Basic Premises of Population Genetics

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1 Population genetics is concerned with the origin, amount and distribution of genetic variation present in populations of organisms, and the fate of this variation through space and time. The fate of genetic variation through space and time defines evolution within a species, so population genetics also provides the basis for microevolution Basic Premises of Population Genetics DNA can replicate DNA can mutate and recombine DNA encodes information that interacts with the environment to influence phenotype

2 DNA Can Replicate Because of replication, a single type of gene can exist both in time and space in a manner that transcends the individuals that temporarily bear the gene. Identity by Descent Some alleles are identical because they are replicated descendants of a single ancestral allele

3 The Existence of Genes in Space and Time Is manifest only at the level of a reproducing population Provides the spatial and temporal continuity that is necessary for evolution Deme A Deme is a local population of reproducing individuals that has physical continuity over time and space. Demes are the lowest biological level that can evolve. 3

4 Demes are Characterized by Genotype Frequencies. E.g., Consider a Population of Pueblo Indians Scored for the MN Blood Group Type Blood Type M MN N Genotype MM MN NN Total Number Genotype Freq. 83/40= /40= 0.33 /40= 0.08 Demes are Characterized by Genotype Frequencies. E.g., Consider a Population of Australian Aborigines Scored for the MN Blood Group Type Blood Type M MN N Genotype MM MN NN Total Number Genotype Freq. 9/37 = / 37 = / 37 =

5 Demes with the Same Alleles Can Have Very Different Genotype Frequencies: Pueblo Indians MM 0.59 MN 0.33 NN.08 MM 0.04 MN Australian Aborigines NN 0.67 Gene Pool A Gene Pool is the population of gene copies that are collectively shared by the individuals of a deme. 5

6 Gene Pools are Characterized by Gamete Frequencies (Allele Frequencies when Considering only Locus). E.g., Consider a Population of Pueblo Indians Scored for the MN Blood Group Type Blood Type M MN N Genotype MM MN NN Sum Number Allele (Gamete Type) M N Allele Freq. ( 83+46)/80 = 0.76 ( +46)/80 = 0.4 Gene Pools are Characterized by Gamete Frequencies (Allele Frequencies when Considering only Locus). E.g., Consider a Population of Australian Aborigines Scored for the MN Blood Group Type Blood Type M MN N Genotype MM MN NN Sum Number Allele (Gamete Type) Allele Freq. M ( 9+3)/744 = 0.76 N ( 50+3)/744 =

7 Gene Pool (Alternative Definition) A Gene Pool is the population of potential gametes that can be produced by the individuals of a deme. The Gene Pool As a Population of Potential Gametes Gametes are the bridge from one generation to the next This definition emphasizes the genetic continuity over time of a deme This definition is more useful in evolutionary theory 7

8 Demes and Gene Pools Meiosis Interconnects the Deme to the Gene Pool Therefore, Given Mendel s Laws and Normal Meiosis, You Can Always Calculate the Allele Frequencies in the Gene Pool From the Genotype Frequencies in the Deme Demes and Gene Pools: diploid Pueblo Indian Deme MM MN NN.08 Meiosis Mendelian Probabilities / / In Meiosis haploid M (0.59) + / (0.33) = 0.76 Pueblo Indian Gene Pool N (.08) + / (.33) =.4 8

9 Demes and Gene Pools: MM 0.04 Australian Aborigine Deme diploid MN NN Meiosis / Mendelian Probabilities / In Meiosis haploid M (.04) + / (.304) = 0.76 N (0.67) + / (0.304) = 0.84 Australian Aborigine Gene Pool Demes with the Same Alleles Can Have Gene Pools With Different Allele Frequencies: Pueblo Indians M 0.76 N 0.4 M 0.76 Australian Aborigines N

