Primer in Popultion Genetics
Hierrchicl Orgniztion of Genetics Diversity Primer in Popultion Genetics
Defining Genetic Diversity within Popultions Polymorphism number of loci with > 1 llele Number of lleles t given locus Heterozygosity t given locus Thet or θ = 4N e μ (for diploid genes) where N e = effective popultion size μ = per genertion muttion rte
Defining Genetic Diversity mong Popultions Genetic diversity mong popultions occurs if there re differences in llele nd genotype frequencies between those popultions. Cn be mesured using severl different metrics, tht re ll bsed on llele frequencies in popultions. Fst nd nlogues Genetic distnce, e.g., Nei s D Sequence divergence
Estimting Observed Genotype nd llele Frequencies Suppose we genotyped 100 diploid individuls (n = 200 gene copies). Genotypes Number 58 40 2 Genotype Frequency 0.58 0.40 0.02 # obs. for genotype llele Observed llele Frequencies 116 40 0 156/200 = 0.78 (p) 0 40 4 44/200 = 0.22 (q)
Estimting Expected Genotype Frequencies Mendelin Inheritnce Offspring inherit one chromosome nd thus one llele independently nd rndomly from ech prent Mom Dd Mom Dd Mom nd dd both hve genotype, their offspring hve three possible genotypes: Mom Dd Mom Dd
Estimting Expected Genotype Frequencies Much of popultion genetics involves mnipultions of equtions tht hve bse in either probbility theory or combintion theory. -Rule 1: If you ccount for ll possible events, the probbilities sum to 1. [e.g., p + q = 1 for two-llele system]. -Rule 2: The probbility tht two independent events occur is the product of their individul probbilities. [e.g., probbility of homozygote with genotype is q*q = q 2 ]. Thus, under idel conditions, expected genotype frequencies re p 2 for, 2pq for, nd q 2 for ; nd the genotype frequencies sum to 1 such tht: p 2 + 2pq +nd q 2 = 1 (Hrdy Weinberg Equilibrium)
Expected Genotype Frequencies under HWE
Testing for Devitions from HWE Genotypes Totl Observed numbers (O) 16 20 4 40 p = 52/80 = 0.65 s q = 28/80 = 0.35 Expected frequencies p 2 0.65 2 0.42 2pq 2*0.65*0.35 0.46 p 2 0.35 2 0.12 1.0 1.0 1.0 Expected numbers (E) 17 18 5 40 (expected frequency * 40)
Testing for Devition from HWE χ 2 = Σ (O E) 2 /E with Chi-squre test χ 2 = (16 17) 2 /17 + (20 18) 2 /18 + (4 5) 2 /5 χ 2 = 0.4 Probbility of obtining χ 2 of 7.2 or greter (1 df) = 0.53 Thus, observed genotypes do not devite from HWE
Estimting Expected Heterozygosity when >2 lleles When there re more thn 2 lleles, simple wy to clculte HW expected heterozygosity is: H e = 1 Σ p i 2 For exmple, if llele frequencies for 3 lleles re 0.5, 0.3, nd 0.2, HW expected heterozygosity is: H e = 1 (0.5 2 + 0.3 2 + 0.2 2 ) = 1 (0.25 + 0.09 + 0.04) = 0.62
Estimting Genomic Diversity To fully ssess the demogrphic history nd evolutionry potentil of species, genome-wide ssessment of genetic diversity is needed (mmmls hve ~35,000 loci). Genetic diversity mesures re estimted over severl loci tht re presumed to be rndom smple of the genome Heterozygosity is often verged over multiple loci to obtin n estimte of genome-wide genetic diversity
Evolutionry Processes tht Influence Genetic Diversity Genetic Drift rndom chnge in llele frequencies in popultion from genertion to genertion due to finite popultion size. Muttion n error in the repliction of DN tht cuses structurl chnge in gene. Only source of new genetic vrition in popultions (sex cells only). Gene Flow exchnge of genetic informtion mong popultion vi migrtion of individuls. Nturl Selection differentil contribution of genotypes to the next genertion due to differences in survivl nd reproduction.
