1

Subject: Principles of Genetics

Topic :Population genetics

1

2

POPULATION GENETICS:

The study of the rules governing the maintenance and transmission of genetic variation in natural populations.

3

DARWINIAN EVOLUTION BY NATURAL SELECTION

Many more individuals are born than survive (COMPETITION).

Individuals within species are variable (VARIATION).

Some of these variations are passed on to offspring (HERITABILITY).

Survival and reproduction are not random. There must be a correlation between fitness and phenotype.

4

Gregor Mendel

The “rediscovery” of Mendel’s genetic studies in 1902 by William Bateson completed the missing model for the inheritance of genetic factors.

Mendel published his work in the Transactions of the Brunn Society of Natural History in 1866.

551

6

SEXUAL REPRODUCTION CONTRIBUTES TO VARIATION

Example – A Line Cross Experiment

Consider 2 diploid individuals with 3 loci and 2 alleles,

Parents: aabbcc x AABBCC

F1 progeny: AaBbCc

F2 progeny:AABBCC AABBCc AABBccAABbCC AABbCc AABbccAAbbCC AAbbCc AAbbccAaBBCC AaBBCc AaBBccAaBbCC AaBbCc AaBbccAabbCC AabbCc AabbccaaBBCC aaBBCc aaBBccaaBbCC aaBbCc aaBbccaabbCC aabbCc aabbcc

27 COMBINIATIONS

7

Mechanisms of Evolution: Mendelian Genetics in Populations

Genetic variation is the raw material of evolutionary change: how do we measure it?

What are the forces that cause genetic changes within populations? That is, what mechanisms cause evolutionary change?

8

Population Genetics

Evolution can be defined as a change in gene frequencies through time.

Population genetics tracks the fate, across generations, of Mendelian genes in populations.

Population genetics is concerned with whether a particular allele or genotype will become more or less common over time, and WHY.

9

A few things to keep in mind as we take an excursion into population genetic theory:

“Make things as simple as possible, but no simpler.”---Einstein

“All models are wrong, some are useful.”---Box

“No theory should fit all the facts because some of the facts are wrong.”

---Bohr

10

Some Definitions:

Population: A freely interbreeding group of individuals. Gene Pool: The sum total of genetic information present in a

population at any given point in time. Phenotype: A morphological, physiological, biochemical, or

behavioral characteristic of an individual organism. Genotype: The genetic constitution of an individual organism. Locus: A site on a chromosome, or the gene that occupies the

site. Gene: A nucleic acid sequence that encodes a product with a

distinct function in the organism. Allele: A particular form of a gene. Gene (Allele) Frequency: The relative proportion of a particular

allele at a single locus in a population (a number between 0 and 1). Genotype Frequency: The relative proportion of a particular

genotype in a population (a number between 0 and 1).

11

The Gene PoolThe Gene Pool

Members of a species can interbreed & produce fertile offspringSpecies have a shared gene poolGene pool – all of the alleles of all individuals in a population

11

2

12

The Gene PoolThe Gene PoolDifferent species do NOT exchange genes by interbreedingDifferent species that interbreed often produce sterile or less viable offspring e.g. Mule

12

13

Assumptions:

1) Diploid, autosomal locus with 2 alleles: A and a

2) Simple life cycle:

PARENTS GAMETES ZYGOTES(DIPLIOD) (HAPLOID) (DIPLOID)

These parents produce a large gamete pool (Gene Pool) containing alleles A and a.

a A A a a A A a A a a a A A a a A a A A a a A A a a a a A a a A A A a A

14

Gamete (allele) Frequencies:

Freq(A) = pFreq(a) = q

⇒ p + q = 1

Genotype Frequencies of 3 Possible Zygotes:

AA Aa aa

Freq (AA) = pA x pA = pA2

Freq (Aa) = (pA x qa) + (qa x pA) = 2pAqa

Freq (aa) = qa x qa = qa2

⇒ p2 + 2pq + q2 = 1

15

General Rule for Estimating Allele Frequencies from Genotype Frequencies:

Genotypes: AA Aa aa

Frequency: p2 2pq q2

⇒Frequency of the A allele:

p = p2 + ½ (2pq)

⇒Frequency of the a allele:

q = q2 + ½ (2pq)