10 Evolution Is a change in the frequency of alleles or allele combinations over space and time in the gene pool of a reproducing population Is a process that is manifest only at the level of a reproducing population Can never be understood in terms of individuals alone. Requires Genetic Variation Importance of Mutation If DNA replication were 00% accurate, there would be no possibility of genetic change over time: NO EVOLUTION Mutation is the ultimate source of all genetic variation 0

11 DNA Can Mutate & Recombine Occurs at the molecular level before the informational content of DNA is expressed; Hence, mutation is random with respect to the needs of the individual in coping with its environment. Proof of Randomness - Replica Plating

12 Randomness Means Mutations Have a Broad Spectrum of Impacts on Their Bearers Neutral Unfavorable Favorable Effects of 50 Spontaneous Mutation Lines Derived from a Strain of Yeast Growing in a Laboratory Environment. Distribution of fitness effects caused by single-nucleotide substitutions in bacteriophage f Peris, J. B. et al. Genetics 00;85: Copyright 00 by the Genetics Society of America

13 Mutation Creates Allelic Variation Recombination and Diploidy Amplify It E.g., We now know of,000,000 single nucleotide polymorphisms (SNPs), most of which are bi-allelic and can form 3 genotypes each. Recombination Can Produce Gametic Combinations of These 4 million Alleles These Gametes Can Create Genotypes There are Humans In the World There are 0 80 Electrons in the Universe High Genetic Variation Implies: Each Individual Is Unique Evolution Can Occur 3

14 Basic Premises of Population Genetics DNA can replicate DNA can mutate and recombine DNA encodes information that interacts with the environment to influence phenotype A phenotype is a measurable trait of an individual. DNA encodes information that interacts with the environment to influence phenotype Among The Traits That Can Be Influenced By Genetically Determined Responses to the Environment Are:. The Viability in the Environment. Given Alive, the Mating Success in the Environment 3. Given Alive and Mated, Fertility or Fecundity in the Environment. 4

15 Physical Basis of Evolution DNA can replicate DNA can mutate and recombine DNA encodes information that interacts with the environment to influence phenotype Viability Mating Success Fecundity/Fertility These Are Combined Into A Single Phenotype of Reproductive Success Or FITNESS How to Model Microevolution Evolution is a change over time in the frequency of alleles or allele combinations in the gene pool, so any model of evolution must include at the minimum the passing of genetic material from one generation to the next. Hence, our fundamental time unit will be the transition between two consecutive generations at comparable stages. All such trans-generational models of microevolution have to make assumptions about three major mechanisms: Mechanisms of producing gametes Mechanisms of uniting gametes Mechanisms of developing phenotypes. 5

16 How to Model Microevolution In order to specify how gametes are produced, we have to specify the genetic architecture. Genetic architecture refers to the number of loci and their genomic positions, the number of alleles per locus, the mutation rates, and the mode and rules of inheritance of the genetic elements. For example, the first model we will develop assumes a single autosomal locus with two alleles with no mutation. Under this genetic architecture, we need only to use Mendel s first law of inheritance to specify how genotypes produce gametes. Demes and Gene Pools Meiosis Interconnects the Deme to the Gene Pool Therefore, Given Mendel s Laws and Normal Meiosis, You Can Always Calculate the Allele Frequencies in the Gene Pool From the Genotype Frequencies in the Deme Can You Predict the Deme (Genotype Frequencies) from the Gene Pool (Allele Frequencies)? 6

17 AA aa / / Demes AA / 4 Aa aa / / 4 / / A a / / Gene Pools A a / / Hardy (and Weinberg) Solution FERTILIZATION To Go From Gene Pool (Gametes) to Deme (Initially Zygotes),Need to Specify The Rules by Which Gametes Unite (Fertilization) 7