Genetic Drift Rndom chnges in llele frequencies cross genertions due to finite popultion size Breeding Individuls (2) Gen 1 Gmetes (mny) Breeding Individuls (2) Gmetes (mny) Breeding Individuls (2) Gen 2 Gen 3 P = 0.5 P = 0.5 P = 0.75 P = 0.25 P = 1.0 P = 0
p (frequency of llele ) Genetic Drift llele frequencies chnge over time rndomly nd some lleles cn go extinct or become fixed. Which lleles frequencies cn drift in different directions for different popultions, resulting in greter differences mong popultions 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0 5 10 15 20 Time (genertions)
Probbility of Losing llele Loss of llelic Diversity The probbility of n llele being lost during bottleneck of size N e : (1 p) 2Ne, where p is the frequency of the llele, in the genertion following the bottleneck 1 0.8 0.6 0.4 0.2 0 0.01 0.1 0.5 0 100 200 300 Effective Popultion Size p Rre lleles re lost first during bottlenecks
Loss of Heterozygosity Loss of heterozygosity occurs due to the loss of lleles, but occurs more slowly, prticulrly compred to rre lleles. Per genertion loss of heterozygosity (increse in homozygosity) = 1/2N e Over t genertions, the loss of heterozygosity = 1 (1 1/2N e ) t
Loss of Genetic Diversity in Smll Popultions Theoreticl Expecttions
Muttion n error in the repliction of DN tht cuses structurl chnge in gene. Entire chromosoml complements Trnsloctions: the movement of nucleotides from one prt of the genome to nother. Dupliction: smll number of nucleotides or lrge pieces of chromosomes Single nucleotides: removls, substitutions, or insertions E.g., substitution Muttions
Frequency of llele Muttions Muttions cn offset loss of genetic diversity due to genetic drift, but muttion rtes in nture re low, ~10-9 muttions per locus per genertion in protein coding nucler genes. lso, most muttions re hrmful nd get weeded out of the popultion, reltively few muttions re beneficil Muttion occurs, generting llele ---- Beneficil muttion 0 ---- Hrmful muttion Time (genertions)
Selection Whether selection increses within-popultion diversity depends on if selection is stbilizing, disruptive, or directionl Whether selection increses withinpopultion diversity lso depends on if selection is stbilizing, disruptive, or directionl Frequency of Phenotype
p (frequency of llele ) Selection In popultions of finite size, selection is not the only fctor responsible for chnges in llele nd genotype frequencies. For exmple, stochstic fluctutions occur in the frequency of llele due to genetic drift, despite generl increse due to directionl selection. 1 0.9 0.8 p 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0 5 10 15 20 Time (genertions) Genertions
p (frequency of llele ) Gene Flow Increses genetic vrition within popultions becuse it brings in new lleles. Reduces genetic differences mong popultions, becuse lleles re being exchnged E.g., Five popultions with different initil frequencies (p) of llele connected by migrtion rte (m) of 0.05. 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 subpop1 (p0 = 1) subpop2 (p0 = 0.75) subpop3 (p0 = 0.5) subpop4 (p0 = 0.25) subpop5 (p0 = 0) 0 20 40 60 80 100 Time (number of genertions)
Evolutionry Processes tht Influence Genetic Diversity Level of Genetic Vrition Within Pops mong Pops Genetic Drift Muttion Gene Flow Selection
Potentil Effects of Hbitt Frgmenttion on Genetic Diversity Disrupting gene flow between popultion nd B nd frgmenting hbitt between nd C reduces genetic vrition in nd C. Ultimtely llele t or T nd llele s or S gets fixed in popultions B nd C.
Increse in Genetic Vrition mong Popultions