16

Sample Calculation: Allele Frequencies

Assume N = 200 indiv. in each of two populations 1 & 2

Pop 1 : 90 AA 40 Aa 70 aa Pop 2 : 45 AA 130 Aa 25 aa

In Pop 1 :

p = p2 + ½ (2pq) = 90/200 + ½ (40/200) = 0.45 + 0.10 = 0.55 q = q2 + ½ (2pq) = 70/200 + ½ (40/200) = 0.35 + 0.10 = 0.45

In Pop 2 :

p = p2 + ½ (2pq) = 45/200 + ½ (130/200) = 0.225 + 0.325 = 0.55 q = q2 + ½ (2pq) = 25/200 + ½ (130/200) = 0.125 + 0.325 = 0.45

17

Main Points:

p + q = 1 (more generally, the sum of the allele frequencies equals one)

p2 + 2pq +q2 = 1 (more generally, the sum of the genotype frequencies equals one)

Two populations with markedly different genotype frequencies can have the same allele frequencies

18

PopulationsPopulationsA group of the same species living in an areaNo two individuals are exactly alike (variations)More Fit individuals survive & pass on their traits

18

19

SpeciationSpeciationFormation of new speciesOne species may split into 2 or more speciesA species may evolve into a new speciesRequires very long periods of time

19

2020

21

Modern Synthesis TheoryModern Synthesis TheoryCombines Combines Darwinian Darwinian

selection selection and and Mendelian Mendelian inheritanceinheritance

Population genetics Population genetics - - study of genetic variation study of genetic variation within a populationwithin a population

Emphasis on Emphasis on quantitative characters quantitative characters (height, size …)(height, size …)

21

22

Modern Synthesis TheoryModern Synthesis Theory1940s – comprehensive 1940s – comprehensive

theory of evolution theory of evolution (Modern (Modern Synthesis Theory)Synthesis Theory)

Introduced by Fisher & Introduced by Fisher & WrightWright

Until thenUntil then, many did not , many did not accept that Darwin’s theory accept that Darwin’s theory of natural selection could of natural selection could drive evolutiondrive evolution

22

S. Wright

A. Fisher

23

Modern Synthesis Theory• TODAY’S theory on evolution Recognizes that GENES are responsible for the

inheritance of characteristics Recognizes that POPULATIONS, not individuals,

evolve due to natural selection & genetic drift Recognizes that SPECIATION usually is due to the

gradual accumulation of small genetic changes

23

24

MicroevolutionMicroevolution

Changes occur in gene pools due to mutation, natural selection, genetic drift, etc.

Gene pool changes cause more VARIATION in individuals in the population

This process is called MICROEVOLUTIONExample: Bacteria becoming unaffected by

antibiotics (resistant)

24

2525

Hardy-Hardy-Weinberg Weinberg PrinciplePrinciple

26

The Hardy-Castle-Weinberg Law

A single generation of random mating establishes H-W equilibrium genotype frequencies, and neither these frequencies nor the gene frequencies will change in subsequent generations.

Hardy

p2 + 2pq + q2 = 1

27

The Hardy-Weinberg PrincipleThe Hardy-Weinberg Principle

Used to describe a non-evolving population.

Shuffling of alleles by meiosis and random fertilization have no effect on the overall gene pool.

Natural populations are NOT expected to actually be in Hardy-Weinberg equilibrium.

27

28

The Hardy-Weinberg PrincipleThe Hardy-Weinberg Principle

Deviation from Hardy-Weinberg equilibrium usually results in evolution

Understanding a non-evolving population, helps us to understand how evolution occurs

28                       

.

29

5 Assumptions of the H-W Principle5 Assumptions of the H-W Principle1. Large population size

- small populations have fluctuations in allele frequencies (e.g., fire, storm).

2. No migration- immigrants can change the frequency of an allele by bringing in new alleles to a population.

3. No net mutations- if alleles change from one to another, this will change the frequency of those alleles

29

30

5 Assumptions of the H-W Principle5 Assumptions of the H-W Principle

4. Random mating- if certain traits are more desirable, then individuals with those traits will be selected and this will not allow for random mixing of alleles.

5. No natural selection- if some individuals survive and reproduce at a higher rate than others, then their offspring will carry those genes and the frequency will change for the next generation.

