Charles Darwin s Theory of Evolution by Natural Selection Population Genetics For selection to be the cause of evolution 1 variation in traits phenotype among individuals 2 variation is in part heritable genotype 3 There is differential reproductive success 4 Differential is because of particular variants successful variants contribute their alleles to the gene pool their alleles therefore increase in frequency Accounting of alleles was recognized as possible after Mendel Darwin did not know the source of new variation nor the mechanism of inheritance independent assortment and segregation of alleles Mendel rediscovered early 1900s mutation is the source of genetic variation 1920s and 1950s Evolution is a change in frequency of inherited traits over generations Evolution is a change in the frequency of alleles over generations GG and GT have dark color TT have light color G to T cysteine replaced with phenylalanine Heterozygote A a Homozygote A A or a a gametes Mendelian Genetics a a A a a A A A Meiosis II A a A A a a Pre meiosis S phase Meiosis I gametes Allele freq a 2 4 0 5 Allele freq A 2 4 0 5 This is for one individual s potential contribution to the gene pool The gene pool is the set of all copies of all alleles in a population that potentially could be passed on to the next generation Population a group of interbreeding individuals and offspring Punnett Square Mating Simulation based on Punnett Square gene pool population of sperm A a 0 6 0 4 f o n o i t a l u p o p s g g e A 0 6 0 36 0 24 a 0 4 0 24 0 16 Population that does not evolve is in equilibrium For 100 adults each making 10 gametes AA 36 A a 48 a a 16 360A gametes 240A and 240a gametes 160a gametes Allele frequencies in the gene pool A 360 240 a 160 240 1000 1000 Hardy Weinberg Equilibrium Principle 1 Allele frequencies in a population will not change from generation to generation 2 If allele frequencies in a population are given by p and q the genotype frequencies will be given by p2 2pq and q2 1 Allele frequencies p freq of allele A q freq of allele a p q 1 sperm a A p p2 pq q pq q2 eggs A a p q 2 Genotype frequencies p2 2pq q2 1 Hardy Weinberg Equation 3 Calculate allele frequencies in the next generation pn p2 pq qn q2 pq Hardy Weinberg Equilibrium Principle a null model Predicts what allele and genotype frequencies do when evolution does not happen The null model has 5 assumptions Assumptions 1 No selection 2 No mutation 3 No chance events genetic drift 4 No migration 5 Mating is random In other words these are the mechanisms that cause a population to evolve Hardy Weinberg provides a null hypothesis and a modifiable mathematical model that makes predictions Can then do experiments to test predictions Selection and Hardy Weinberg equilibrium 1 Assume differential mortality 25 for B1 B2 50 for B2 B2 2 Assume 10 gametes individual 3 Gametes with B1 and B2 alleles B1 B1 360 B1 gametes B1 B2 180 B1 and 180 B2 B2 B2 80 B2 gametes 4 Final allele frequencies Total gametes 800 B1 540 800 0 675 B2 260 800 0 325 Violation of no selection assumption results in allele change evolution Population is not in Hardy Weinberg equilibrium Modifying Hardy Weinberg to predict selection s effect on evolution Fitness genotype s lifetime reproductive success Fitness of genotypes w survival rate assume equal offspring B1 B1 x w11 B1 B2 x w12 B2 B2 x w22 p B1 allele frequency p2 B1 B1 genotype frequency Mean fitness of the population w p2w11 2pqw12 q2w22 1 Starting allele frequencies p and q 2 New genotype frequencies among surviving adults p2w11 w 2pqw12 w q2w22 w 3 New allele frequencies p2w11 pqw12 pqw12 q2w22 qn w w pn Change in allele frequencies under different degrees of selection Initial frequencies p B1 0 01 q B2 0 99 w11 w12 w22 1 0 99 0 98 Will the HIV epidemic increase the frequency of the CCR5 32 allele Northern Europe CCR5 32 frequency 0 10 to 0 20 infection rates 1 sub Saharan Africa CCR5 32 frequency 0 01 25 infected and die Phenotype varies depending on the genotype genotypes homozygotes and heterozygotes A A a a A a An allele can be dominant recessive or have incomplete dominance selection for a dominant allele selection for a recessive allele Also overdominance that is selection for heterozygote and underdominance that is selection against the heterozygote Change in allele frequencies depends on the relationship of the paired alleles to the phenotype under selection Selection against a recessive lethal allele L locus and l alleles l allele is lethal 1 Initial population is all heterozygotes freq 0 5 l freq 0 5 2 Zygotes assuming 100 individuals l l l 25 50 25 3 Assume 10 gametes individual 250 gametes l 250 and 250 l gametes l l 0 gametes selection against 4 Allele freq 500 750 0 67 l 250 750 0 33 Why does allele only reach 90 Selection Dominant or Recessive alleles Rate of evolution is slow when a recessive allele is rare Recessive alleles are hidden by the heterozygote Selection for heterozygote overdominance also called heterozygote superiority Frequency for V allele at fixation expected to be 94 as with the beetle experiment but survival rates favor the heterozygote survival rate wVV wVL and wLL Blue line 2nd experiment set initial V allele frequency at 0 975 Even though LL is lethal the allele increases in frequency Overdominance maintains genetic variation in the population Stable and unstable equilibria Stable equilibria with overdominance maintains genetic variation Equilibrium is when p 0 A1A1 A1A2 A2A2 1 s 1 1 t genotype fitness Red line Population evolves towards maximum fitness which includes both alleles Unstable equilibria with underdominance reduces genetic variation Blue line Population evolves towards maximum fitness which is mutually exclusive either allele A1 rises to fixation or allele A2 rises to fixation Summary of HWE and selection HWE p2 2pq q2 1 has reached HWE modified HWE p2w11 2pqw12 q2w22 1 w w w allows quantitative predictions A1A1 A1A2 A2A2 w11 w12 w22 Selection For Recessive 1 s 1 s 1 Dominant 1 1 1 s Het Superiority 1 s 1 1 t Het Inferiority 1 s 1 1 t at HWE Genetic variation Notes Reduced slow evo Low freq A2 alleles rapid evo Maintained Trade offs Reduced constraint Most interesting is the trait you are studying Another situation maintaining allelic diversity Frequency dependent selection Bee pollinators alternate visits to yellow and purple flower For less common color individual flowers get more visits Elderflower orchids Rare color advantage might be explanation for two