Population genetics

Michèle Sale, Ph.D.Center for Public Health Genomics

msale@virginia.eduTel: 982-0368

Additional reading

• Campbell, N.A., Reece, J.B. et al. (2008). Biology. 8th edition. Benjamin/Cummings Publishing Company, Inc. http://www.mansfield.ohio-state.edu/~sabedon/campbl23.htm

• A.H. Sturtevant, (2001) A History of Genetics. Cold Spring Harbor Laboratory Press.

http://www.esp.org/books/sturt/history/contents/sturt-history-ch-17.pdf

Review of terminology

• Mutation– A permanent, heritable change in genomic

sequence

• Variant– Any mutated site, irrespective of frequency

• Allele– A DNA sequence variant– All DNA sequences, not just genes, can have

more than one allele

A C G A A T A T T

A C G A T T A T T

Allele

A C G A A T A T T

A C G A T T A T T

Genotype

A C G A A T A T T

A C G A T T A T T

Genotype

A C G A A T A T T

A C G A T T A T T

Haplotype

A C G A A T A T T

A C G A T T A T T

Haplotype

A C G A A T A T T

A C G A T T A T T

Diplotypeor

Haplogenotype

More than 2 alleles at a locus in a population

1/1

1/2 1/2

1/21/1

1/2

1/2

1/2

2/2

1/2

1/2

2/2

1/3

1/1

1/1

1/1

1/2 1/2

1/21/1

1/2

1/2

1/2

2/2

1/2

1/2

2/2

1/3

1/1

1/1

More than 2 alleles at a locus in a population…

Phenotype vs. Genotype

• Phenotype is the observable property of an organism; a trait such as height, weight, medical condition, etc.

• Genotype is the DNA sequence of an organism at a specific, defined location.

Population genetics

• The study of allele and genotype frequencies in a population

What do we mean by a population?

• Population– A localized group of interbreeding individuals– Note: For this part of the course – human genetics –we

are dealing with a single species, but many of the concepts of population genetics apply more broadly

• Gene pool– A gene pool consists of all alleles at all loci in all

individuals in a population

Allele frequency

• All alleles possess a frequency that is somewhere between 0.0 and 1.0

• Allele frequency refers to the frequency of alleles in a gene pool, not in single individuals

Punnett square

• Used to predict the probability of possible genotypes of offspring

Punnett square

Punnet

Reginald C. Punnett

• In 1900, Mendel's work was rediscovered by Carl Correns, Erich Tschermak von Seysenegg and Hugo de Vries

• William Bateson had Mendel's work translated into English

• Bateson and Punnett helped established the new science of genetics at Cambridge

• Mendelism (1905) by Punnett was probably the first popular science book to introduce genetics to the public

• Punnett and Bateson co-founded the Journal of Genetics in 1910

1875 –1967

http://www.dnaftb.org/dnaftb/concept_5/con5bio.html

Explaining the allele frequency in a population

• The discrete alleles Mendel discovered exist at some frequency in natural populations

• Biologists wondered how and if these frequencies would change

• Many thought that the more common versions of genes would increase in frequency simply because they were already at high frequency

Godfrey Harold Hardy1877– 1947Cambridge mathematician

http://en.wikipedia.org/wiki/G._H._Hardy

Asked by a student why recessive alleles don’t disappear from the population

Hardy-Weinberg theorem

• The Hardy-Weinberg Law states that allele and genotype frequencies remain constant in succeeding generations in a population at equilibrium

• For a two allele system, let:p = the frequency of the dominant allele (e.g. A)q = the frequency of the recessive allele (e.g. a)

• For a population in genetic equilibrium:p + q = 1 (The sum of the frequencies of both alleles is 100%.)

