population genetics with qs
TRANSCRIPT
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Population
Genetics
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The Gene PoolThe Gene Pool
•Members of a species can interbreed & produce fertile offspring
•Species have a shared gene pool
•Gene pool – all of the alleles of all individuals in a population
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The Gene PoolThe Gene Pool
•Different species do NOT exchange genes by interbreeding
•Different species that interbreed often produce sterile or less viable offspring e.g. Mule
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Populations
•A group of the same species living in an area
•No two individuals are exactly alike (variations)
•More Fit individuals survive & pass on their traits
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Speciation
•Formation of new species
•One species may split into 2 or more species
•A species may evolve into a new species
•Requires very long periods of time
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Modern Evolutionary Thought
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Modern Synthesis TheoryModern Synthesis Theory
•Combines Combines Darwinian Darwinian selectionselection and and Mendelian Mendelian inheritanceinheritance
•Population Population geneticsgenetics - study of - study of genetic variation genetic variation within a populationwithin a population
•Emphasis on Emphasis on quantitative quantitative characterscharacters
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Modern Synthesis TheoryModern Synthesis Theory
•1940s – 1940s – comprehensive comprehensive theory of evolution theory of evolution (Modern Synthesis (Modern Synthesis Theory)Theory)
•Introduced by Fisher Introduced by Fisher & Wright& Wright
•Until thenUntil then, many did , many did not accept that not accept that Darwin’s theory of Darwin’s theory of natural selection natural selection could drive evolutioncould drive evolution
S. Wright
A. Fisher
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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
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Microevolution
•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 MICROEVOLUTION
•Example: Bacteria becoming unaffected by antibiotics (resistant)
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Allele 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
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Species & Populations
•PopulationPopulation - a localized group of individuals of the same species.
•SpeciesSpecies - a group of populations whose individuals have the ability to breed and produce fertile offspring.
•Individuals near a population Individuals near a population centercenter are, on average, more closely related to one another than to members of other populations.
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Gene Pools
•A population’s gene poolgene pool is the total of all genes in the population at any one time.
•If all members of a population are homozygous for a particular allele, then the allele is fixed in the gene pool.
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The Hardy-Weinberg TheoremThe Hardy-Weinberg Theorem
•Used to describe a non-non-evolving population.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.
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The Hardy-Weinberg TheoremThe Hardy-Weinberg Theorem
•Deviation from Hardy-Weinberg equilibrium usually results in evolution
•Understanding a non-evolving population, helps us to understand how evolution occurs
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Assumptions of the H-W TheoremAssumptions of the H-W Theorem
1.Large population size - small populations can have chance 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
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Assumptions of the H-W TheoremAssumptions of the H-W Theorem
3.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.
4.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.
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Hardy-Weinberg Equilibrium The gene pool of a non-evolving population remains constant over multiple generations; i.e., the allele frequency does not change over generations of time. The Hardy-Weinberg Equation: 1.0 = p2 + 2pq + q2
where p2 = frequency of AA genotype; 2pq = frequency of Aa plus aA genotype; q2 = frequency of aa genotype
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But we know that evolution does occur within populations.
Evolution within a species/population = microevolution.
Microevolution refers to changes in allele frequencies in a gene pool from generation to generation. Represents a gradual change in a population.
Causes of microevolution: 1) Genetic drift
2) Natural selection (1 & 2 are most important)
3) Gene flow
4) Mutation
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1) Genetic drift
Genetic drift = the alteration of the gene pool of a small population due to chance.
Two factors may cause genetic drift: a) Bottleneck effect may lead to reduced genetic
variability following some large disturbance that removes a large portion of the population. The surviving population often does not represent the allele frequency in the original population.
b) Founder effect may lead to reduced variability when a few individuals from a large population colonize an isolated habitat.
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*Yes, I realize that this is not really a cheetah.
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2) Natural selection As previously stated, differential success in reproduction based on heritable traits results in selected alleles being passed to relatively more offspring (Darwinian inheritance).
The only agent that results in adaptation to environment.
3) Gene flow -is genetic exchange due to the migration of fertile individuals or gametes between populations.
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4) Mutation Mutation is a change in an organism’s DNA and is represented by changing alleles. Mutations can be transmitted in gametes to offspring, and immediately affect the composition of the gene pool.
