Population Genetics: Hardy

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Population Genetics: Hardy-Weinberg
5 Conditions for Null Model
1) No Migration
2) No Genetic Drift/ random effects
3) Random Mating
4) No Mutation
5) No Selection
Calculation of allele frequencies:
Genotype frequencies AA(.8) Aa(.10) aa (.10)
Allele frequencies p= .8 + (.10)(1/2)= .85
q= .10 + (.10)(1/2)= .15
Calculation of genotype frequencies:
p=.75 q=.25
f(AA)= p2= 0.5625 f(Aa) = 2pq= 0.375 f(aa)= q2= .0625
Checking if a population is under Hardy-Weinberg:
Calculate allele frequencies, calculate genotype frequencies expected if
population is under H-W and compare it to the observed genotype frequency.
Population Genetics: Natural Selection
3 requirements for Evolution by Natural Selection
1) Phenotypic variation
2) Inheritance of variants
3) Differences in fitness are associated with variants
Natural Selection…
- Acts on individuals, evolutionary change occurs in populations
- Acts on phenotypes, evolution is change in allele frequencies
- Mechanical
- Non-random, but not progressive.
- Causes adaptation
Absolute fitness- Percentage survival overall
Relative fitness(W)- How well one genotype does relative to other genotypes
- Divide by the genotype with the greatest fitness.
Selection Coefficient (1-W)
Mean population fitness (Wbar)= p2(WAA) +2pq(WAa) + q2(Waa)
Tells what population is composed of after selection
New genotype frequencies after selection
f(AA’)=p2WAA/ Wbar
f (Aa’)= 2pqWAa/ Wbar
f (aa’)=q2Waa/ Wbar
New Allele frequencies after selection
f(A’)= p’= f(AA’) + ½ f (Aa’)
f(a’)=q’= f(aa’)+ ½ f (Aa’)
How much evolution has happened?
∆P=p’-p
- If negative, the frequency has decreased by that amount.
Eugenics- Increase in quality of species by elimination of less fit individuals
Population Genetics: Genetic Drift
Genetic Drift- The intrusion of random events into the genetics of a population
Population size
- The probability of an allele getting fixed is equal to its starting frequency
- Smaller population sizes are fixed faster and fluctuate more
- Larger population sizes- allele frequency doesn’t change as much
- The smaller the population size, the faster lose of heterozygosity
Population structure- random mating going on in subpopulations but not in the population
- Decreases heterozygosity
- Increases drift
Effective population size- size of an ideal population that shows the same decrease in
heterozygosity as the population in question
1. Unequal Sex Ratio
Makes population behavior smaller than they are. Male groups are going to be
overrepresented in next population relative to genes of any given female.
2. Population size fluctuation
Bottleneck- small population size, sampling small section o the population
Founder effect- allele frequencies in new population are different from the source
population.
3. Variation in reproductive success
-All individuals don’t contribute equal to the genepool because not having the
same number of offspring.
Conservation Genetics
- Northern elephant seal: highly hunted and experienced bottleneck. No
heterozygosity exists. Genetic variation lost at all loci.
-collard lizards in ozarks: drift occurs which lead to fixation of different genetic
types.
Population Genetics: Inbreeding
Genotype frequencies
Decreases heterozygosity
Increases homozygosity
Allele frequencies- Inbreeding doesn’t change
The more they are related, the faster the loss in heterozygosity
F: Inbreeding Coefficient
: Measure of the decrease in the frequency of heterozygotes relative to random mating
0- No inbreeding, complete outcrossing 1- completely inbreed
To calculate need to take into account all alleles and add them together
Adjusting H-W for interbreeding
f(AA)= p2(1-F) + pF
f(aa)=q2(1-F) + qF
f(Aa)=2pq(1-F)
If F=0 get H-W so f(AA)=p2
If F=1 complete inbreeding f(AA)=p
Consequences of Inbreeding
1. Inbreeding depression- reduction in fitness associated with inbreeding due to
expression of these recessive deleterious alleles.
2. Habitual inbreeding- inbreeding as a habit
a. Ex. Plants self all the time and selection purges the genome of deleterious
alleles from population.
b. In Sri Lanka there is ritual mating of 1st cousins so they have no lethal
genes in their genome.
Prairie chicken- bottleneck effect and founder effect occurred so imported prarie chickens
form different state
Maintenance of Genetic Variation
Mutation
1. Mutation rates
a. Point mutation- nucleotide substitution
b. Chromosomal inversion- double stranded break and reannneals
c. Translocation- swapping of a portion at 2 nonhomologous
chromosomes. Changes which genes are next to each other
2. Importance to evolution
a. It causes a change in allele frequency but is a weak evolutionary force.
It does not maintain genetic variation
b. Mutation takes a long time to produce appreciable changes in allele
frequency
3. Mutation-selection balance
a. A (u) a (s)
b. Mutation switches A to at a rate of u. Selection acts to remove
mutations that aren’t beneficial. When s cancels with u get balance.
c. Mutation Selection Balance- When the rate at which copies of a
deleterious allele are being eliminated by selection is equal to the rate
at which new copies are created by mutation.
d. q*: frequency of a allele at mutation/selection balance (√(u/s))
u= mutation rate, s= selection coefficient
If the s is small, the allele is mildly deleterious then u will be high and
the equilibrium frequency will be high.
4. Migration as an evolutionary process
a. pI= frequency of allele A1 in island pop. pC= frequency of A1 in
mainland population
b. How does the frequency of A1 on the island change as a result of
migration pI’= (1-m)(pI) +mpC pI(t)=pI (t-1)(1-m) + mpC
c. (1-m)fraction of population that aren’t migrants, mpC fraction of
migrants
5. Frequency-dependent Selection
a. Positive frequency dependence- as the allele becomes more common,
its fitness effects increase. Leads to fixation
b. Negative frequency dependence- as allele becomes rare, it becomes
less fit. Maintains genetic variation.
c. When fitness of individuals with a particular phenotype depends on the
frequency in the population
Terms for Laura Galloway’s section Biology 302:
p: frequency of the A allele
q: Frequency of the a allele
W: relative fitness for each genotype
s: selection coefficient. 1-W
Wbar: mean population fitness. =p2(Waa)+2pq(WAa)+q2(Waa)
Ne: effective population size. The size of an idealized population that shows the same
amount of genetic drift as the population of interest. Smaller than the actual population.
F: the inbreeding coefficient. The probability that two alleles are identical by descent
u: mutation rate
q*: frequency of a allele at mutation/selection balance (=square root (u/s))
m: proportion of a population that is made up of migrants
QTL: quantitative trait loci
h2: narrow sense heritability (VA/VP)
VP: phenotypic variation
VA: additive genetic variance
VD: dominance genetic variance
VI: interaction genetic variance (more than one locus contributes to trait)
VG: genetic variance.=Va+Vd+Vi
VE: environmental variance
VGXE: genetic by environment interaction variance
Xbarp: mean phenotype of parent population
Xbars: mean phenotype of parent population after selection
Xbaro: mean phenotype of offspring of parent population after selection
S: selection differential (Xbars- Xbarp)
R: response to selection (XbarO- Xbarp)(h2S)
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