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# Population genetics with qs

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• Outline 2 lectures Why is gen var important?
• The method of counting alleles was used in the preceding example to compute allele frequencies. This method can be used only when the actual numbers of genotypes are given. Another method of computing allele frequencies can be used when frequencies, rather than numbers, of genotypes are given. Allele frequencies can be computed from the genotypic frequencies. As long as genotypic frequencies are given, the following formulas work regardless of whether or not the population is in equilibrium:
• Allele frequencies in the offspring can be computed from genotypic frequencies as: f(B) = .35 + 1/2(.50) = .6 f(b) = .15 + 1/2(.50) = .4
• Note that the allele frequencies in the offspring are equal to the average of allele frequencies in the parents (averaged over sires and dams). i.e., f(B) = 1/2 (.5 + .7) = .6 f(b) = 1/2 (.5 + .3) = .4
• For a trait displaying dominance/recessiveness, it is usually not possible to distinguish between homozygous dominant versus heterozygous individuals. In such situations, it is usually impossible to know the exact genotypic, and thus, allele frequencies. However, in such cases it is sometimes possible to estimate genotypic and allele frequencies by use of the Hardy-Weinberg Theorem.
• H-W formulas will not be accurate if population does not at least approximated equilibrium.
• For a trait displaying dominance/recessiveness, it is usually not possible to distinguish between homozygous dominant versus heterozygous individuals. In such situations, it is usually impossible to know the exact genotypic, and thus, allele frequencies. However, in such cases it is sometimes possible to estimate genotypic and allele frequencies by use of the Hardy-Weinberg Theorem.
• For a trait displaying dominance/recessiveness, it is usually not possible to distinguish between homozygous dominant versus heterozygous individuals. In such situations, it is usually impossible to know the exact genotypic, and thus, allele frequencies. However, in such cases it is sometimes possible to estimate genotypic and allele frequencies by use of the Hardy-Weinberg Theorem.
• For a trait displaying dominance/recessiveness, it is usually not possible to distinguish between homozygous dominant versus heterozygous individuals. In such situations, it is usually impossible to know the exact genotypic, and thus, allele frequencies. However, in such cases it is sometimes possible to estimate genotypic and allele frequencies by use of the Hardy-Weinberg Theorem.
• We can assume that the population is sufficiently near equilibrium, because: it is a large population there has been no selection for this particular trait closed population implies no migration mutation can generally be assumed to be negligible Therefore, we can use the Hardy-Weinberg formulas.
• Start with the known: f(black) = f(bb) = .09 =q 2 Then, calculate the allele frequencies, starting with the recessive allele. Then, p = 1 – q = 1 - .3 = .7 = f(B) because P + q = 1 We already know that f(bb) = .09. The other genotypic frequencies are then calculated as: f(BB) = p 2 = .49 f(Bb) = 2pq = .42
• Again, f(bb) = .04 is known. The other genotypic frequencies and the allele frequencies are estimates. Question: Does equilibrium ever exist? Many loci may at least approximate equil.
• The effects of mutation alone are usually very small in one generation. The effects can be much greater if the mutation has a selective advantage (i.e., combined effects of mutation and selection). For example, the polled allele in cattle is thought to originally have arisen as the result of mutation, and its frequency in some breeds was increased by selection. Also, in very small populations, mutation effects can sometimes be important because of random drift.
• Migration can be thought of on several levels: herd, breed, commercial population, etc. Examples: 1. Bringing in a new herd sire. 2. The herd books of a previously “pure” breed are opened to allow the registration of animals that are not strict purebreds. 3. &quot;Under-the-counter&quot; additions of a different breed to a supposedly pure breed (against breed regulations). 4. Importation of continental European “exotic” cattle into the U.S. 5. A wildlife agency transports animals from an “outside” population into a small, isolated population in order to widen the genetic base (i.e., reduce inbreeding depression).
• Δ p mig = m(P m -P o ) New allele frequency: P 1 = P o + ∆p For migration to have a significant effect: 1. m must be quite large 2. difference between P m and P o must be large
• Note: Δ p = - Δ q so that Δ p + Δ q = 0
• Random (chance) deviations due to the Law of Random Segregation. That is, for any gene pair of a parent, random chance determines which member of the gene pair gets passed on to a gamete and thus to an offspring. Changes in allele frequencies due to genetic drift should be random and cancel one another out in most situations. However, in very small, isolated populations, it is possible for random drift to have rather significant effects on allele frequencies simply due to chance occurrences. Not usually very important in most livestock populations. Can be important in small populations such as endangered breeds or endangered species.