The original source of variation.
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Genetic Variation, the Substrate for Natural Selection Genetic (heritable) variation within and between populations: exists both as what we can see (e.g., eye color) and what we cannot see (e.g., blood type). Not all variation is heritable.
Environment also can alter an individual’s phenotype [e.g., the hydrangea we saw before, and…
…Map butterflies (color changes are due to seasonal difference in hormones)].
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Variation within populations
Most variations occur as quantitative characters (e.g., height); i.e., variation along a continuum, usually indicating polygenic inheritance.
Few variations are discrete (e.g., red vs. white flower color).
Polymorphism is the existence of two or more forms of a character, in high frequencies, within a population. Applies only to discrete characters.
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Variation between populations
Geographic variations are differences between gene pools due to differences in environmental factors.
Natural selection may contribute to geographic variation.
It often occurs when populations are located in different areas, but may also occur in populations with isolated individuals.
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Geographic variation between isolated populations of house mice.
Normally house mice are 2n = 40. However, chromosomes fused in the mice in the example, so that the diploid number has gone down.
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Cline, a type of geographic variation, is a graded variation in individuals that correspond to gradual changes in the environment.
Example: Body size of North American birds tends to increase with increasing latitude. Can you think of a reason for the birds to evolve differently? Example: Height variation in yarrow along an altitudinal gradient. Can you think of a reason for the plants to evolve differently?
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Mutation and sexual recombination generate genetic variation a. New alleles originate only by mutations (heritable only in gametes; many kinds of mutations; mutations in functional gene products most important). - 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.)
b. Sexual recombination is the source of most genetic differences between individuals in a population. - Vast numbers of recombination possibilities result in varying genetic make-up.
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Diploidy and balanced polymorphism preserve variation a. Diploidy often hides genetic variation from selection in the form of recessive alleles.
Dominant alleles “hide” recessive alleles in heterozygotes. b. Balanced polymorphism is the ability of natural selection to maintain stable frequencies of at least two phenotypes. Heterozygote advantage is one example of a balanced polymorphism, where the heterozygote has greater survival and reproductive success than either homozygote (Example: Sickle cell anemia where heterozygotes are resistant to malaria).
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Frequency-dependent selection = survival of one phenotype declines if that form becomes too common.
(Example: Parasite-Host relationship. Co-evolution occurs, so that if the host becomes resistant, the parasite changes to infect the new host. Over the time, the resistant phenotype declines and a new resistant phenotype emerges.)
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Neutral variation is genetic variation that results in no competitive advantage to any individual. - Example: human fingerprints.
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A Closer Look: Natural Selection as the Mechanism of Adaptive Evolution Evolutionary fitness - Not direct competition, but instead the difference in reproductive success that is due to many variables.
Natural Selection can be defined in two ways: a. Darwinian fitness- Contribution of an individual to the gene pool, relative to the contributions of other individuals.
And,
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b. Relative fitness
- Contribution of a genotype to the next generation, compared to the contributions of alternative genotypes for the same locus.
- Survival doesn’t necessarily increase relative fitness; relative fitness is zero (0) for a sterile plant or animal.
Three ways (modes of selection) in which natural selection can affect the contribution that a genotype makes to the next generation. a. Directional selection favors individuals at one end of the phenotypic range. Most common during times of environmental change or when moving to new habitats.
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Directional selection
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Diversifying selection favors extreme over intermediate phenotypes.
- Occurs when environmental change favors an extreme phenotype.
Stabilizing selection favors intermediate over extreme phenotypes.
- Reduces variation and maintains the current average.
- Example = human birth weights.
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Diversifying selection
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Natural selection maintains sexual reproduction
-Sex generates genetic variation during meiosis and fertilization.
-Generation-to-generation variation may be of greatest importance to the continuation of sexual reproduction.
-Disadvantages to using sexual reproduction: Asexual reproduction produces many more offspring.
-The variation produced during meiosis greatly outweighs this disadvantage, so sexual reproduction is here to stay.
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All asexual individuals are female (blue). With sex, offspring = half female/half male. Because males don’t reproduce, the overall output is lower for sexual reproduction.
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Sexual selection leads to differences between sexes
a. Sexual dimorphism is the difference in appearance between males and females of a species.