30

31

The Hardy-Weinberg PrincipleThe Hardy-Weinberg PrincipleThe gene pool of a NON-EVOLVING population remains CONSTANT over multiple generations (allele frequency doesn’t change)

The Hardy-Weinberg Equation:

               1.0 = p2 + 2pq + q2

 Where:p2 = frequency of AA genotype2pq = frequency of Aa q2 = frequency of aa genotype

31

32

The Hardy-Weinberg PrincipleThe Hardy-Weinberg PrincipleDetermining the Allele Frequency using Hardy-

Weinberg:               

1.0 = p + q Where:p = frequency of A alleleq = frequency of a allele

32

3333

Allele Frequencies Define Gene PoolsAllele Frequencies Define Gene Pools

As there are 1000 copies of the genes for color, the allele frequencies are (in both males and females):

320 x 2 (RR) + 160 x 1 (Rr) = 800 R; 800/1000 = 0.8 (80%) R160 x 1 (Rr) + 20 x 2 (rr) = 200 r; 200/1000 = 0.2 (20%) r

500 flowering plants

480 red flowers 20 white flowers

320 RR 160 Rr 20 rr

3434

35

IMPLICATIONS OF THE H-W PRINCIPLE:

1) A random mating population with no external forces acting on it will reach the equilibrium H-W frequencies in a single generation, and these frequencies remain constant there after.

2) Any perturbation of the gene frequencies leads to a new equilibrium after random mating.

3) The amount of heterozygosity is maximized when the gene frequencies are intermediate.

2pq has a maximum value of 0.5 when p = q = 0.5

36

GENOTYPE VERSUS GENE FREQUENCIES

3

37

FOUR PRIMARY USES OF THE H-W PRINCIPLE:

1) Enables us to compute genotype frequencies from generation to generation, even with selection.

2) Serves as a null model in tests for natural selection, nonrandom mating, etc., by comparing observed to expected genotype frequencies.

3) Forensic analysis.

4) Expected heterozygosity provides a useful means of summarizing the molecular genetic diversity in natural populations.

38

DETECTING DEPARTURES FROM HWE

A χ2-test (a standard goodness-of-fit test) can be used to detect statistically significant departures from Hardy-Weinberg Equilibrium.

Step 1: Determine allele frequencies. (N = 100).

AA Aa aa

Observed: 30 60 10

p = 0.30 + 0.30 = 0.60 and q = 0.10 + 0.30 = 0.40

Step 2: Based on allele frequencies, calculate the expected number of each genotype.

AA Aa aa

p2N 2pqN q2N

Expected: 36 48 16

39

AA Aa aaObserved: 30 60 10

Expected: 36 48 16

Step 3: Calculate χ2 test statistic.

χ2 = Σ [(O-E)2/E]

= (30-36)2/36 + (60-48)2/48 + (10-16)2/16 = 6.25

Step 4: Compare this result to critical value from the χ2 statistical table. This test has 1 degree of freedom, so the critical value for α = 0.05 is 3.84.

6.25 > 3.84, so this is a significant departure from HWE!

DETECTING DEPARTURES FROM HWE

40

IMPLICATIONS OF A STATISTICAL DEPARTURE FROM HWE

If the null hypothesis is true (i.e., we are in H-W equilibrium), we would expect a sample of this size to show this much (or more) of a departure from expectations (purely by chance sampling) less than 5 percent of the time.

One or more of the assumptions of the H-W principle are not satisfied in this population.

Further research will be necessary to establish which assumption is violated. [Excess of heterozygotes could be due to overdominant selection, for example].

NOTE: A failure to detect a departure from H-W equilibrium does not guarantee that the population satisfies all of the assumptions of the model. The departure may simply not be statistically detectable.

See Box 6.5 in F&H for more on X2 tests.

41

EVOLUTIONARY THOUGHT AFTER DARWIN

By the 1870s, most scientists accepted the historical reality of evolution (and this has been true ever since).

It would be at least 60 years after the publication of The Origin of Species before natural selection would come to be widely accepted.

People seemed to want life itself to be purposeful and creative, and consequently did not find natural selection appealing.

Neo-Lamarckism -- inheritance of acquired characteristics.

Orthogenesis -- variation that arises is directed toward a goal.

Mutationism -- discrete variations are all that matter.

42

Outcomes of the “MODERN SYNTHESIS”

Populations contain genetic variation that arises by random mutation.

Populations evolve by changes in gene frequency.

Gene frequencies change through random genetic drift, gene flow, and natural selection.

