Chpt. 23 The Evolution of Populations-- Population Genetics
Dec 14, 2015
PopulationsPopulations = unit of evolution
Natural selectionNatural selection =
mechanism of evolution
GradualismGradualism =
accumulation of small changes in
gene pool over LONG periods of
time
Hardy-WeinbergHardy-Weinberg TheoremTheorem
examines the gene structure of a NON-evolving population
Hardy-WeinbergHardy-Weinberg TheoremTheorem examines the gene
structure of a NON-evolving population.
Obviously, this is not common, however, gives a base-line / model NULL HYPOTHESIS for determining if and why populations evolve
Hardy-WeinbergHardy-Weinberg TheoremTheorem even though alleles are shuffled and recombined during meiosis and random
fertilization.This has no effect on This has no effect on the the overalloverall gene pool gene pool
percentages.percentages.
Hardy-WeinbergHardy-Weinberg TheoremTheorem
Gene pool frequenciesGene pool frequencies
(percentages) will (percentages) will
remainremain unchangedunchanged if if nono
mechanismmechanism thatthat cancan
causecause evolutionevolution toto
occuroccur actsacts onon aa
populationpopulation..
Hardy-WeinbergHardy-Weinberg TheoremTheoremGene pool frequencies Gene pool frequencies
will remain unchanged will remain unchanged if:if:
Mutations are not occurring
Hardy-WeinbergHardy-Weinberg TheoremTheoremGene pool frequencies Gene pool frequencies
will remain unchanged will remain unchanged if:if:
Natural selection is not occurring
Hardy-WeinbergHardy-Weinberg TheoremTheoremGene pool frequencies Gene pool frequencies
will remain unchanged will remain unchanged if:if:
Population is LARGE
Hardy-WeinbergHardy-Weinberg TheoremTheoremGene pool frequencies Gene pool frequencies
will remain unchanged will remain unchanged if:if:
EVERYONE breeds…
Hardy-WeinbergHardy-Weinberg TheoremTheoremGene pool frequencies Gene pool frequencies
will remain unchanged will remain unchanged if:if:
EVERYONE randomly mates…
Hardy-WeinbergHardy-Weinberg TheoremTheoremGene pool frequencies Gene pool frequencies
will remain unchanged will remain unchanged if:if:
EVERYONE produces the same number of offspring
Hardy-WeinbergHardy-Weinberg TheoremTheoremGene pool frequencies Gene pool frequencies
will remain unchanged will remain unchanged if:if:
NOONE migrates in or out of the population… everyone stays
5 Agents of evolutionary change:Mutation Gene Flow (migration)
Genetic Drift (same # of offspring) Selection
Non-random mating
Hardy-WeinbergHardy-Weinberg TheoremTheorem
remember:remember: H.W. H.W. explains: explains: the the
frequencyfrequency of allelesof alleles remainsremains constantconstant in a in a population… population… unless unless
acted upon by agents acted upon by agents OTHER THAN sexual OTHER THAN sexual recombination.recombination.
Hardy-Weinberg Hardy-Weinberg Principle Principle
p2 + 2pq + q2 = 1p2 + 2pq + q2 = 1
Mathematical statement Mathematical statement about the relative about the relative frequency of alleles frequency of alleles (genotypes) in a (genotypes) in a population.population.p +q = 1p +q = 1
Hardy-WeinbergHardy-Weinberg TheoremTheorem
Frequency of alleles Frequency of alleles remainsremains constantconstant in a in a population, population, unless unless acted upon by agents acted upon by agents OTHER THAN sexual OTHER THAN sexual recombination.recombination.InheritanceInheritance doesdoes notnot causecause changeschanges inin alleleallele frequencyfrequency..
Hardy-Weinberg Hardy-Weinberg Principle Principle
p + q = 1p + q = 1
p = frequency of p = frequency of dominant dominant allele allele
Hardy-Weinberg Hardy-Weinberg Principle Principle
p + q = 1p + q = 1
q = frequency of q = frequency of recessive recessive allele allele
Hardy-Weinberg Hardy-Weinberg Principle Principle
in most cases, we in most cases, we only know the only know the phenotypic phenotypic frequenciesfrequencies
Mathematical statement Mathematical statement about the relative about the relative frequency of alleles frequency of alleles (genotypes) in a (genotypes) in a population.population.
Hardy-Weinberg Hardy-Weinberg Principle Principle
qq2 2 = # of aa = # of aa individualsindividuals
qq22 = frequency of = frequency of homozygotehomozygote recessiverecessive individualsindividuals
Hardy-Weinberg Hardy-Weinberg Principle Principle
pp2 2 = # of AA = # of AA individualsindividuals
pp22 = frequency of = frequency of homozygotehomozygote dominantdominant individualsindividuals
Hardy-Weinberg Hardy-Weinberg Principle Principle
p = # of (AA) + 2 p = # of (AA) + 2 (# Aa)(# Aa)
p = frequency of p = frequency of dominantdominant alleleallele
Hardy-Weinberg Hardy-Weinberg Principle Principle
q = # of (aa) + 2 q = # of (aa) + 2 (# Aa)(# Aa)
q = frequency of q = frequency of recessiverecessive alleleallele
Hardy-Weinberg Hardy-Weinberg Principle Principle
2pq2pq = # of Aa = # of Aa individualsindividuals
2pq = frequency of 2pq = frequency of heterozygoteheterozygote individualsindividuals
Hardy-Weinberg Hardy-Weinberg Principle Principle by comparing genotypic by comparing genotypic frequencies from one frequencies from one generation to the next, generation to the next, you can learn you can learn whetherwhether oror notnot evolution has evolution has occurred…occurred…
Hardy-Weinberg Hardy-Weinberg Principle Principle if genotypic if genotypic frequencies have frequencies have changed from your changed from your original count… original count…
evolution has evolution has occurred!occurred!