-Intrasexual selection is the direct competition between members of the same sex for mates of the opposite sex.
-This gives rise to males most often having secondary sexual equipment such as antlers that are used in competing for females.
-In intersexual selection (mate choice), one sex is choosy when selecting a mate of the opposite sex.
-This gives rise to often amazingly sophisticated secondary sexual characteristics; e.g., peacock feathers.
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Natural selection does not produce perfect organisms a. Evolution is limited by historical constraints (e.g., humans have back problems because our ancestors were 4-legged). b. Adaptations are compromises. (Humans are athletic due to flexible limbs, which often dislocate or suffer torn ligaments.) c. Not all evolution is adaptive. Chance probably plays a huge role in evolution and not all changes are for the best. d. Selection edits existing variations. New alleles cannot arise as needed, but most develop from what already is present.
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Genes Within Populations
Chapter 21
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Gene Variation is Raw Material
Natural selection and evolutionary changeSome individuals in a population possess certain
inherited characteristics that play a role in producing more surviving offspring than individuals without those characteristics.
The population gradually includes more individuals with advantageous characteristics.
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Gene Variation In Nature
Measuring levels of genetic variationblood groups – 30 blood grp genesEnzymes – 5% heterozygous
Enzyme polymorphismA locus with more variation than can be explained by
mutation is termed polymorphic.Natural populations tend to have more polymorphic loci
than can be accounted for by mutation.15% Drosophila5-8% in vertebrates
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Hardy-Weinberg Principle
Population genetics - study of properties of genes in populationsblending inheritance phenotypically intermediate
(phenotypic inheritance) was widely acceptednew genetic variants would quickly be diluted
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Hardy-Weinberg Principle
Hardy-Weinberg - original proportions of genotypes in a population will remain constant from generation to generationSexual reproduction (meiosis and fertilization) alone
will not change allelic (genotypic) proportions.
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Hardy-Weinberg Equilibrium
Population of cats n=10016 white and 84 blackbb = whiteB_ = black
Can we figure out the allelic frequencies of individuals BB and Bb?
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Hardy-Weinberg Principle
Necessary assumptionsAllelic frequencies would remain constant if…population size is very largerandom matingno mutationno gene input from external sourcesno selection occurring
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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 allele2pq = individuals heterozygous for allelesq2 = individuals homozygous for second allele
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p2 + 2pq + q2
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
Q = square root of q2 = q √.16 q=0.4p + q = 1 then p = .6 (.6 +.4 = 1)P2 = .36All we need now are those that are
heterozygous (2pq) (2 x .6 x .4)=0.48
.36 + .48 + .16
Hardy-Weinberg Principle
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Hardy-Weinberg Equilibrium
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Five Agents of Evolutionary Change
MutationMutation rates are generally so low they have little
effect on Hardy-Weinberg proportions of common alleles.
ultimate source of genetic variation
Gene flowmovement of alleles from one population to another
tend to homogenize allele frequencies
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Five Agents of Evolutionary Change
Nonrandom matingassortative mating - phenotypically similar individuals
mateCauses frequencies of particular genotypes to
differ from those predicted by Hardy-Weinberg.
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Five Agents of Evolutionary Change
Genetic drift – statistical accidents.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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Five Agents of Evolutionary Change
Selection – Only agent that produces adaptiveevolutionary changeartificial - breeders exert selection natural - nature exerts selection
variation must exist among individualsvariation must result in differences in numbers of
viable offspring producedvariation 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 predatorsmatching climatic conditionpesticide resistance
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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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Interactions Among Evolutionary Forces
Levels of variation retained in a population may be determined by the relative strength of different evolutionary processes.
Gene flow versus natural selectionGene flow can be either a constructive or a
constraining force.Allelic frequencies reflect a balance between
gene flow and natural selection.
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Natural Selection Can Maintain Variation
Frequency-dependent selectionPhenotype fitness depends on its frequency within the
population.Negative frequency-dependent selection favors rare
phenotypes.Positive frequency-dependent selection eliminates
variation.
Oscillating selectionSelection favors different phenotypes at different times.
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Heterozygote Advantage
Heterozygote advantage will favor heterozygotes, and maintain both alleles instead of removing less successful alleles from a population.Sickle cell anemia
Homozygotes exhibit severe anemia, have abnormal blood cells, and usually die before reproductive age.
