Hardy‐Weinberg Principle • Population genetics ‐ study of properties of genes in populations • Hardy‐Weinberg ‐ original proportions of genotypes in a population will remain constant from generation to generation – Sexual reproduction (meiosis and fertilization) alone will not change allelic (genotypic) proportions. 1
Hardy‐Weinberg Principle • Necessary assumptions Allelic frequencies would remain constant if… – population size is very large – random mating – no mutation – no gene input from external sources – no selection occurring
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FREQUENCY OF ALLELES IN THE POPULATIONS ≈ FREQUENCY OF ALLELES IN GAMETES
A
a
A
AA
Aa
a
Aa
aa
3
FREQUENCY OF ALLELES IN THE POPULATIONS ≈ FREQUENCY OF ALLELES IN GAMETES
A
a 0,9
A
AA 0,9
Aa 0,81
Aa
a 0,1
0,1
0,09 aa
0,09
0,01
4
FREQUENCY OF ALLELES IN THE POPULATIONS ≈ FREQUENCY OF ALLELES IN GAMETES
A
a 0,9
0,1 p
A
Aa
AA 0,9
q 0,09
0,81 p2
p a
Aa 0,1
aa 0,09
q
pq 0,01
pq
q2 5
FREQUENCY OF ALLELES IN THE POPULATIONS ≈ FREQUENCY OF ALLELES IN GAMETES
a
A 0,9
0,1 p
A
Aa
AA 0,9
q 0,09
0,81 p2
p a
Aa 0,1
aa 0,09
q
0,01 pq
AA 2Aa aa
pq
0,81 p2 0,18 2pq 0,01 q2
q2
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Hardy‐Weinberg Equilibrium
Population of cats n=100 16 white and 84 black bb = white B_ = black Can we figure out the allelic frequencies of individuals BB and Bb?
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Hardy‐Weinberg Principle • Calculate genotype frequencies with a binomial expansion (p+q)2 = p2 + 2pq + q2 • p2 = individuals homozygous for first allele • 2pq = individuals heterozygous for alleles • q2 = individuals homozygous for second allele
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Hardy‐Weinberg Principle 2 2 p + 2pq + q and
p+q = 1 (always two alleles) 16 cats white = 16bb then (q2 = 0.16) This we know we can see and count!!!!! If p + q = 1 then we can calculate p from q2 square root of q2 = q √.16 q=0.4 p + q = 1 then p=1‐q p = .6 (.6 +.4 = 1) p2 = .36 All we need now are those that are heterozygous (2pq) (2 x .6 x .4)=0.48 • .36 + .48 + .16 = 1
• • • • • • •
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Hardy‐Weinberg Equilibrium
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Five Agents of Evolutionary Change • 1‐Mutation – Mutation rates are generally so low they have little effect on Hardy‐Weinberg proportions of common alleles. • ultimate source of genetic variation
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Severe Autosomal Recessive disease
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• 2‐Gene flow – movement of alleles from one population to another • tend to homogenize allele frequencies
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Migrations
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Five Agents of Evolutionary Change • 3‐Nonrandom mating – assortative mating ‐ phenotypically similar individuals mate • Causes frequencies of particular genotypes to differ from those predicted by Hardy‐Weinberg.
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Five Agents of Evolutionary Change • 4‐Genetic drift – statistical accidents. •
Random fluctuations in the frequency of the appearance of a gene in a small isolated population, presumably owing to chance rather than natural selection.
– Frequencies of particular alleles may change by chance alone. • important in small populations – founder effect ‐ few individuals found new population (small allelic pool) – bottleneck effect ‐ drastic reduction in population, and gene pool size
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Genetic Drift ‐ Bottleneck Effect
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5‐Five Agents of Evolutionary Change
• Selection – Only agent that produces adaptive evolutionary change – artificial ‐ breeders exert selection – natural ‐ nature exerts selection
• variation must exist among individuals • variation must result in differences in numbers of viable offspring produced • variation must be genetically inherited – natural selection is a process, and evolution is an outcome
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Five Agents of Evolutionary Change • Selection pressures: – avoiding predators – matching climatic condition – pesticide resistance
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Natural Selection Biston Betularia
1848
Rare black animals
1900
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Severe Autosomal Recessive disease
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Next generation
Severe Autosomal Recessive disease
A
a
A
a
AA
81
162
‐‐
162
Aa
18
18
18
18
‐‐
2
‐‐
180
20
180
18
180/200
20/200
180/198
18/198
.9
.1
.91
.09
aa
1 lethal 100
AA
.91 x .91
.828
Aa
2 x .91 x .09
.164
aa
.09 x .09
.008
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Heterozygote Advantage • Heterozygote advantage will favor heterozygotes, and maintain both alleles instead of removing less successful alleles from a population.
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Measuring Fitness • Fitness is defined by evolutionary biologists as the number of surviving offspring left in the next generation. – relative measure • Selection favors phenotypes with the greatest fitness.
