 25. Polymorph systems (biochemical: blood groups, proteins, MHC;

and DNA: microsatellites, SNPs) and their use in animal breeding

• 26. Qualitative population genetics in animal breeding: features of

monogenic traits

• 27. Qualitative population genetics in animal breeding: Hardy-

Weinberg law

• 38. Breeding methods and mating systems, interspecies hybrids 2

0. Characteristics of a population

Base of comparison Qualitative traits Quantitative traits

number of genes: 1 (monogenic) or few

(oligogenic)

several or many

description: classified measured

unit of measurement: individual number cm, g, sec, etc.

characteristics: segregation ratio,

rel. gene-, genotype

frequencies

mean, variance,

standard deviation

relationship bw. loci: linkage correlation

number of categories: 1, 2, 3 many, continuous

distribution

phenotype → genotype: easily slightly

environmental influence: practically no extensively

inheritance: intermediate, dominant-

recessive

complex

(coeff. of inheritance, h2)

Threshold traits

(all-or-non traits, quasi quantitative traits)

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Qualitative traits

• Blood type

• Enzyme-defect

• DNA-marker

• Eye color

• Coat type

• Fleece or coat color

• Horns

• Wattles

• Beards

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• Entropion

– medical condition in which the eyelid folds

inward

• Spider lamb disease

– Hereditary chondrodysplasia, semilethal, reces.

• Cryptorchidism

– absence of one or both testes from the scrotum

• Myotonia congenita

– a disorder that affects muscles used for

movement (skeletal muscles) and that prevent

muscles from relaxing normally

Qualitative traits - Inherited defects

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I. Definition

• Qualitative population genetics is the

study of the allele- and genotype

frequency distribution.

• four evolutionary forces:

– natural selection

– genetic drift

– mutation

– gene flow

– (artificial selection)6

1. Natural

selection

• Survival of the fittest! 7

• Favourable heritable traitsbecome more common.

• Acts on the phenotype.

• The phenotype’s geneticbasis will increase infrequency over thefollowing generations.

• Adaptation: specialiseorganisms for particularecological niches.

• Emergence of new species.

2. Genetic driftA change in population’s gene pool by chance

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• Founder effect• A few individuals from a population

start a new population with a

different allele frequency than the

original population.

• Loss of genetic variation.

• It can lead in dom. animals to new

subpopulations or completely new

breeds!

• Bottleneck effect

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2. Genetic driftA change in population’s gene pool by chance

• It is an evolutionary event in which a significant percentage of a pop. is killed or prevented fromreproducing.

• Very small pop. shows increasedsensitivity to genetic drift , and increase in inbreeding, and relativelly low genetic variation – e.g. European bison: the animals livingtoday are all descendent only from12 individuals.

• Not a rare phenomenon in domesticanimal breeds.

3. Mutation

- Mutation = any change in DNA.

- It have very subtle effect on allele frequencies.

- Germ line mutations: can be passed on to descendants.

- Somatic mutations: are not transmitted to descendants.

• They can be positive, negative or neutral in regard to

fitness.

•Mutations can happen randomly, as in this Scottish fold cat.

Cat enthusiasts bred these cats for a mutation of the ears.

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4. Gene flow - migration

▪ Genetically links two or more population together.

▪ Allele frequencies will becomemore homogenous among thepopulations.

▪ Non-random mating - Wahlundeffect:

▪ artificial insemination(used for selective breedingof dom. animals especially)

▪ sires from other population(rare-male mating)

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II. Assumptions

Genetic Equilibrium

A situation in which allele frequencies of a population

remain constant (V + F + M!).

Five conditions required to maintain genetic equilibrium:• Random mating (panmixis).

• Population must be very large.

• There can be no movement into or out of the population

(migration).

• No mutations.

• No natural selection.

When all 5 are met evolution not occur! 12

Polymorphic systems

in blood:

haemoglobin

HgA

HgB

Polymorphic systems invisible – codominant

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Coat colour inheritance

Red(bb) Black(BB, Bb)

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Red (RR) Roan (RW) White (WW)

Coat colour inheritance

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Allele frequency derived from allele numbers

intermediate inheritance

pR = (2 x RR+ RW) / 2 x Σ = 0.304 → ≈ 0.3

qW = (2 x WW+ RW) / 2 x Σ = 0.696 → ≈ 0.7

genotype RR RW WW total

individual 756 3780 4169 8705

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genotype RR RW WW total

No. individuals 756 3780 4169 8705

GT frequencies 0.087 0.434 0.479 1.000

pR = 0,087 + (0,434 / 2) = 0,304 → ≈ 0,3

qW = 0,479 + (0,434 / 2) = 0,696 → ≈ 0,7

Allele frequency derived from GT frequencies

- intermediate inheritance

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• 891 white sheep (BB, Bb)

• 9 black sheep (bb)

• Total pop. = 900 sheep

Allele frequency derived from allele numbers

dominant-recessive inheritance

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One of the basic principle of probability

theory

• The probability of common occurrence of

independents events is equal to the product of

the probability of individual events.