Most adaptive variants have small effects on the phenotype so changes are typically gradual.

Diversification comes about through speciation.

43

MUTATION SELECTION

DRIFTMIGRATION

POPULATIONS

Phenotypic Evolution: Process

+

+/ —

—

—

44

MEASURING GENETIC VARIATION IN NATURAL POPULATIONS

TWO COMMONLY USED MEASURES TO QUANTIFY GENETIC VARIATION ARE:

P – the proportion of polymorphic loci (those that have 2 or more alleles)

H – the average heterozygosity = proportion of loci at which a randomly chosen individual is heterozygous.

4545

46

Causes of MicroevolutionCauses of Microevolution

Genetic Drift- the change in the gene pool of a small population due to chance

Natural Selection - success in reproduction based on heritable traits results in selected alleles being passed to relatively more offspring (Darwinian inheritance)- Cause ADAPTATION of Populations

Gene Flow-is genetic exchange due to the migration of fertile individuals or gametes between populations

46

47

Causes of MicroevolutionCauses of Microevolution

• Mutation- a change in an organism’s DNA- Mutations can be transmitted in gametes to offspring

• Non-random mating- Mates are chosen on the basis of the best traits

47

4848

Genetic DriftGenetic Drift

49

Factors that Cause Genetic DriftFactors that Cause Genetic Drift•Bottleneck Effect- a drastic reduction in population (volcanoes,

earthquakes, landslides …)

- Reduced genetic variation

- Smaller population may not be able to adapt to new selection pressures

•Founder Effect- occurs when a new colony is started by a few

members of the original population

- Reduced genetic variation

- May lead to speciation

49

5050

4

51

Loss of Genetic VariationLoss of Genetic Variation

•Cheetahs have little genetic variation in their gene pool

•This can probably be attributed to a population bottleneck they experienced around 10,000 years ago, barely avoiding extinction at the end of the last ice age

51

52

Founder’s EffectFounder’s Effect

52

5

5353

54

Modes of Natural SelectionModes of Natural Selection

• Directional Selection- Favors individuals at one end of the phenotypic range- Most common during times of environmental change

or when moving to new habitats

• Disruptive selection- Favors extreme over intermediate phenotypes

- Occurs when environmental change favors an extreme phenotype

54

55

Modes of Natural SelectionModes of Natural Selection Stabilizing Selection

- Favors intermediate over extreme phenotypes- Reduces variation and maintains the cureent average- Example: Human birth weight

55

5656

5757

Variations in Variations in PopulationsPopulations

58

Geographic VariationsGeographic Variations

•Variation in a species due to climate or another geographical condition

• Populations live in different locations

• Example: Finches of Galapagos Islands & South America

58

59

59

6

60

Heterozygote AdvantageHeterozygote Advantage• Favors heterozygotes (Aa)• Maintains both alleles (A,a) instead of removing less

successful alleles from a population• Sickle cell anemia

> Homozygotes exhibit severe anemia, have abnormal blood cell shape, and usually die before reproductive age.> Heterozygotes are less susceptible to malaria

60

61

Other Sources of VariationOther Sources of Variation• Mutations

- In stable environments, mutations often result in little or no benefit to an organism, or are often harmful

- Mutations are more beneficial (rare) in changing environments (Example: HIV resistance to antiviral drugs)

• Genetic Recombination- source of most genetic differences between individuals in a

population

• Co-evolution-Often occurs between parasite & host and flowers & their

pollinators

61

62

CoevolutionCoevolution

62

7

63

• References

• Fig 1 http://www.docstoc.com/docs/121720670/Figure-151-The-chromosomal-basis-of-Mendels--laws

• Fig 2 http://www.windows2universe.org/earth/Life/genetics_microevolution.html

• Fig 3 http://sites.sinauer.com/ecology2e/webext06.1.html

• Fig 4 http://science.nayland.school.nz/graemeb/yr13%20work/evolution/genetic_drift_and_so_on.htm

• Fig 5 http://theflamboyantcuttlefish.weebly.com/evolution.html 6 http://www.slideshare.net/marmayy/chapter23-6769543

• Fig 6 http://scienceblogs.com/pharyngula/2006/06/10/clausen-keck-hiesey/

• Fig 7 https://biologyeoc.wikispaces.com/CoEvolution

• Principles of inheritance Mendal’s laws and and genetic models by Springer

63

6464