Suppose there are 1,000 individuals in a population
Genotype Number Genotypic Frequency AA 490 0.49
Aa 420 0.42
aa 90 0.09
total 1000 1.00
Suppose there are 1,000 individuals in a population
Genotypic Frequency 0.49
0.42
0.09
total 1.00
Genotypic frequency = the proportion of a particular genotype found in a
population
AA
Aa
aa
Suppose there are 1,000 individuals in a population
Phenotype Number Phenotypic Frequency dominant 9100.91
recessive 900.09
total 10001.00
Suppose there are 1,000 individuals in a population
Phenotypic Frequency 0.91
0.09
total 1.00
Phenotypic frequency = the proportion of a particular phenotype found in a population
Suppose there are 1,000 individuals in a population
Allele Number Allele Frequency A 1400 0.7
a 4200.3
total 20001.00
480
Allele frequency
Pssst…(There are 1,000 copies of the flower color gene in this population of 500 total flowers…)
q =
q = frequen
cy of recessi
ve allele
However, we do
not know how
many a’s
there are
just by looking
at phenoty
pe
480
Allele frequency
q = .2
q = frequen
cy of recessi
ve allele
p = frequen
cy of dominan
t allele
p + q = 1p + .2 = 1p = 1 - .2p = .8
480
Some of the pink Some of the pink flowers will be AA and flowers will be AA and some will be Aasome will be Aa
p2 + 2pq + q2 = p2 + 2pq + q2 = 11
p = .8 q = .2
480
Some of the pink Some of the pink flowers will be AA and flowers will be AA and some will be Aasome will be Aa
.64 + .32 + .04 .64 + .32 + .04 = 1= 1
480
How many of the pink How many of the pink flowers will be AA and flowers will be AA and how many will be Aahow many will be Aa
.64 X 500 .64 X 500 individualsindividuals320 individuals are 320 individuals are AAAA
480
How many of the pink How many of the pink flowers will be AA and flowers will be AA and how many will be Aahow many will be Aa
.32 X 500 .32 X 500 individualsindividuals160 individuals are 160 individuals are AaAa
Hardy-Weinberg Hardy-Weinberg Principle Principle
Under ideal conditions, the relative allele frequencies are the same in the offspring generation as in the parent generation.
pp22 + 2pq + + 2pq + qq22 = 1 = 1
IFIF: frequencies in a population deviate from Hardy-Weinberg (these are set numbers)…
THENTHEN: we know the population is evolving.
Oh Hardy, why did you quit your job at
ABERCROMBIE?
Weinburg, I keep telling you, I got
sick of changing genes!!!
changechange overover timetime is a result of is a result of changes in a changes in a population’s population’s frequency of frequency of genotypes genotypes / /
geneticgenetic
Lets Hardy!!What percentage of the human population are carriers for the allele for PKU?
1 out of 10,000 babies are born with this1 out of 10,000 babies are born with this recessiverecessive disease disease
Most of the time you will Most of the time you will begin by determining the begin by determining the
frequency of the frequency of the homozygoushomozygous recessiverecessive genotypegenotype
Find q2 Find q2 (frequency of homo (frequency of homo recessive)recessive)
Lets Hardy!!What percentage of the human population are carriers for the allele for PKU?
1 out of 10,000 babies are born with this1 out of 10,000 babies are born with this recessiverecessive disease disease
Hint: q2 = 1 / 10,000 Hint: q2 = 1 / 10,000 (frequency of aa)(frequency of aa)
Find qFind q
Find p Find p Find Find pqpq
AP Problems Using AP Problems Using Hardy-WeinbergHardy-Weinberg
• Solve for q2 (% of total)
• Solve for q (equation)
• Solve for p (1- q)
• H-W is always on the national AP Bio exam (but no calculators are allowed).
AP Problems Using AP Problems Using Hardy-WeinbergHardy-Weinberg
• Solve for q2 (% of total)
• Solve for q (equation)
• Solve for p (1- q)
• H-W is always on the national AP Bio exam (but no calculators are allowed).
AP Problems Using AP Problems Using Hardy-WeinbergHardy-Weinberg
• Solve for q2 (% of total)
• Solve for q (equation)
• Solve for p (1- q)
• H-W is always on the national AP Bio exam (but no calculators are allowed).
AP Problems Using AP Problems Using Hardy-WeinbergHardy-Weinberg
• Solve for q2 (% of total)
• Solve for q (equation)
• Solve for p (1- q)
• H-W is always on the national AP Bio exam (but no calculators are allowed)
AP Problems Using AP Problems Using Hardy-WeinbergHardy-Weinberg
population: 100 cats84 black, 16 whiteHow many of each genotype?
population: 100 cats84 black, 16 whiteHow many of each genotype?
q2 (bb): 16/100 = .16
q (b): √.16 = 0.40.4
p (B): 1 - 0.4 = 0.60.6
q2 (bb): 16/100 = .16
q (b): √.16 = 0.40.4
p (B): 1 - 0.4 = 0.60.6
bbBbBB
p2=.36p2=.36 2pq=.482pq=.48 q2=.16q2=.16
AP Problems Using AP Problems Using Hardy-WeinbergHardy-Weinberg
bbBbBB
p2=.36p2=.36 2pq=.482pq=.48 q2=.16q2=.16
Assuming H-W equilibriumAssuming H-W equilibrium
Sampled data Sampled data bbBbBB
p2=.20p2=.20 2pq=.642pq=.64 q2=.16q2=.16
How do you explain the data? How do you explain the data?
Null hypothesis Null hypothesis