• P=0.5

• P=0.5 x 0.5=0.25

• P=0.5 x 0.5 x 0.5=0.125

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„Weinberg-Hardy-Tsetverikov rule”(1908)

Wilhelm Weinberg

(1862-1937)

Godfrey Harold Hardy

(1877-1947)

Sergey Sergeyevits

Csetverikov (1880-1959)

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III. Hardy-Weinberg rule(in two-allelic system, in genetic equilibrium)

dominant

homozygous

heterozygous recessive

homozygous

genotypes AA Aa aa

genotypefrequencies

p2 +2pq +q2 = 1 /*N

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• The frequency of homozygous genotypes (AA%, aa%) is equal to the allele frequency squared (AA% = p2, aa% = q2).

• The frequency of heterozygous genotype (Aa%) is equal to twice the product of the allele frequencies (Aa% = 2pq).

• The sum of the genotype frequencies is equal to 1.

III. Hardy-Weinberg rule(in two-allelic system, in genetic equilibrium)

dominant

homozygous

heterozygous recessive

homozygous

genotypes AA Aa aa

genotypefrequencies

p2 + 2pq + q2 = 1 /*N

genotype numbers

p2N + 2pqN + q2N = N

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• The sum of the genotype numbers is equal to the population size (N).

• If the observed frequencies do not show a significant difference fromthese expected frequencies, the population is said to be in Hardy-Weinberg equilibium (HWE).

• 891 white sheep (BB, Bb)

• 9 black sheep (bb)

• Total pop. = 900 sheep

Allele frequency derived from allele numbers

dominant-recessive inheritance

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Not all genetic traits strictly follow the

laws discovered by Mendel

• Incomplete dominance

• Polygenic inheritance

• Sex-linked: on X or Y chromosome

– E.g.: hemophilia

• Sex-limited: all or none expressed by

sex

– E.g.: milk production

• Sex-influenced: genotype + sex

determines

– E.g.: horns in most sheep and beards in

goats 24

Sex-linked trait (to sex-chromosome-linked

inheritance)

female (XX):

XOXO: orange coat colour (patched tabby)

XOXo: mixed coat colour tortoise shell phenotype (Torby)

XoXo: no orange colour in coat

male (XY, hemizygote):

XOY: orange coat colour

XoY: no orange colour in coat

• [orange gene (O and o) in cat]

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female (XX):

XOXO: orange coat colour

XOXo: mixed coat colour → tortoise shell phenotype (Torbie)

XoXo: no orange colour in coat

male (XY, hemizygote):

XOY: orange coat colour

XoY: no orange colour in coat

• In males the allele frequency is equal to genotype frequency

(p = A% = AA%, q = a% = aa%).

• In females the allele frequency is equal to the square root of the genotype frequency (p = , q = ).

• Sex-linked recessive genetic disease (XLGD; recessive homozygous genotype) occurs more frequent in males than in females.

Sex-linked trait - sex-chromosome-linked inheritanceorange gene (O and o) in cat

%AA %aa

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Possible number of genotypes (GT) when there are

more allelic forms at a locus

number of allelic forms

(n)

number of genotypes

(GT)

1 1

2 3

3 6

4 10

5 15

10 55

20 210

50 390 27

Hardy-Weinberg proportions

in three-allelic system:

1 = p + q + r =

(p + q + r)2 =

p2 + q2 + r2 + 2pq + 2pr + 2qr

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number of allelic forms

(n)

number of genotypes

(GT)

1 1

2 3

3 6

4 10

5 15

10 55

20 210

50 390

Calculation of gene frequency for more than two alleles

- of transferrin - using observed numbers of genotype

Transferrin is a blood plasma protein for iron ion delivery that is encoded by

the TF gene. Transferrin is a glycoprotein, which binds iron very tightly but

reversibly.29

Polymorph systems in blood: transferrin

TfA

TfB

TfD

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allelic

form

allelic

frequencygenotypes and number of each total

TfA/TfA TfA/TfB TfA/TfD TfB/TfB TfB/TfD TfD/TfD

18 5 2 20 32 26 103

TfA pA --- ---

---

--- …. …. ….

TfB qB …. …. --- ---

---

….