Heterozygotes are less susceptible to malaria.
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Sickle Cell and Malaria
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Forms of Selection
Disruptive selectionSelection eliminates intermediate types.
Directional selectionSelection eliminates one extreme from a phenotypic
array.
Stabilizing selectionSelection acts to eliminate both extremes from an
array of phenotypes.
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Kinds of Selection
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Selection on Color in Guppies
Guppies are found in small northeastern streams in South America and in nearby mountainous streams in Trinidad.Due to dispersal barriers, guppies can be found in
pools below waterfalls with high predation risk, or pools above waterfalls with low predation risk.
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Evolution of Coloration in Guppies
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Selection on Color in Guppies
High predation environment - Males exhibit drab coloration and tend to be relatively small and reproduce at a younger age.
Low predation environment - Males display bright coloration, a larger number of spots, and tend to be more successful at defending territories.In the absence of predators, larger, more colorful fish
may produce more offspring.
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Evolutionary Change in Spot Number
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Limits to Selection
Genes have multiple effectspleiotropy
Evolution requires genetic variationIntense selection may remove variation from a
population at a rate greater than mutation can replenish.
thoroughbred horses
Gene interactions affect allelic fitnessepistatic interactions
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Variations in genotype arise by random fusion of gametes, mutation, and ______.
85
25% 25%25%25%
201 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30
1.Recombination2.Translation3.Transcription4.Sorting by
phenotype
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The total genetic information in a population is called the
86
Allele fr
equency
Phenotype fr
equency
Gene pool
Dist
ribution of t
raits
25% 25%25%25%
201 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30
1.Allele frequency2.Phenotype
frequency3.Gene pool4.Distribution of
traits
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Saint Bernards and Chihuahuas can’t mate normally owing to great differences in size. What type of reproductive isolationg mechanism is operating here?
87
Deve
lopmental
Prezy
gotic
Postzygo
tic
Geogra
phic
25% 25%25%25%
201 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30
1.Developmental2.Prezygotic3.Postzygotic4.Geographic
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If a population is in genetic equilibrium,
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Evolution is
occurin
g
Specia
tion is occ
uring
Allelic
frequencie
s are c.
..
Allelic
frequencie
s are r.
..
25% 25%25%25%
201 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30
1.Evolution is occuring
2.Speciation is occuring
3.Allelic frequencies are changing
4.Allelic frequencies are remaining stable
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Mutations affect genetic equilibrium by
89
Maintai
ning it
Intro
ducing n
e...
Causing im
migr...
Causing emigr
a...
25% 25%25%25%
201 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30
1.Maintaining it2.Introducing new
alleles3.Causing
immigration4.Causing
emigration
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Directional selection, disruptive selection, and stabilizing selection are all examples of
90
Genetic e
quilibriu
m
Natu
ral s
election
Muta
tion
Specia
tion
25% 25%25%25%
201 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30
1.Genetic equilibrium
2.Natural selection3.Mutation4.Speciation
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The most common way for new species to form is through
91
Muta
tion
Stabiliz
ing selecti
on
Geogra
phic and re
prod...
Genetic e
quilibriu
m
25% 25%25%25%1.Mutation2.Stabilizing
selection3.Geographic and
reproductive isolation
4.Genetic equilibrium
201 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30
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Population genetics
• genetic structure of a population
group of individualsof the same speciesthat can interbreed
• alleles
• genotypes
Patterns of genetic variation in populations
Changes in genetic structure through time
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Describing genetic structure
• genotype frequencies
• allele frequencies
rr = white
Rr = pink
RR = red
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200 white
500 pink
300 red
• genotype frequencies
• allele frequencies
200/1000 = 0.2 rr
500/1000 = 0.5 Rr
300/1000 = 0.3 RR
total = 1000 flowers
genotypefrequencies:
Describing genetic structure
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200 rr
500 Rr
300 RR
• genotype frequencies
• allele frequencies
900/2000 = 0.45 r
1100/2000 = 0.55 R
total = 2000 alleles
allelefrequencies:
= 400 r
= 500 r= 500 R
= 600 R
Describing genetic structure
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for a populationwith genotypes:
100 GG
160 Gg
140 gg
Genotype frequencies
Phenotype frequencies
Allele frequencies
calculate:
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for a populationwith genotypes:
100 GG
160 Gg
140 gg
Genotype frequencies
Phenotype frequencies
Allele frequencies
100/400 = 0.25 GG160/400 = 0.40 Gg140/400 = 0.35 gg
260/400 = 0.65 green140/400 = 0.35 brown
360/800 = 0.45 G440/800 = 0.55 g
0.65260
calculate:
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another way to calculateallele frequencies:
100 GG
160 Gg
140 gg
Genotype frequencies
Allele frequencies
0.25 GG
0.40 Gg
0.35 gg
360/800 = 0.45 G440/800 = 0.55 g
OR [0.25 + (0.40)/2] = 0.45 [0.35 + (0.40)/2] = 0.65
G
g
Gg
0.250.40/2 = 0.200.40/2 = 0.200.35
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Population genetics – Outline
What is population genetics?
