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Genética populacional: Origenes de la variación genética - Prof. 8228, Ejercicios de Biología

Universitat de València (UV)Biología

Los orígenes de la variación genética en poblaciones naturales, desde la estructura de la herencia hasta los efectos de mutaciones y cambios cromosómicos. Se discuten los conceptos básicos de la genética populacional, como el equilibrio de hardy-weinberg y la herencia codominante. Se incluyen ejemplos de mutaciones en genes como el β-globina y el impacto en enfermedades como la anemia falciforme.

Tipo: Ejercicios

2017/2018

Subido el 24/06/2018

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Lesson 2.
Genetic variability and selection
EVOLUTIONARY PROCESSES AND MECHANISMS
2.1.Geneticvariationinnaturalpopulations
2.2.Sourcesofgeneticvariation
2.3.Quantifyinggeneticvariation
2.4.PopulationGenetics
2.4.TheHardy‐Weinbergequilibrium
2.5.Naturalselection:singlelocusmodels
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Lesson 2.

Genetic variability and selection

EVOLUTIONARY PROCESSES AND MECHANISMS

2.1. Genetic variation in natural populations

2.2. Sources of genetic variation

2.3. Quantifying genetic variation

2.4. Population Genetics

2.4. The Hardy‐Weinberg equilibrium

2.5. Natural selection: single locus models

2.1. Genetic variation in natural populations

At the time when the nature and structure of the hereditary material was deduced by Watson and Crick (1953), the same authors observed that the complementarities of the nitrogen bases provided both a mechanism for replication but also for mutation.

2.1. Genetic variation in natural populations

  • Point mutations in coding regions:
    • Insert ion/deletions in coding regions:

2.2. Sources of genetic variation

Single nucleotide substitutions

A single nucleotide change in the DNA encoding the ‐globin gene (CTC to CAC) leads to an altered mRNA codon (GAG to GUG) and the insertion of a different amino acid (Glu to Val), producing an altered version of the ‐globin protein, which is the cause of the sickle cell anemia.

2.2. Sources of genetic variation

10 – 2

10 – 3

10 – 4

10 – 5

10 – 6

10 – 7

10 – 8

10 – 9

10 – 10

10 – 11

10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 9 10 10 Genome size

Mutation rate

Viroids

RNA

viruses

ssDNA

viruses

dsDNA

viruses Bacteria

Lower

eukaryotes

Higher

eukaryotes

 is measured in nucleotide

substitutions per nucleotide position

and generation.

Mutation rate () variation in different organisms

2.2. Sources of genetic variation

2.2. Sources of genetic variation

The origin and propagation of a allopolyploid or amphidiploid. Species A contains 2 distinct chromosomes, and species B 2 distinct chromosomes. Following fertilization between members of the two species and chromosome doubling, a fertile amphidiploid containing two complete diploid genomes (AABB) is formed.

Chromosome changes in the origin of new species

2.2. Sources of genetic variation

  • The simplest way to analyse population genetic structures is through the estimation of

the frequencies of the alleles present in individuals of a population.

  • For this, we need to determine the genotype of individuals in the population (or at least

from a representative sample of individuals) at different loci.

  • From these genotype frequencies, we can then estimate allele frequencies (also called

gene frequencies).

  • In the case of haploid individuals, allelic frequencies are equal to genotype frequencies,

which in turn, are equal to the phenotypic frequencies.

  • In the case of diploid individuals, allelic frequencies can be estimated from genotypic

frequencies by:

 

 

n

j

f Ai f AiAi f AiAj 1

( ) 2

1 ( ) ( )

Homozygote

frequencies

Heterozygote

frequencies

  • For a locus with only 2 alleles:

( ) 2

1 f ( A ) f ( AA ) f Aa ( ) 2

1 f ( a ) f ( aa ) f Aa

2.3. Quantifying genetic variation

  • As seen, in haploids, allele frequencies are directly estimated from phenotypic frequencies.
  • However, in the case of diploids, genotypic frequencies cannot always be estimated directly from phenotypic frequencies (it depends on the type of inheritance).
  • If inheritance is not dominant (intermediate, codominance, partial dominance, etc.), in which each genotype shows a different phenotype, genotypic frequencies can be estimated from phenotypic.
  • However, when inheritance is dominant, it is not possible:
  • To determine whether an individual with dominant phenotype is homozygous or heterozygous, we should analyze whether their progeny is homogeneous or heterogeneous in a cross with a homozygous recessive individual (called test cross), but this is cumbersome or impossible in many cases (e.g. in humans).
  • Another possibility is to determine if certain conditions are met (the so‐called Hardy‐Weinberg equilibrium) that will facilitate the estimation of allele frequencies, as discussed in the next section.

f (dominant phenotype) f ( AA ) f ( Aa )

f (recessive phenotype) f ( aa )

2.3. Quantifying genetic variation

Allozyme analysis: differences in electrophoretic mobility of allelic variants of enzymes, detected by their enzymatic activity.

Restriction analysis of DNA: detection of nucleotide substitutions located in restriction sites.