• For genotype frequencies,(p + q)2 = 1, orp2 + 2pq + q2 = 1

• The three terms of this binomial expansion indicate the frequencies of the three genotypes:p2 = frequency of AA (homozygous dominant)2pq = frequency of Aa (heterozygous)q2 = frequency of aa (homozygous recessive)

Wilhelm Weinberg1862-1937German physician

G.H. Hardy

Hardy Weinberg Equilibrium

Gen

otyp

e fr

eque

ncy

Allele frequency

p2 + 2pq + q2 = 1

G.H. Hardy

• “… I should have expected the very simple point which I wish to make to have been familiar to biologists”

Hardy-Weinberg Equilibrium

• Given the appropriate conditions, it takes only a single generation to reach Hardy-Weinberg equilibrium

Reaching HWE

AA

x

Most extreme situation (takes 2 generations):Start with two population with different fixed alleles:

AA

AA

AA AA

AAaa

aa

aa

aa

aa

aa

AaAa

Aa

Aa

Aa

Aa AaAa

Aa

aa

AaAa

AA

AA

AAAA

aa

aaaa

AaAa AaAa

Aa Aa

Calculating allele frequencies

– Remember that a diploid organism has two (not necessarily different) alleles at each locus

– The frequency of an allele within a population is equal to the number of alleles of a given type within the population divided by the total number of alleles found at a given locus

– Thus, if:• 200 A alleles and • 400 a allelesare found within a given population, then the frequency of A alleles is 200 / (200 + 400) = 1/3 = 0.33

– If this is a diploid population, how many individuals are in this population? 300

Calculating allele frequencies from genotype frequencies

• Genotype frequency information can be used to calculate allele frequency

• If a population has – 100 Aa individuals– 200 aa individuals, and– 300 AA individualsthen the number of

A alleles is 100*1 + 300*2 = 700;the number of a alleles is 100*1 + 200*2 = 500;the frequency of A therefore is 700 / (500 + 700) = 7/12 = 0.58

• Remember diploid individuals contribute two alleles from each locus to the gene pool (hence the *2 in the above calculations)

• How many diploid individuals are present in the above example? 600

Calculating genotype frequencies from allele frequencies

• If the frequency of allele A is 0.4 and that the frequency of allele a is 0.6, what is the frequency of genotypes AA, Aa, and aa?

– For a locus for which only two alleles are present in a population:• p2 + 2pq + q2 = 1 = (p + q)2

– Substitute p for the frequency of A (i.e., in this example p = 0.4) and q for the frequency of a (i.e., in this example q = 0.6)

• Frequency AA = p * p = p2

• Frequency aa = q * q = q2

• Frequency Aa = p * q + q * p = 2pq

• Frequency AA = 0.4 * 0.4 = 0.16• Frequency aa = 0.6 * 0.6 = 0.36• Frequency Aa = 0.4 * 0.6 + 0.6 * 0.4 = 0.48

– Keep in mind that:• p + q = 1, i.e.• p = 1 – q• q = 1 – p

– If a has a frequency of 0.01, then• Frequency AA = 0.99 * 0.99 = 0.98• Frequency Aa = 2 * 0.99 * 0.01 = 0.02• Frequency aa = 0.01 * 0.01 = 0.0001

– In this example there are 200 times more heterozygotes carrying the recessive allele than there are recessive homozygotes

– As recessive alleles become rare, many more carriers of this allele will be heterozygotes rather than homozygotes

Calculating genotype frequencies from allele frequencies

Hardy-Weinberg equilibrium only holds true if:

• No mutation • Large population• No migration• No selection• No selective mating

(Note: It is possible that balanced mutation and selection could exist)

Hardy-Weinberg equilibrium only holds true if:

• No mutation • Large population• No migration• No selection• No selective mating

Mutation

• Changes allele frequency since it involves the conversion of one allele into another allele

• Doesn’t play a large direct role in changing allele frequency because mutation rates per locus tend to be low

• Mutations rarely affect phenotype• However, all allelic variation ultimately has a mutational origin

• Mutation rates differ between species and between different regions of the genome of a single species, e.g. CpG islands

• Mutation rate may change in response to environmental stress, e.g. UV damage

• It is estimated that a human DNA sequence differs from that of one's parents at about 100 nucleotide positions