Calculate
Why is genetic variation important?
- genotype frequencies
- allele frequencies
How does genetic structure change?
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Genetic variation in space and time
Frequency of Mdh-1 alleles in snail colonies in two city blocks
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Changes in frequency of allele F at the Lap locusin prairie vole populations over 20 generations
Genetic variation in space and time
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Why is genetic variation important?potential for change in genetic structure
• adaptation to environmental change- conservation
Genetic variation in space and time
•divergence of populations- biodiversity
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Why is genetic variation important?
variation
no variation
EXTINCTION!!
globalwarming survival
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Why is genetic variation important?
variation
no variation
north
south
north
south
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Why is genetic variation important?
variation
no variation
divergence
NO DIVERGENCE!!
north
south
north
south
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Natural selection
Resistance to antibacterial soap
Generation 1: 1.00 not resistant 0.00 resistant
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Natural selection
Generation 1: 1.00 not resistant 0.00 resistant
Resistance to antibacterial soap
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Natural selection
Resistance to antibacterial soap
mutation!
Generation 1: 1.00 not resistant 0.00 resistant
Generation 2: 0.96 not resistant 0.04 resistant
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Natural selection
Resistance to antibacterial soap
Generation 1: 1.00 not resistant 0.00 resistant
Generation 2: 0.96 not resistant 0.04 resistant
Generation 3: 0.76 not resistant 0.24 resistant
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Natural selection
Resistance to antibacterial soap
Generation 1: 1.00 not resistant 0.00 resistant
Generation 2: 0.96 not resistant 0.04 resistant
Generation 3: 0.76 not resistant 0.24 resistant
Generation 4: 0.12 not resistant 0.88 resistant
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Natural selection can causepopulations to diverge
divergencenorth
south
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Selection on sickle-cell allele
aa – abnormal ß hemoglobin sickle-cell anemia
very lowfitness
intermed.fitness
highfitness
Selection favors heterozygotes (Aa).Both alleles maintained in population (a at low level).
Aa – both ß hemoglobins resistant to malaria
AA – normal ß hemoglobin vulnerable to malaria
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• sampling error
genetic change by chance alone
• misrepresentation• small populations
How does genetic structure change?
• mutation
• migration
• natural selection
• genetic drift
• non-random mating
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Genetic drift
8 RR8 rr
Before:
After:2 RR6 rr
0.50 R0.50 r
0.25 R0.75 r
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• mutation
• migration
• natural selection
• genetic drift
• non-random mating
cause changes inallele frequencies
How does genetic structure change?
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• mutation
• migration
• natural selection
• genetic drift
• non-random mating
• non-random mating
non-random allele combinations
mating combines alleles into genotypes
How does genetic structure change?
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AA x AA
AA
aa x aa
aa
AA0.8 x 0.8
Aa0.8 x 0.2
aA0.2 x 0.8
A0.8
A0.8
a0.2
a0.2
aa0.2 x 0.2
genotype frequencies:AA = 0.8 x 0.8 = 0.64Aa = 2(0.8 x0.2) = 0.32aa = 0.2 x 0.2 = 0.04
allele frequencies:A = 0.8A = 0.2
A
AA A
AA
A A
a
a
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Example: Coat color
B__ = blackbb = red
Herd of 200 cows: 100 BB, 50 Bb and 50 bb
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Allele frequency
No. B alleles = 2(100) + 1(50) = 250No. b alleles = 2(50) + 1(50) = 150Total No. = 400
Allele frequencies:f(B) = 250/400 = .625 f(b) = 150/400 = .375
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genotypic frequencies f(BB) = 100/200 = .5 f(Bb) = 50/200 = .25 f(bb) = 50/200 = .25
phenotypic frequenciesf(black) = 150/200 = .75f(red) = 50/200 = .25
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Previous example: counted alleles to compute
frequencies. Can also compute allele frequency
from genotypic frequency.