• Occurs whenever some individuals (genotypes) leave more offspring than others. i.e. differential reproductive rate. Some individuals contribute more genetic material to future generations than other individuals. No new genes are created. However, gene frequencies are changed. New combinations of genes (i.e. genotypes) may be created. Primary tool that we use as breeders to make genetic change in livestock herds. * Primary effect of selection - to change gene freq. 2 General Types of Selection 1. Natural Selection - those most fit (most desired or adapted) leave most offspring (Darwin Th. Survival of Fittest). - Still occurs in most domestic species - Important from evolutionary standpoint 2. Artificial - imposed by humans, who determine which individuals contribute the most genetic material to the next generation.
• Initial frequencies prior to selection.
•  q = .111 - .2 = -.089 (change in freq. of undesired allele)
•  q = .25 -.70 = -.45 (change in freq. of horned gene) Note: more change can be made when the initial freq. of the gene that you&apos;re selecting against is high, or when initial frequency of the gene that you&apos;re selecting for is low.
• Easiest to select against recessive allele when it’s at higher frequency (fewer are hidden in heterozygotes. When q is low, most of the recessive genes are hidden in the heterozygote & sel. progress is slow.

## Population genetics with qsPresentation Transcript

• Population Genetics
• The 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
• The Gene Pool
• Different species do NOT exchange genes by interbreeding
• Different species that interbreed often produce sterile or less viable offspring e.g. Mule
• 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
• 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
• Modern Evolutionary Thought
• Modern Synthesis Theory
• Combines Darwinian selection and Mendelian inheritance
• Population genetics - study of genetic variation within a population
• Emphasis on quantitative characters
• Modern Synthesis Theory
• 1940s – comprehensive theory of evolution (Modern Synthesis Theory)
• Introduced by Fisher & Wright
• Until then , many did not accept that Darwin’s theory of natural selection could drive evolution
S. Wright A. Fisher
• 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
• 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)
• 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%) R 160 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
• Species & Populations
• Population - a localized group of individuals of the same species.
• Species - a group of populations whose individuals have the ability to breed and produce fertile offspring.
• Individuals near a population center are, on average, more closely related to one another than to members of other populations.
• Gene Pools
• A population’s gene 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.
• The Hardy-Weinberg Theorem
• Used to describe a non-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 .
• The Hardy-Weinberg Theorem
• Deviation from Hardy-Weinberg equilibrium usually results in evolution
• Understanding a non-evolving population, helps us to understand how evolution occurs
.
• Assumptions of the H-W Theorem
• Large population size - small populations can have chance fluctuations in allele frequencies ( e.g. , fire, storm).
• No migration - immigrants can change the frequency of an allele by bringing in new alleles to a population.
• No net mutations - if alleles change from one to another, this will change the frequency of those alleles
• Assumptions of the H-W Theorem
• 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.
• 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.
• 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 = p 2 + 2 pq + q 2                                                 where p 2 = frequency of AA genotype; 2 pq = frequency of Aa plus aA genotype; q 2 = frequency of aa genotype
• 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
• Natural selection (1 & 2 are most important)
• Gene flow
• Mutation
• 1) Genetic drift
• Genetic drift = the alteration of the gene pool of a small population due to chance.
• Two factors may cause genetic drift:
•
• 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.
• Founder effect may lead to reduced variability when a few individuals from a large population colonize an isolated habitat.
• *Yes, I realize that this is not really a cheetah.
• 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.
• 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.
• 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)].
• 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.
• 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.
• 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.
• 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?
• 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.
• 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).
• 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.)
• Neutral variation is genetic variation that results in no competitive advantage to any individual.                                     - Example:  human fingerprints.
• 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,
• 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.
• Directional selection
• 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.
• Diversifying selection
• 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.
• 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.
• 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.
• 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.
• Genes Within Populations Chapter 21
• Gene Variation is Raw Material
• Natural selection and evolutionary change
• Some individuals in a population possess certain inherited characteristics that play a role in producing more surviving offspring than individuals without those characteristics.
• Gene Variation In Nature
• Measuring levels of genetic variation
• blood groups – 30 blood grp genes
• Enzymes – 5% heterozygous
• Enzyme polymorphism
• A 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% Drosophila
• 5-8% in vertebrates
• Hardy-Weinberg Principle
• Population genetics - study of properties of genes in populations
• blending inheritance phenotypically intermediate (phenotypic inheritance) was widely accepted
• new genetic variants would quickly be diluted
• Hardy-Weinberg Principle
• 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.
• 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?