• These sites generally represent germline mutations that have arisen during the production of gametes in the parental generation

• The human mutation rate is higher in the male germ line (sperm) than the female (egg cells)

Hardy-Weinberg equilibrium only holds true if:

• No mutation • Large population• No migration• No selection• No selective mating

Evolution

• Evolution:– Change over time (many definitions!)– A process that results in heritable changes in a

population spread over many generations

• The two most important forces of evolution are:– Genetic drift– Selection

Genetic drift

• Varies with population size• If a population is finite in size – as all populations are –

and if a given pair of parents have only a small number of offspring, then the frequency of an allele/genotype will not be exactly reproduced in the next generation because of sampling error

• Each generation is an independent event• Results in a random increase or decrease in the

frequency of a given allele• The final result is that the population eventually drifts to

p=1 or p=0. After this point, no further change is possible; the population has become homozygous.

• This problem increases in magnitude as population sizes become smaller

Genetic drift

https://www3.nationalgeographic.com/genographic/population.html

Genetic drift

https://www3.nationalgeographic.com/genographic/population.html

Genetic drift

https://www3.nationalgeographic.com/genographic/population.html

Genetic drift

https://www3.nationalgeographic.com/genographic/population.html

Genetic drift

https://www3.nationalgeographic.com/genographic/population.html

Genetic drift

https://www3.nationalgeographic.com/genographic/population.html

Fixed allele

• A locus for which only a single allele exists for an entire gene pool

• The frequency of a fixed allele within a gene pool is 1.0

• An allele with a frequency of 0.0 is said to be extinct

• Remember: this allele may still exist in other populations!

Some types of genetic drift

• Two situations in which the effects of genetic drift are particularly dramatic include – Bottleneck– Founder effect

Bottleneck

• Population bottlenecks occur when a population's size is reduced for at least one generation, e.g. via a natural disaster

• Sampling error means the allele frequencies of the new population are not likely to match the allele frequencies in the original population

• Because genetic drift acts more quickly to reduce genetic variation in small populations, undergoing a bottleneck can reduce a population's genetic variation by a lot, even if the bottleneck doesn't last for very many generations

• The longer a population remains at a reduced size, the greater the effect of genetic drift on allele frequency

• Ultimately, the result of genetic bottlenecks is the loss of allelic variation, i.e., the fixing of alleles

http://cgland.inha.ac.kr/bbs/special/life-ori33.gif

Example of a genetic bottleneck: Bubonic plague

http://www.chobham.info/medieval.htm

One village: Surrey Heath

http://blue.utb.edu/paullgj/geog3320/lectures/populationgeography.html

Europe

Founder effect

• Occurs when a new colony is started by a few members of the original population (founders)

New population may have:• Reduced genetic variation from the original

population• A non-random sample of the genes in the original

population (sampling error)

• Term is frequently used when a deleterious allele can be traced to a founder or founders

http://www.blackwellpublishing.com/korfgenetics/figure.asp?chap=07&fig=Fig7-8

Example of a founder effect: Polydactyly in the Old Order Amish

• Lancaster county, Pennsylvania Old Order Amish founded by a small number of German immigrants: about 200 individuals

• High concentrations of rare inherited disorders, especially recessive

• Ellis-van Creveld syndrome (a form of dwarfism)– Short stature – Polydactyly (extra fingers or toes)– Abnormalities of the nails and teeth– A hole between the two upper chambers of the heart in about half the affected individuals

• Traced back to one couple, Samuel King and his wife, who came to the area in 1744

• In 1964, almost as many persons were known in this one kindred as had been reported in all the medical literature up to that time

http://www.pbs.org/wgbh/evolution/library/06/3/l_063_03.html

Example of a founder effect: Glaucoma caused by myocilin mutations

Hardy-Weinberg equilibrium only holds true if:

• No mutation • Large population• No migration• No selection• No selective mating