f(A) = f(AA) + 1/2 f(Aa)f(a) = f(aa) + 1/2 f(Aa)
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Previous example, we had f(BB) = .50, f(Bb) = .25, f(bb) = .25.
allele frequencies can be computed as:f(B) = f(BB) + 1/2 f(Bb)
= .50 + 1/2 (.25) = .625
f(b) = f(bb) + 1/2 f(Bb) = .25 + 1/2 (.25) = .375
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Mink color example:
B_ = brown bb = platinum (blue-gray)
Group of females (.5 BB, .4 Bb, .1 bb) bred toheterozygous males (0 BB, 1.0 Bb, 0 bb).
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Allele frequencies among the females?f(B) = .5 + 1/2(.4) = .7f(b) = .1 + 1/2(.4) = .3
Allele frequencies among the males?f(B) = 0 + 1/2(1) = .5f(b) = 0 + 1/2(1) = .5
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Expected genotypic, phenotypic and allele frequencies in the offspring?
sires .5 B .5 b
________________dams .7 B .35 BB .35 Bb
.3 b .15 Bb .15 bb
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Expected frequencies in offspring
Genotypic
.35 BB
.50 Bb
.15 bb
Phenotypic
.85 brown
.15 platinum
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Allele frequencies in offspring
f(B) = f(BB) + .5 f(Bb)= .35 + .5(.50) = .6
f(b) = f(bb) + .5 f(Bb)= .15 + .5(.50) = .4
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Also note: allele freq. of offspring = average of sire and dam
f(B) = 1/2 (.5 + .7) = .6f(b) = 1/2 (.5 + .3) = .4
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Hardy-Weinberg Theorem
Population gene and genotypic frequencies don’t change over generations if is at or near equilibrium.
Population in equilibrium means that the populations isn’t under evolutionary forces (Assumptions for Equilibrium*)
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Assumptions for equilibrium
large population (no random drift)Random matingno selectionno migration (closed population)no mutation
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Hardy-Weinberg Theorem
Under these assumptions populations remains stable over generations.
It means: If frequency of allele A in a population is =.5, the sires and cows will generate gametes with frequency =.5 and the frequency of allele A on next generation will be =.5!!!!!
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Hardy-Weinberg Theorem
Therefore:It can be used to estimate frequencies when the
genotypic frequencies are unknown.Predict frequencies on the next generation.
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Hardy-Weinberg Theorem
If predicted frequencies differ from observed frequencies Population is not under Hardy-Weinberg Equilibrium.
Therefore the population is under selection, migration, mutation or genetic drift.
Or a particular locus is been affected by the forces mentioned above.
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Hardy-Weinberg Theorem (2 alleles at 1 locus)
Allele freq.
f(A) = pf(a) = q
p + q = 1
Sum of all alleles = 100%
Genotypic freq.
f(AA) = p2 Dominant homozygousf(Aa) = 2 pq Heterozgousf(aa) = q2 Recessive homozygous
p2 + 2 pq + q2 = 1
Sum of all genotypes = 100%
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Hardy-Weinberg Theorem
Allele freq.f(A) = pf(a) = qp + q = 1Sum of all alleles = 100%
Genotypic freq.f(AA) = p2 Dominant homozygousf(Aa) = 2 pq Heterozgousf(aa) = q2 Recessive homozygousp2 + 2 pq + q2 = 1Sum of all genotypes = 100%
Gametes A (p) a(q)
A(p) AA (pp)
Aa(pq)
a(q) aA (qp)
aa (qq)
AA = p*p = p2
Aa = pq + qp = 2pqAa = q*q = q2
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Example use of H-W theorem
1000-head sheep flock. No selection for color. Closed to outside breeding.