• 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
• Hardy-Weinberg Principle
• Calculate genotype frequencies with a binomial expansion
• (p+q) 2 = p 2 + 2pq + q 2
• p2 = individuals homozygous for first allele
• 2pq = individuals heterozygous for alleles
• q2 = individuals homozygous for second allele
• p 2 + 2pq + q 2
• and
• p+q = 1 (always two alleles)
• 16 cats white = 16bb then ( q 2 = 0.16 )
• This we know we can see and count!!!!!
• If p + q = 1 then we can calculate p from q 2
• Q = square root of q 2 = q √.16 q=0.4
• p + q = 1 then p = .6 (.6 +.4 = 1)
• P 2 = .36
• All we need now are those that are heterozygous (2pq) (2 x .6 x .4)= 0.48
• .36 + .48 + .16
Hardy-Weinberg Principle
• Hardy-Weinberg Equilibrium
• Five Agents of Evolutionary Change
• Mutation
• Mutation rates are generally so low they have little effect on Hardy-Weinberg proportions of common alleles.
• ultimate source of genetic variation
• Gene flow
• movement of alleles from one population to another
• tend to homogenize allele frequencies
• Five Agents of Evolutionary Change
• Nonrandom mating
• assortative mating - phenotypically similar individuals mate
• Causes frequencies of particular genotypes to differ from those predicted by Hardy-Weinberg.
• 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
• Genetic Drift - Bottleneck Effect
• 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
• Five Agents of Evolutionary Change
• Selection pressures:
• avoiding predators
• matching climatic condition
• pesticide resistance
• 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.
• 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 selection
• Gene flow can be either a constructive or a constraining force.
• Allelic frequencies reflect a balance between gene flow and natural selection.
• Natural Selection Can Maintain Variation
• Frequency-dependent selection
• Phenotype fitness depends on its frequency within the population.
• Negative frequency-dependent selection favors rare phenotypes.
• Positive frequency-dependent selection eliminates variation.
• Oscillating selection
• Selection favors different phenotypes at different times.
• 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.
• Sickle Cell and Malaria
• Forms of Selection
• Disruptive selection
• Selection eliminates intermediate types.
• Directional selection
• Selection eliminates one extreme from a phenotypic array.
• Stabilizing selection
• Selection acts to eliminate both extremes from an array of phenotypes.
• Kinds of Selection
• 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.
• Evolution of Coloration in Guppies
• 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.
• Evolutionary Change in Spot Number
• Limits to Selection
• Genes have multiple effects
• pleiotropy
• Evolution requires genetic variation
• Intense selection may remove variation from a population at a rate greater than mutation can replenish.
• thoroughbred horses
• Gene interactions affect allelic fitness
• epistatic interactions
• Variations in genotype arise by random fusion of gametes, mutation, and ______.
• Recombination
• Translation
• Transcription
• Sorting by phenotype
20 1 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
• The total genetic information in a population is called the
• Allele frequency
• Phenotype frequency
• Gene pool
• Distribution of traits
20 1 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
• Saint Bernards and Chihuahuas can’t mate normally owing to great differences in size. What type of reproductive isolationg mechanism is operating here?
• Developmental
• Prezygotic
• Postzygotic
• Geographic
20 1 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
• If a population is in genetic equilibrium,
• Evolution is occuring
• Speciation is occuring
• Allelic frequencies are changing
• Allelic frequencies are remaining stable
20 1 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
• Mutations affect genetic equilibrium by
• Maintaining it
• Introducing new alleles
• Causing immigration
• Causing emigration
20 1 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
• Directional selection, disruptive selection, and stabilizing selection are all examples of
• Genetic equilibrium
• Natural selection
• Mutation
• Speciation
20 1 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
• The most common way for new species to form is through
• Mutation
• Stabilizing selection
• Geographic and reproductive isolation
• Genetic equilibrium
20 1 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
• Population genetics
• genetic structure of a population
group of individuals of the same species that can interbreed
• alleles
• genotypes
Patterns of genetic variation in populations Changes in genetic structure through time
• Describing genetic structure
• genotype frequencies
• allele frequencies
rr = white Rr = pink RR = red
• 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 genotype frequencies: Describing genetic structure
• 200 rr 500 Rr 300 RR
• genotype frequencies
• allele frequencies
900/2000 = 0.45 r 1100/2000 = 0.55 R total = 2000 alleles allele frequencies: = 400 r = 500 r = 500 R = 600 R Describing genetic structure
• for a population with genotypes: 100 GG 160 Gg 140 gg Genotype frequencies Phenotype frequencies Allele frequencies calculate:
• for a population with genotypes: 100 GG 160 Gg 140 gg Genotype frequencies Phenotype frequencies Allele frequencies 100/400 = 0.25 GG 160/400 = 0.40 Gg 140/400 = 0.35 gg 260/400 = 0.65 green 140/400 = 0.35 brown 360/800 = 0.45 G 440/800 = 0.55 g calculate: 0.65 260
• another way to calculate allele frequencies: 100 GG 160 Gg 140 gg Genotype frequencies Allele frequencies 0.25 GG 0.40 Gg 0.35 gg 360/800 = 0.45 G 440/800 = 0.55 g OR [0.25 + (0.40)/2] = 0.45 [0.35 + (0.40)/2] = 0.65 0.25 0.40/2 = 0.20 0.40/2 = 0.20 0.35 G g G g
• Population genetics – Outline What is population genetics? Calculate Why is genetic variation important?