18 Population Structure Population Structure refers to the rules at the level of the deme by which gametes are united in fertilization, thereby defining the transition from haploidy to diploidy. Models in Population Genetics Minimally Specify How To Go From One Generation To The Next Deme of Adult Diploid Individuals Meiosis Gene Pool of Haploid Gametes Fertilization Deme of Adult Diploid Individuals Need to Specify Genotype Frequencies, And Therefore Genetic Architecture (Number of Loci, Alleles per Locus, Linkage, Rules of Inheritance, etc.). Need to Specify Population Structure. Need to Specify How Individuals Develop Phenotypes. 8

19 Assumptions of Hardy-Weinberg Mechanisms of Producing Gametes (Genetic Architecture) One Autosomal Locus Two Alleles No Mutation Mendel s First Law (50:50 Segregation in heterozygotes) Mechanisms of Uniting Gametes (Population Structure) System of Mating: Random Size of Population: Infinite Genetic Exchange: None (One Isolated Population) Age Structure: None (Discrete Generations) Mechanisms of Developing Phenotypes All Genotypes Have Identical Phenotypes With Respect to their Ability for Replicating Their DNA Random Mating Random Mating occurs when both of the gametes united in a zygote are drawn at random and independently from the gene pool. This means that the probability of a gamete bearing a specific allele = the frequency of that allele in the gene pool, and this is true for all gametes involved in fertilization. 9

20 Random Mating A a p q = -p Gene Pool Paternal Gamete A p a q Maternal Gamete A p a q AA Aa p p=p pq aa aa qp q q=q Hardy-Weinberg Genotype Frequencies AA p Aa pq aa q 0

21 Weinberg s Derivation Mendelian Probabilities of Offspring (Zygotes) Mating Pair Frequency of Mating Pair AA Aa aa AA AA G AA G AA = G AA 0 0 AA Aa G AA G Aa = G AAG Aa 0 Aa AA G Aa G AA = G AAG Aa 0 AA aa G AA G aa = G AAG aa 0 0 aa AA G aa G AA = G AAG aa 0 0 Aa Aa G Aa G Aa = G Aa Aa aa G Aa G aa = G AaG aa 0 aa Aa G aa G Aa = G AaG aa 0 aa aa G aa G aa = G aa 0 0 Total Offspring G AA G Aa G aa Summing Zygotes Over All Mating Types: G AA=G AA + [G AAG Aa] + G Aa = [G AA+ G Aa] = p G Aa= [ G AAG Aa]+ G AAG aa+ G Aa + [ G AaG aa]= [G AA+ G Aa][G aa+ G Aa] = pq G aa= G Aa + [ G AaG aa] + G aa = [G aa+ G Aa] = q The Life Cycle for a Population Deme of Diploid Individuals AA G AA Aa G Aa aa G aa Meiosis Mendelian Probabilities / / Gene Pool of Haploid Gametes A p=g AA + / G Aa a q=g aa + / G Aa Fertilization Random Mating p p p q q q Deme of Diploid Individuals AA p Aa pq aa q

22 Random Mating Is Locus Specific Although the Pueblo Indians are randomly mating for the MN Blood Group Locus, They Are Not Randomly Mating For All Loci, e.g., the X and Y Chromosomes Hardy-Weinberg Frequencies Represent An Equilibrium No Assumption is Made About These Genotype Frequencies; They May or May Not Be in Hardy-Weinberg Mendelian Probabilities AA G AA A Aa G Aa / / aa G aa a p=g AA + / G Aa q=g aa + / G Aa Random Mating One Generation of Random Mating Insures These Are Hardy-Weinberg Genotype Frequencies p p p q q q AA Aa aa p pq q

23 Hardy-Weinberg Frequencies Represent An Equilibrium The Frequency of The A Allele in the Next Generation s Gene Pool Is: p = p + / pq = p + pq = p(p + q) = p Therefore, the Gene Pool Is Unchanged Random Mating Mendelian Probabilities A p=g AA + / G Aa AA p Aa pq a q=g aa + / G Aa p p p q q q A p =p + / pq =p(p+q) = p / / a aa q q =q + / pq =q(q+p)=q There Is NO Evolution Under The Hardy- Weinberg Model Random Mating Mendelian Probabilities A p=g AA + / G Aa AA p Aa pq a q=g aa + / G Aa p p p q q q A p =p + / pq =p(p+q) = p / / a aa q q =q + / pq =q(q+p)=q 3