TfD rD …. …. --- …. ---

pA = [(2 * 18) + (5 + 2)] / (2 * 103) = 0,209

qB = [(2 * 20) + (5 + 32)] / (2 * 103) = 0,374

rD = 1 - (p + q) = 0,417

Calculation of gene frequency for more than two alleles

- of transferrin - using observed numbers of genotype

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Calculation of gene frequency for more than two alleles (of

REN124 microsatellite) using observed numbers of genotype

number of allelic forms

(n)

number of genotypes

(GT)

1 1

2 3

3 6

4 10

5 15

10 55

20 210

50 390

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GT = n + [(n2 – n)/2]

• Description of population – e.g. genetic defects, genic diversity, carriers.

– Calculate the frequencies of particular alleles basedon the frequency of an autosomal recessive disease.

– Genotype frequency of the disease gene can be calculated.

– Carrier rate may be calculated

(e.g. stress disease in pigs,

DMD and MDR in dogs).

IV. Importance of gene- and genotype frequency

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• Homozygous (mm) individuals:

→ solid black, brown, brown-black, fawn, …

• Heterozygous (Mm) mudis:

→ merle colour.

→ Eye colour: split or odd-eye (heterochromia iridis).

• Homozygous (MM) double merles:

→ separated merle patches divided by extensive white areas.

→ almost always fully blue eyes.

→ congenital auditory and ophthalmologic

disorders (e. g. deafness, microphthalmia).

Description of population – carrier rate – merle factor

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• Practical observations: the colour is caused by a single, autosomal, not completely dominant gene.

• A retrotransposon insertion is responsible for the unique colouration.

• Detection: agarose-gel electrophoresis

Description of population – carrier rate

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Description of population – carrier rate – merle factor

• Merle gene affects eumelanin pigment only.

• If their eumelanin pigment production is inhibited by other genes, it makes genetically merle individuals impossible to recognize (based on their phenotype).

• ‘Hidden merle’: genetically merle, but their coat colour hides their merle pattern.

?

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Description of population – carrier rater – merle factor

• Hair or buccal swab samples collected from hidden merle Mudi dogs.

• PCR: exon 11 of the SILV gene

• Agarose gel electrophoresis

• We compared our genotype results with the dogs' phenotypic traits (colour of the eyes and the fur).

Results:

• Blue or partial blue eyes are solely caused by the merle gene in the Mudi breed.

• Eye colour is not always affected by the merle gene: in our research 4 of the 17 brown eyed dogs tested proved to be heterozygous Mm.

• https://www.youtube.com/watch?v=lIoxAyJ0SFo&app=desktop

?

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• Control of genetic equilibrium

• Control of sameness – e.g. in endangered breeds

IV. Importance of gene- and genotype frequency

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• Comparison of two populations – e.g. in researches

• Comparison of more populations – taxonomy

Dendrogram according to Nei’s genetic distances

IV. Importance of gene- and genotype frequency

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IV. Importance of gene- and genotype frequency

• Information for a more complex evaluation of populations

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Breed identification?..

• 85 breeds (n=414)

• 95 microsatellite markers

• 99% certainty

1. Ancient 2. Herding 3. Hunting 4. Guarding

Genetic Structure of the

Purebred Domestic DogParker et. al. (2004)

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Testing the H-W Equilibrium

in two-allelic system

• If we have a population where we can distinguish all

three genotypes, we can use the chi-square test to see if

the population is in H-W equilibrium. The basic steps:

– Count the numbers of each genotype (observed GT) →

observed GT frequencies.

– Calculate the allele frequencies from the observed GT

frequencies.

– Calculate the expected GT frequencies based upon the

HW equation, then multiply by the total number of offspring

to get expected GT numbers.

– Calculate the chi-square value using the observed and

expected genotype numbers.

– Use 1 degree of freedom (because there are only two

alleles).43

Control of Hardy-Weinberg proportions by

Chi2-test

• The null hypothesis (H0) is the assumption that the difference between observed and expected numbers (or frequencies) is only due to chance in the sampling process.

• If our Chi2-value (χ2-value) is less than the Chi2-value in the table (at given probability and degree of freedom) H0 is not rejected:- no significant difference between observed and expected numbers

• Conclusion: the population is in H-W equilibrium (or there is no significant difference between the groups of animals).

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Control of Hardy-Weinberg proportions by

Chi2-test

• The null hypothesis (H0) is the assumption that the difference between observed and expected numbers (or frequencies) is only due to chance in the sampling process.

• Chi2-value (χ2-value) is higher than the Chi2-value in the table H0 is rejected:– significant difference between observed and expected numbers.

• Conclusion: the population is not in HW equilibrium (or there is significant difference between the groups of animals).

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VI. Genic variation statistics

• Sample size; twice the number of

individuals.

• Observed number of alleles; number of

alleles really found in the investigation.