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Selection and H-W population analysis • Natural selection is caused by differential fitness • Fitness (w) is a measure of a genotype’s success at contributing to the next generation Survival or viability (v) Reproduction or fecundity (f) Fitness
w = (v)(f)
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Single locus, 2 alleles Alleles
A1
A2
Genotype
A1A1
A1A2
A2A2
Frequency
p2
2pq
q2
Absolute fitness*
w11
w12
w22
Mean fitness of population
w = p2 w11 + 2pq w12
+ q2 w22
*calculated directly from survival and viability data
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Result if w11 < w12 > w22 Heterozygous advantage (overdominance)
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Heterozygous Advantage w11=0.60
w12=1.00
w22=0.60
Intense selection without change in allele frequency!
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Heterozygote Advantage in man – Sickle cell anemia • Homozygotes exhibit severe anemia, have abnormal blood cells, and usually die before reproductive age. • Heterozygotes are less susceptible to malaria. 29
The Plasmodium life cycle
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Sickle Cell and Malaria
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Deleterious recessive alleles may, in some cases, provide a small benefit to heterozygotes Phenylketonuria (PKU) autosomal recessive
Heterozygous advantage in PKU seems to operate via protection against mycotoxins produced by Aspergillus and Penicillium that infest stored foods. Mild, wet climate of Ireland and W Scotland encourages mold growth; these areas have suffered repeated famines during which moldy food were eaten. Heterozygous (PKU) women have lower spontaneous abortion rate.
Solution? Test early. Treat w/ low-protein diet. 33
Classic PKU is caused by a complete or near-complete Deficiency of phenylalanine hydroxylase activity; without dietary restriction of phenylalanine, most Children with PKU develop profound and irreversible intellectual disability. PAH deficiency can be diagnosed by newborn screening in virtually 100% of cases based on detection of hyperphenylalaninemia using the Guthrie assay on a blood spot obtained from a heel prick.
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PKU Diet >> No mental retardation - aa will reproduce 1/10.000 incidence of the disease Aa 1/50 in the population aa x AA >>>>
Aa 100%
Expected phenotype >>> normal, but 35
Aa x AA >>> Aa the Maternal PKU Collaborative Study reports that even at maternal plasma Phe concentrations of 120-360 µmol/L, 6% of infants are born with microcephaly and 4% with postnatal growth retardation. If maternal plasma Phe concentrations are greater than 900 µmol/L, the risk is 85% for microcephaly, 51% for postnatal growth retardation, and 26% for intrauterine growth retardation. The risk for these abnormalities is both dose and time dependent. 36
The abnormalities that result from exposure of a fetus to high maternal plasma Phe concentration are the result of 'maternal HPA/PKU' . The likelihood that the fetus will have congenital heart disease, Intrauterine and postnatal growth retardation, microcephaly, and intellectual disability depends upon the severity of the maternal HPA and the effectiveness of the mother's dietary management.
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Population
PAH Deficiency in Live Births
Carrier Rate
Citation
Turks
1/2,600
1/26
Ozalp et al [1986]
Irish
1/4,500
1/33
DiLella et al [1986]
Northern European heritage, East Asian
1/10,000
1/50
Scriver & Kaufman [2001]
Japanese
1/143,000
1/200
Aoki & Wada [1988]
Finnish, Ashkenazi Jewish
1/200,000
1/225
Scriver & Kaufman [2001]
African
~1/100,000
?
Anecdotal
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Cystic fibrosis, (CF), AR disease, affects lungs, sweat glands and digestive system. It is caused by the malfunction of the CFTR protein, which controls intermembrane transport of chloride ions, which is vital to maintaining equilibrium of water in the body. The malfunctioning protein causes viscous mucus to form in the lungs and intestinal tract. In the past children born with CF had a life expectancy of only a few years, now increased to adulthood. However, even in these individuals, male and female, CF typically causes sterility. It is the most common genetic disease among people of European descent. Approximately 1/25 persons of European descent is a carrier, and 1 in 2500 to 3000 children born is affected by cystic fibrosis.
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In CF carriers, survivorship is influenced in relation to diseases involving loss of body fluid, typically due to diarrhea. The most common of them is cholera, patients often die of dehydration due to intestinal water losses. In a mouse model of CF the heterozygote (carrier) mouse had less secretory diarrhea than normal, non-carrier mice. Thus resistance to cholera explained the selective advantage to being a carrier for CF and why the carrier state was so frequent. A second theory is that CF mutation provides resistance to tuberculosis, which was responsible for 20% of all European deaths between 1600 and 1900, so even partial protection against the disease could account for the current high gene frequency.
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Aa frequency
Risk for affected children
Incidence of disease
1/30
1/30 x 1/30 x 1/4
1/3,600
1/50
1/50 x 1/50 x 1/4
1/10,000
1/100
1/100 x 1/100 x 1/4 1/40,000
If I know the incidence of the disease, I can calculate easily the number of Aa in the population 41
I I:1
I:2
II II:1
II:2
II:3 II:2
II:3 1/10,000
1 x 1/50 x 1/4
1/200 affected
II:3 II:2 status not known
199/200 unaffected
1/10,000 2/3 x 1/50 x1/4
1/300 affected
299/300 unaffected
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