24 Importance of Hardy-Weinberg Acceptance of Mendelian Genetics (Punnett s dilemma) Resurrection of Natural Selection (Jenkin s critique) A useful null model of evolutionary stasis. A valuable springboard for the investigation of many forces of evolutionary change by relaxing its assumptions. Despite the many violations of its assumptions, it works sufficiently well in humans that testing for H-W is used as a standard quality-control procedure in modern genetic surveys. Testing for Hardy-Weinberg Genotype Frequencies. E.g., a Population of Pueblo Indians Scored for the MN Blood Group Type Blood Type M MN N Sum Genotype MM MN NN Number H.-W. Freq. Exp. Number (Obs.-Exp.) Exp. (0.76) = (40) = 8. (83-8.) 8. (0.76) (0.4)= (40) = 50.4 ( ) 50.4 (0.4) = (40) = 8.4 (-8.4) Degrees of Freedom = 3 Categories - - estimated parameter = 4

25 Two Locus Hardy Weinberg Gene Pool AB g AB Ab g Ab ab g ab ab g ab Mechanisms of Uniting Gametes (Random Mating) Zygotic/Adult Population AB/AB g AB AB/Ab g AB g Ab AB/aB g AB g ab AB/ab g AB g ab Ab/Ab g Ab Ab/aB g Ab g ab Ab/ab g Ab g ab ab/ab g ab ab/ab g ab g ab ab/ab g ab Mechanisms of Producing Gametes (Mendel's First Law & Recombination) Gene Pool of Next Generation AB g' AB Ab g' Ab ab g' ab ab g' ab Recombination Occurs in All Genotypes, But Can Change The State of the Parental Gametes Only in Double Heterozygotes. 5

26 Two Locus Hardy Weinberg Gene Pool AB g AB Ab g Ab ab g ab ab g ab Mechanisms of Uniting Gametes (Random Mating) Zygotic/Adult Population AB/AB g AB AB/Ab g AB g Ab AB/aB g AB g ab AB/ab g AB g ab Ab/Ab g Ab Ab/aB g Ab g ab Ab/ab g Ab g ab ab/ab g ab ab/ab g ab g ab ab/ab g ab Mechanisms of Producing Gametes (Mendel's First Law & Recombination) Gene Pool of Next Generation AB g' AB Ab g' Ab Double heterozygotes can produce all four gamete types. ab g' ab ab g' ab Two Locus Hardy Weinberg g' AB = g AB + (g ABg Ab ) + (g ABg ab ) + ( r)(g ABg ab ) + r(g Abg ab ) [ ] + rg Ab g ab [ ] + rg Ab g ab rg AB g ab = g AB g AB + g Ab + g ab +( r)g ab = g AB g AB + g Ab + g ab + g ab = g AB + r(g Ab g ab g AB g ab ) = g AB rd Where D = g AB g ab - g Ab g ab D is called Linkage Disequilibrium or Gametic Phase Imbalance 6

27 Two Locus Hardy Weinberg Similarly, can show: gʼab = g AB - rd gʼab = g Ab + rd gʼab = g ab + rd gʼab = g ab - rd Where D = g AB g ab - g Ab g ab D, linkage disequilibrium It measures the degree of association at the population level between the two sites/loci D is created by many evolutionary forces and historical events, including the very act of mutation because the new mutant variant initially exists on only one chromosomal background. 7