• genotype frequencies
• allele frequencies
How does genetic structure change?
• Genetic variation in space and time Frequency of Mdh-1 alleles in snail colonies in two city blocks
• Changes in frequency of allele F at the Lap locus in prairie vole populations over 20 generations Genetic variation in space and time
• Why is genetic variation important? potential for change in genetic structure
• - conservation
Genetic variation in space and time
• divergence of populations
• - biodiversity
• Why is genetic variation important? variation no variation EXTINCTION!! global warming survival
• Why is genetic variation important? variation no variation north south north south
• Why is genetic variation important? variation no variation divergence NO DIVERGENCE!! north south north south
• Natural selection Resistance to antibacterial soap Generation 1: 1.00 not resistant 0.00 resistant
• Natural selection Generation 1: 1.00 not resistant 0.00 resistant Resistance to antibacterial soap
• 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
• 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
• 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
• Natural selection can cause populations to diverge divergence north south
• Selection on sickle-cell allele aa – abnormal ß hemoglobin sickle-cell anemia very low fitness intermed. fitness high fitness 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
• sampling error
genetic change by chance alone
• misrepresentation
• small populations
How does genetic structure change?
• mutation
• migration
• natural selection
• genetic drift
• non-random mating
• Genetic drift 8 RR 8 rr Before: After: 2 RR 6 rr 0.50 R 0.50 r 0.25 R 0.75 r
• mutation
• migration
• natural selection
• genetic drift
• non-random mating
cause changes in allele frequencies How does genetic structure change?
• 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?
• AA x AA AA aa x aa aa genotype frequencies: AA = 0.8 x 0.8 = 0.64 Aa = 2(0.8 x0.2) = 0.32 aa = 0.2 x 0.2 = 0.04 allele frequencies: A = 0.8 A = 0.2 A A A A A A A A a a AA 0.8 x 0.8 Aa 0.8 x 0.2 aA 0.2 x 0.8 A 0.8 A 0.8 a 0.2 a 0.2 aa 0.2 x 0.2
• Example: Coat color
• B__ = black
• bb = red
• Herd of 200 cows:
• 100 BB, 50 Bb and 50 bb
• Allele frequency
• No. B alleles = 2(100) + 1(50) = 250
• No. b alleles = 2(50) + 1(50) = 150
• Total No. = 400
• Allele frequencies:
• f(B) = 250/400 = .625
• f(b) = 150/400 = .375
• genotypic frequencies
• f(BB) = 100/200 = .5
• f(Bb) = 50/200 = .25
• f(bb) = 50/200 = .25
• phenotypic frequencies
• f(black) = 150/200 = .75
• f(red) = 50/200 = .25
• 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)
• 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
• Mink color example:
• B_ = brown
• bb = platinum (blue-gray)
• Group of females (.5 BB, .4 Bb, .1 bb) bred to
• heterozygous males (0 BB, 1.0 Bb, 0 bb).
• Allele frequencies among the females?
• f(B) = .5 + 1/2(.4) = .7
• f(b) = .1 + 1/2(.4) = .3
• Allele frequencies among the males?
• f(B) = 0 + 1/2(1) = .5
• f(b) = 0 + 1/2(1) = .5
• Expected genotypic, phenotypic and allele frequencies in the offspring?
• Expected frequencies in offspring
• Genotypic
• .35 BB
• .50 Bb
• .15 bb
• Phenotypic
• .85 brown
• .15 platinum
• 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
• Also note: allele freq. of offspring = average of sire and dam
• f(B) = 1/2 (.5 + .7) = .6
• f(b) = 1/2 (.5 + .3) = .4
• 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*)
• Assumptions for equilibrium
• large population (no random drift)
• Random mating
• no selection
• no migration (closed population)
• no mutation
• 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!!!!!