Gene flow (migration) between populations• Transfer of alleles from one population into another• Movement of an allele into or out of a population changes

allele frequency (either increasing or decreasing allele frequency)

Hardy-Weinberg equilibrium only holds true if:

• No mutation • Large population• Isolation from other populations• No selection• No selective mating

Natural selection

• Acts on an individual’s phenotype, which is exposed to the environment

• Individuals with favorable phenotypes are more likely to survive and reproduce than those with less favorable phenotypes

• Indirectly adapts a population to its environment by increasing (or maintaining) favorable genotypes in the gene pool

• Selection acting at the haploid stage reduces allele frequency directly

• Selection acting at the diploid stage reduces the contribution of genotypes to the gene pool

• The effect of natural selection is to reduce the absolute number of genotypes or alleles

• If the environment should change, selection responds by favoring phenotypes (genotypes) adapted to the new conditions, but the degree of adaptation can be extended only within the realm of the genetic variability present in the population or through the occurrence of new mutations

Selection: Sickle cell anemia

• Sickle cell anemia is a heritable blood disease that can cause red blood cell destruction and poor blood flow, resulting in a lack of oxygen to the body's tissues and damage.

• Persons who inherit the mutant hemoglobin gene from each parent develop sickle cell anemia.

• But those who inherit the variant gene from only one parent, and a normal gene from the other, are merely carriers of the sickle cell trait (dubbed heterozygous) who often display no signs of the disease.

• Heterozygous individuals are resistant to malaria. The beneficial aspects of the variant gene ensure its continued natural selection, despite the risk of disease if the gene is inherited from each parent.

http://www.dartmouth.edu/~toxmetal/TXQAfe.shtml

Selection: Sickle cell anemia

https://www3.nationalgeographic.com/genographic/population.html

Stabilizing (purifying) selection

• Genetic diversity decreases as the population stabilizes on a particular trait value

• Extreme values of the character are selected against• This is probably the most common mechanism of action for natural

selection

• Example: human birth weight– Babies of low weight lose heat more quickly are more likely to become ill from infections,

experience high rates of pulmonary and ocular problems, etc.– Babies of large body weight are more difficult to deliver through the pelvis

– However, improvements in neonatal care have increased survival of low birthweight infants– Rising rates of Caesarean sections in developed nations; many reasons, may include larger

size babies (improved nutrition, higher rates of diabetes)

Other types of selection

• Directional selection: Selection against only one phenotypic extreme

• Diversifying selection (disruptive selection): Selection against the intermediate form

• Sexual selection (sexual dimorphism, secondary sexual characteristics)– Phenotypic differences between males and females (other

than sexual organs); referred to as sexual dimorphisms or secondary sexual characteristics

– Sexual dimorphisms often are involved in mate procurement

• Intrasexual selection: Direct competition among individuals of one sex (usually the males in vertebrates) for mates of the opposite sex

• Intersexual selection (mate choice): Any trait that increases the attractiveness of an individual to members of the opposite gender will confer a selective advantage

Hardy-Weinberg equilibrium only holds true if:

• No mutation • Large population• Isolation from other populations• No selection• No selective mating

Correlation between spousal height

Women with shorter spouses

Tall men with tall wives!

Mom’s height (cm)

Da

d’s

he

igh

t (c

m)

Non-random (assortative) mating

• Positive assortative mating (of alike individuals) tends to increase homozygosity (more likely to share the same alleles)

• Negative assortative mating (of unlike individuals) tends to increase heterozygosity

http://anthro.palomar.edu/synthetic/synth_8.htm

http://anthro.palomar.edu/synthetic/synth_8.htm

http://anthro.palomar.edu/synthetic/synth_8.htm

Review

• HWE– Can be reached within one (or two) generations

– Can be used to calculate allele and genotype frequencies under conditions of equilibrium

• Mechanisms of microevolution– Mutation

– Genetic drift (e.g. bottlenecks, founder effect)

– Gene flow between populations (migration)

– Nonrandom mating

– Selection

ENDQuestions?