28 Two Locus Hardy Weinberg g AB =g AB -D g Ab =g Ab +D g ab =g ab +D g ab =g ab -D g ij g ij if r > 0 and D 0 That is, Evolution Occurs! Two Locus Hardy Weinberg g AB =g AB -D 0 g Ab =g Ab +D 0 g ab =g ab +D 0 g ab =g ab -D 0 D =g AB g ab -g Ab g ab =D 0 (-r) and D t =D 0 (-r) t The two locus equilibrium is Approached gradually, at a rate determined by r. Historical Information is Encoded in D (and other Multi-locus/site measures) That decays gradually with time! This information persists for long periods of time for tightly linked sites. 8

29 Theoretical Decay of LD in a Random-Mating Population In a genomic region with no recombination, the LD created by mutation never dissipates. Two Locus Hardy Weinberg Equilibrium ( )( g AB + g ab ) p A = g AB + g Ab so p A p B = g + g AB Ab p B = g AB + g ab = g AB + g AB g ab + g AB g Ab + g Ab g ab ( ) + g Ab g ab = g AB g AB + g ab + g Ab = g AB ( g ab ) + g Ab g ab = g AB g AB g ab + g Ab g ab = g AB D As t goes to infinity, D goes to 0 (the equilibrium), so at the two-locus equilibrium, g AB =p A p B, and similarly for the other gamete frequencies. 9

30 At equilibrium the two loci associate at random (proportional to their allele frequencies) in the Population s Gene Pool: B k b m A p a q AB pk=g AB ab qk=g ab Ab pm=g Ab ab qm=g ab D = g AB g ab - g Ab g ab =pkqm-pmqk=0 D 0 measures the degree of non-random association at the population gene pool level between the two sites/loci Many Factors Create Disequilibrium, Including the Very Act Of Mutation Once created, disequilibrium decays at a rate determined in part by recombination, and in part by population structure (as we will see later). 30

31 Linkage disequilibrium is created when mutation creates new variation D = g AB g ab - g Ab g ab = g AB 0-0g ab =0 Initial Gene Pool: A B a B a B Mutation At A Second Site Produces Three Gamete Types: Gene Pool After Mutation: A B a B a b D = g AB g ab - g Ab g ab = g AB g ab - 0g ab = g AB g ab 0 Can see the effects of mutation on Linkage disequilibrium more clearly through D D min p A p B,p a p b D'= D min p A p b,p a p B ( ), D < 0 ( ), D > 0 D varies between - and +, and when mutation first creates the third gamete type, D =- or +, so mutation creates maximal linkage disequilibrium. 3

32 D (or D ) decays with recombination: A B A B a B a B D=0 Mutation At A Second Site Produces Three Gamete Types: A B A B a B a b D = g Recombination AB g ab Produces Four Dʼ = Gamete Types A B A b a B a b D = g AB g ab - g Ab g ab < g AB g ab ; Dʼ < Another Common Measure of Linkage Disequilibrium is r r = D p A p a p B p b r varies from 0 to when the allele frequencies are the same at both loci; otherwise, its range is affected by allele frequencies and are from 0 to some number less than. 3

33 In regions of little to no recombination, the pattern of disequilibrium is determined primarily by the historical conditions that existed at the time of mutation, resulting in little to no correlation of D with physical distance Indel Xmn I TaqI PstI SstI Pvu II Apo AI Apo CIII Apo AIV Significant linkage disequilibrium On larger physical scales, D is negatively correlated with physical distance D S U D i s t a n c e (kb) kb Utah Swed AllYor YorBot YorTop Reich et al. (00 Nature 4:99-04) 33

34 Disequilibrium and Historical Effects Create Both Opportunities and Difficulties for the Analysis of Population Genetic Data, As We Shall See Some lessons from vs. -locus HW: A seemingly slight change in the model can create qualitative differences (e.g., no evolution in locus HW vs. evolution in -locus HW; instantaneous equilibrium in locus HW vs. gradual or no equibrium in locus HW) Scale matters (e.g., the relationship between D and physical distance on different scales of physical distance). The inferences made from a model are often very sensitive to the assumptions of that model. Generalize with care! 34

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