DNA sequencing: nucleotide differences in genome sequences.

2.3. Quantifying genetic variation

18/09/2016 Procesos y Mecanismos Evolutivos 19

The origins of population genetics

MendelismMendelism

DarwinismDarwinism

ModernModern synthesissynthesis

XIX century XX century

Population genetics

Founders of population genetics:

2.4. Population Genetics

Ronald A. Fisher

Sewall G. Wright

John B.S. Haldane

Object of study: Population genetics studies the structure of the genetic

characteristics of populations of organisms, as well as the processes responsible of its

change from generation to generation (evolution).

  • Population: a reproductive community of individuals sharing a common set of genes

(gene pool).

  • Evolutionary forces: mechanisms that promote genetic change in populations from

generation to generation.

The evolutionary forces are:

‐ Mutation: mechanism involved in the generation of genetic

variability

‐ Selection: differential transmision of genetic variants from

generation to generation due to differences in the fitness of the

bearers.

‐ Gene flow (Migration): changes in gene frequences due to the

movement of individuals or gametes between populations.

‐ Genetic drift: differential transmision of genetic variants from

generation to generation due to random events.

2.4. Population Genetics

Random mating Progeny genotypes

Cross type

Cross

frequency

P^2 1 x P^2 0 x P^2 0 x P^2

2PH ½ 2PH ½ 2PH 0 x 2PH

2PQ 0 x 2PQ 1 x 2PQ 0 x 2PQ

H 2 ¼ H 2 ½ H 2 ¼ H 2

2HQ 0 x 2HQ ½ 2HQ ½ 2HQ

Q^2 0 x Q^2 0 x Q^2 1 x Q^2

Progeny genotype

frequencies

P^2 +

2P(½H) +

(½H) 2

2P(½H) +

2PQ + 2(½

H) 2 + 2Q

(½H)

Q 2 +

2Q(½H)

+ (½H) 2

F( ) = P

F( ) = H

F( ) = Q

x

x

x

x

x

x

Let’s suppose there is a mouse population with 2 alleles (A y a) for an specific locus

exhibiting intermediate inheritance, hence, genotype frequencies are as follows:

And the allele

frequencies are:

F(A) = P + ½ H = p

F(a) = Q + ½ H = q

If mice mate randomly

and all individuals have

the same probability to

reproduce, the

genotypic frequencies in

the next generation will

be as described in the

next table:

2.5. The Hardy‐Weinberg equilibrium

F’( ) = P^2 + 2P(½H) + (½H) 2 = (P + ½H)^2 = [F(AA) + ½ F(Aa)]^2 = F(A)^2 = p^2

F’( ) = 2P(½H) + 2PQ + 2(½ H)^2 + 2Q (½H) = 2[(P + ½H) (Q + ½ H)] = 2[F(AA) + ½ F(Aa)] [F(aa) + ½ F(Aa)] = 2 F(A) F(a) = 2pq

F’( ) = Q 2 + 2Q(½H) + (½H)^2 = (Q + ½H) 2 = [F(aa) + ½ F(Aa)]^2 = F(a) 2 = q^2

After one generation of random mating, the new genotype frequencies are:

1 st^ conclussion :

The progeny genotype frequencies are determined by the parental allelic frequencies.

This is equivalent to a random sampling of gametes from the parental population to

generate the zygotes of the next generation.

2.5. The Hardy‐Weinberg equilibrium

And the allele frequencies in the next generation are:

F’(A) = p’ = F’(AA) + ½ F’(Aa) = p 2 + ½ 2pq = p 2 + pq = p (p + q) = p

F’(a) = q’ = F’(aa) + ½ F’(Aa) = q 2 + ½ 2pq = q 2 + pq = q (p + q) = q

F’(A) = p’ = p = F(A) and F’(a) = q’ = q = F(a).

p + q = 1

2 nd^ conclussion :

In a random mating population, allele frequencies are constant from generation to

generation. AA Aa aa

A a

2.5. The Hardy‐Weinberg equilibrium

Let’s see an example: f(AA) = 0,36; f(Aa) = 0.48 y f(aa) = 0,

Gametes…

With frequencies f(A) = 0,6 y f(a) = 0,4.

2.5. The Hardy‐Weinberg equilibrium

Gametes with frequencies f(A) = 0,6 y f(a) = 0,4, will mate randomly to produce zygotes with genotype frequencies f(AA) = 0,36; f(Aa) = 0,48 y f(aa) = 0,16.

These zygotes will develope to adults that will produce gametes with frequencies f(A) = 0,6 y f(a) = 0,4, etc., etc.:

An equilibrium is reached!

Allelic and genotypic frequencies will remain constant

generation after generation of random mating!

2.5. The Hardy‐Weinberg equilibrium

  • The first scientist interested in the allele dynamics in a population over generations was the statistician and biometrician G. Udny Yule (Pearson’s disciple). ‐ He studied the case of a diallelic locus with allele frequencies of 0.5 each. He concluded that they should remain in an equilibrium. ‐ However, he erroneously concluded that all diallelic genes should reach an equilibrium at values of 0.5 for each allele. ‐Since this was not observed in the analysis of real data, Yule used his conclusions to rebate Mendelism (remember that he was a biometrician).