• Hardy-Weinberg Theorem
• Therefore:
• It can be used to estimate frequencies when the genotypic frequencies are unknown.
• Predict frequencies on the next generation.
• 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.
• Hardy-Weinberg Theorem (2 alleles at 1 locus)
• Allele freq.
• f(A) = p
• f(a) = q
• p + q = 1
• Sum of all alleles = 100%
• Genotypic freq.
• f(AA) = p 2 Dominant homozygous
• f(Aa) = 2 pq Heterozgous
• f(aa) = q 2 Recessive homozygous
• p 2 + 2 pq + q 2 = 1
• Sum of all genotypes = 100%
• Hardy-Weinberg Theorem
• Allele freq.
• f(A) = p
• f(a) = q
• p + q = 1
• Sum of all alleles = 100%
• Genotypic freq.
• f(AA) = p 2 Dominant homozygous
• f(Aa) = 2 pq Heterozgous
• f(aa) = q 2 Recessive homozygous
• p 2 + 2 pq + q 2 = 1
• Sum of all genotypes = 100%
AA = p*p = p 2 Aa = pq + qp = 2pq Aa = q*q = q 2 Gametes A (p) a(q) A(p) AA (pp) Aa (pq) a(q) aA (qp) aa (qq)
• Example use of H-W theorem
• 1000-head sheep flock. No selection for color. Closed to outside breeding.
• 910 white (B_)
• 90 black (bb)
• Then, p = 1 – q = .7 = f(B)
• f(BB) = p 2 = .49
• f(Bb) = 2pq = .42
• f(bb) = q 2 = .09
• 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) = p 2 = .49 (est.)
• f(Bb) = 2pq = .42 (est.)
• f(bb) = q 2 = .09 (actual)
• Mink example using H-W
• Group of 2000 (1920 brown, 80 platinum) in equilibrium. We know f(bb) = 80/2000 = .04 = q 2
• f(b) =  (q 2 ) =  .04 = .2
• f(B) = p = 1- q = .8
• f(BB) = p 2 = .64
• f(Bb) = 2pq = .32
• Forces that affect allele freq.
• 1. Mutation
• 2. Migration
• 3. Selection
• 4. Random (genetic) drift
• Selection and migration most important for livestock breeders.
• Mutation
• Change in base DNA sequence.
• Source of new alleles.
• Important over long time-frame.
• Usually undesirable.
• 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.
• Change in allele freq. due to migration
•  p mig = m(P m -P o ) where
• P m = allele freq. in migrants
• P o = allele freq. in original population
• m = proportion of migrants in mixed pop.
• Migration example
• 100 Red Angus (all bb, p 0 = 0)
• purchase 100 Bb (p m = .5)
•  p = m(p m - p o ) = .5(.5 - 0) = .25
• new p = p 0 +  p = 0 + .25 = .25 = f(B)
• new q = q 0 +  q = 1 - .25 = .75 = f(b)
• Random (genetic) drift
• Changes in allele frequency due to random segregation.
• Aa  .5 A, .5 a gametes
• Important only in very small pop.
• 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.
• 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. Calculate
• allele and genotypic frequencies after culling?
• After culling
• f(HH) = .7/.9 = .778
• f(Hh) = .2/.9 = .222
• f(hh) = 0
• f(H) = .778 + .5(.222) = .889
• f(h) = 0 + .5(.222) = .111
•  p = .889 - .8 = .089
• 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) = .3
• f(h) = .6 + 1/2(.2) = .7
• Again, cull all horned cows.
• Genotypic Allele freq.
• freq (HH) = .2/.4 = .5 f(H) = .5 + 1/2(.5) = .75
• freq (Hh) = .2/.4 = .5 f(h) = 0 + 1/2(.5) = .25
• freq (hh) = 0
•  p = .75 - .3 = .45
• Note: more change can be made when the initial
• frequency of desirable gene is low.
• 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.
• Genotypic Allele freq.
• f (HH) = .2/.7 = .2857 f(H) = .2857 + 1/2(.2857) = .429
• f (Hh) = .2/.7 = .2857 f(h) = .4286 + 1/2(.2857) = .571
• f (hh) = .3/.7 = .4286
•  p = .429 - .3 = .129
• Note: the higher proportion that can be culled, the
• more you can change allele freq.
• 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
• Factors affecting response to selection
• 1. Selection intensity
• 2. Degree of dominance
• (dominance slows progress)
• Initial allele frequency (for a one locus)
• Genetic Variability (Bell Curve)