910 white (B_)90 black (bb)
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Start with known: f(black) = f(bb) = .09 =q2
Then, p = 1 – q = .7 = f(B)
f(BB) = p2 = .49f(Bb) = 2pq = .42f(bb) = q2 = .09
)(3.09.2 bfqq
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In summary:
Allele freq.f(B) = p = .7 (est.)f(b) = q = .3 (est.)
Phenotypic freq.f(white) = .91 (actual)f(black) = .09 (actual)
Genotypic freq.f(BB) = p2 = .49 (est.)f(Bb) = 2pq = .42 (est.)f(bb) = q2 = .09 (actual)
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Mink example using H-W
Group of 2000 (1920 brown, 80 platinum) in equilibrium. We know f(bb) = 80/2000 = .04 = q2
f(b) = (q2) = .04 = .2f(B) = p = 1- q = .8
f(BB) = p2 = .64f(Bb) = 2pq = .32
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Forces that affect allele freq.
1. Mutation2. Migration3. Selection4. Random (genetic) drift
Selection and migration most important for livestock breeders.
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Mutation
Change in base DNA sequence.Source of new alleles.Important over long time-frame.Usually undesirable.
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Migration
Introduction of allele(s) into a population from an outside source.
Classic example: introduction of animals into an isolated population.
others:new herd sire.opening herd books.“under-the-counter” addition to a breed.
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Change in allele freq. due to migration
pmig = m(Pm-Po) where
Pm = allele freq. in migrants
Po = allele freq. in original population
m = proportion of migrants in mixed pop.
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Migration example
100 Red Angus (all bb, p0 = 0)
purchase 100 Bb (pm = .5)
p = m(pm - po) = .5(.5 - 0) = .25
new p = p0 + p = 0 + .25 = .25 = f(B)
new q = q0 + q = 1 - .25 = .75 = f(b)
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Random (genetic) drift
Changes in allele frequency due to random segregation.
Aa .5 A, .5 a gametes
Important only in very small pop.
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Selection
Some individuals leave more offspring than others.
Primary tool to improve genetics of livestock.Does not create new alleles. Does alter freq.Primary effect change allele frequency of
desirable alleles.
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Example: horned/polled cattle
100-head herd (70 HH, 20 Hh, and 10 hh).
Genotypic freq.:f(HH) = .7, f(Hh) = .2, f(hh) = .1
Allele freq.:f(H) = .8, f(h) = .2
Suppose we cull all horned cows. Calculateallele and genotypic frequencies after
culling?
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After culling
f(HH) = .7/.9 = .778f(Hh) = .2/.9 = .222f(hh) = 0
f(H) = .778 + .5(.222) = .889f(h) = 0 + .5(.222) = .111
p = .889 - .8 = .089
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2nd example
Cow herd with 20 HH, 20 Hh, and 60 hh
Initial genotypic freq.: .2HH, .2Hh, .6hh
Initial allele frequencies:f(H) = .2 + 1/2(.2) = .3f(h) = .6 + 1/2(.2) = .7
Again, cull all horned cows.
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Genotypic Allele freq.
freq (HH) = .2/.4 = .5 f(H) = .5 + 1/2(.5) = .75freq (Hh) = .2/.4 = .5 f(h) = 0 + 1/2(.5) = .25freq (hh) = 0
p = .75 - .3 = .45
Note: more change can be made when the initial frequency of desirable gene is low.
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3rd example
initial genotypic freq. .2 HH, .2 Hh, .6 hh.
Initial allele freq. f(H) = .3 and f(h) = .7
Cull half of the horned cows.
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Genotypic Allele freq.f (HH) = .2/.7 = .2857 f(H) = .2857 + 1/2(.2857) = .429f (Hh) = .2/.7 = .2857 f(h) = .4286 + 1/2(.2857) = .571f (hh) = .3/.7 = .4286
p = .429 - .3 = .129
Note: the higher proportion that can be culled, the
more you can change allele freq.
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Selection Against Recessive Allele
Allele Freq. Genotypic Freq. A a AA Aa aa.1 .9 .01 .18 .81.3 .7 .09 .42 .49 .5 .5 .25 .50 .25.7 .3 .49 .42 .09.9 .1 .81 .18 .01
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Factors affecting response to selection
1. Selection intensity2. Degree of dominance
(dominance slows progress)
Initial allele frequency (for a one locus)
Genetic Variability (Bell Curve)