George Udny Yule (1871-1951)

Reginald C. Punnett (1875-1967)

‐ During a conference of R. C. Punnett on the dominant inheritance of brachydactyly, Yule used his argument against Mendelism. ‐ Yule said that if Mendelism were correct, brachydactylic alleles should be in human populations in an equilibrium frequency of 0.5. Because brachydactyly is a dominant trait, this would imply that every four people, three would be brachydactylic !!.

Punnet was sure that Yule conclusions should be wrong, but

he couldn’t prove it at that moment.

2.5. The Hardy‐Weinberg equilibrium

As Hardy indicates in his article this equilibrium only holds in the case of:

  1. Random mating, and
  2. The character has no influence on fertility.

Therefore, a population will reach a HWE when:

  • Individual are mating randomly.
  • There is no evolutionary mechanism (selection, mutation, genetic drift or gene

flow) acting to change allelic frequencies.

HWE is an ideal situation that can be used as a null hypothesis to determine the action

of evolutionary mechanisms or the presence of nonrandom mating in natural

populations.

2.5. The Hardy‐Weinberg equilibrium

Hardy-Weinberg equilibrium (HWE)

1. Diploid organisms.

2. Sexually reproducing population.

3. Non‐overlapping generations

4. Random mating

5. Very large population size (infinite)

6. No migration

7. Mutation can be assumed to be irrelevant

8. Natural selection does not act on the gene considered

THEN

Allele and genotype frequencies in consecutive generations are related according to

the expressions:

and they will remain constant generation after generation until conditions are

changed.

2.5. The Hardy‐Weinberg equilibrium

P ൌ ݌ ଶ^ ; Q ൌ ݍ ଶ^ ; H ൌ 2ݍ݌

18/09/2016 Procesos y Mecanismos Evolutvos 33

p = 0.36 + 0.48/2 = 0.60 q = 0.16 + 0.48/2 = 0.

p = P + ½ H q = Q + ½ H

Computing allele frequencies from genotype frequencies

2.5. The Hardy‐Weinberg equilibrium

Sperm

18/09/2016 Procesos y Mecanismos Evolutvos 34

Expected genotype frequencies from

allele frequencies

2.5. The Hardy‐Weinberg equilibrium

18/09/2016 Procesos y Mecanismos Evolutvos 37

Hardy‐Weinberg equilibrium with >2 alleles or polyploids

  • One locus with 3 alleles A1, A2, A3 of frequencies p , q , r :

ݎ ൅ ݍ ൅ ݌ ଶ^ ൌ ݌ ଶ^ ൅ ݍ ଶ^ ൅ ݎ ଶ^ ൅ ݍ݌2 ൅ ݎ݌2 ൅ ݎݍ

f (A1A1), f (A2A2), f (A3A3), f (A1A2), f (A1A3), f (A2A3)

  • One locus with n alleles of frequencies A (^) i. Genotype frequencies are derived from the polynomial:

and, in consequence, genotype frequencies are:

௡

௜ୀଵ

݂ଶ

ܣ ௜ ܣ ௜ ݂ൌ ܣ ௜ ଶ^ ݂y ܣ ௜ ܣ௝ ݂2 ൌ ܣ ݂௜ ܣ௝

  • K‐ ploidy with n alleles of frequencies A (^) i. Genotype frequencies are derived from the polynomial: .

௡

௜ୀଵ

௞

2.5. The Hardy‐Weinberg equilibrium

18/09/2016 Procesos y Mecanismos Evolutvos 38

Heterozygosity is at a maximum for p = q = 0.5.

In any case, given p and q , H‐W equilibrium equals the expected heterozygosity.

We must note that heterozygosity is frequently used to measure genetic variability.

2 1 ( )

2 p p p E H i

i i j

  i j    

Gene diversity, , is the expected heterozygosity H under Hardy‐Weinberg equilibrium:

2.5. The Hardy‐Weinberg equilibrium

H‐W equilibrium and heterozygosity

The special case of a sex‐linked gene

Let us consider a gene in the X chromosome with two alleles A and a, with frequencies p and q respectively.

In the equilibrium female genotype frequencies are:

And male genotype frequencies:

, since there is only one allele.

One important difference with autosomal genes is that equilibrium is not reached in a single generation.

fሺXAXAሻ ൌ ݌ ଶ^ ; fሺXaXaሻ ൌ ݍ ଶ^ ; fሺXAXaሻ ൌ 2ݍ݌.

2.5. The Hardy‐Weinberg equilibrium

fሺXAYሻ ൌ ݌; fሺXaYሻ ൌ ݍ

18/09/2016 Procesos y Mecanismos Evolutvos 40

DRIFT

SELECTION

MIGRATION

MUTATION

Main population genetic processes

2.5. The Hardy‐Weinberg equilibrium