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VI. Genic variation statistics

Locus

(STR)

Sample size Observed

number of

alleles

CSRD247 84 19

HSC 80 11

INRA063 98 13

MAF214 84 9

OarAE129 96 7

OarCP49 94 15

OarFCB11 96 9

OarFCB304 90 18

Mean 90.25 12.6250

±Std. Dev 4.4058 47

The effective number of alleles

corresponds to the ideal situation where the

allele frequencies are equal, for the same

level of heterozygosity

AEP = 1 / Σ pi2

Alleles A a ä

pi 0.33 0.33 0.33

pi2 0.11 0 .11 0 .11

AEP 1/0.33 = 3.06

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The effective number of alleles

corresponds to the ideal situation where the

allele frequencies are equal, for the same

level of heterozygosity

AEP = 1 / Σ pi2

Alleles A a ä

pi 0.1 0.1 0.8

pi2 0.01 0 .01 0 .64

AEP 1/0.66 = 1.52

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Effective number of alleles

• Generally show lower values than the observed ones.

• It takes account of uneven allele frequencies: a rare neutral allele will most probably be lost in the next generation, and have a very low weight in the calculation of the effective allele number.

• The figures of effective number of alleles estimate the reciprocal of expected homozygosity (n = 1/Fexp).

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Allele frequencies of WILMS-Microsatellite in

dogs

Allele

Fre

qu

en

cie

s

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Locus Sample size Observed

number of

alleles

Effective

number of

alleles

CSRD247 84 19 9.8547

HSC 80 11 8.0605

INRA063 98 13 7.4312

MAF214 84 9 4.2050

OarAE129 96 7 3.9656

OarCP49 94 15 7.7782

OarFCB11 96 9 4.9870

OarFCB304 90 18 7.6271

Mean 90.25 12.6250 6.7387

±Std. Dev 4.4058 2.1039

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Shannon’s information index (H)

• Shannon’s entropy value depends only on frequencies of alleles.• The values of entropy are especially important in maintenance

of rare domestic farm animals.• When the frequency of a certain allele variant decreases,

entropy decreases as well.

• When entropy is increased, the chance to keep this certain allele in population is also increased.

n

H = -Σ pi * log2 (pi)i

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Shannon’s indices (entropy) in three-allelic system

Frequencies Entropy

A a ä

.1 .1 .8 .639

.1 .2 .7 .802

.1 .3 .6 .898

.1 .4 .5 .943

.2 .2 .6 .950

.2 .3 .5 1.030

.2 .4 .4 1.055

.3 .3 .4 1.089

.33 .33 .33 1.09954

Locus Sample size Observed

number of

alleles

Effective

number of

alleles

Shannon's

information

index

CSRD247 84 19 9.8547 2.5576

HSC 80 11 8.0605 2.1950

INRA063 98 13 7.4312 2.1762

MAF214 84 9 4.2050 1.6853

OarAE129 96 7 3.9656 1.6441

OarCP49 94 15 7.7782 2.2588

OarFCB11 96 9 4.9870 1.8529

OarFCB304 90 18 7.6271 2.4179

Mean 90.25 12.6250 6.7387 2.0985

±Std. Dev 4.4058 2.1039 0.3362

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A fully satisfactory genetic and phenotypic description of

a population for all loci with their all allelic forms is

impossible.

But, when the animals differ in n gene-pairs (loci) from

each others, so we receive in F3 3n different

genotypes (with constant relative frequencies in the

next generations) and 2n + 1 phenotypes.

Description of a population

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• Fatal degenerative disease that affects the nervous system of

sheeps and goats.

• It is one of several transmissible spongiform

encephalopathies (TSEs).

• Scrapie is caused by a prion.

• Variation in the ovine prion protein amino acid sequence

influences scrapie progression.

•Known since 1732, and does not appear to be transmissible

to humans.

• National Scrapie Plan (NSP)

• https://www.youtube.com/watch?v=WiUK7ftkauU

Scrapie

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Genetics of scrapie susceptibilityRisk group Genotype Degree of resistance/susceptibility

NSP1 ARR/ARR most resistant

NSP2 ARR/AHQ

ARR/ARH

ARR/ARQ

most resistant, careful selection needed for further

breeding.

NSP3 AHQ/AHQ

AHQ/ARH

AHQ/ARQ

ARH/ARH

ARH/ARQ

ARQ/ARQ

little resistance, need careful selection when used for

further breeding

NSP4 ARR/VRQ Susceptible, controlled breeding program

NSP5 AHQ/VRQ

ARH/VRQ

ARQ/VRQ

VRQ/VRQ

highly susceptible, should not be used for breeding

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Thank You For Your Attention!

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