1 A review of fitness Fitness has two components: 1. Viability; - PDF document

Functional divergence 1: FFTNS and Shifting balance theory There is no conflict between neutralists and selectionists on the role of natural selection: Natural selection is the only explanation for adaptation 1

A review of fitness Fitness has two components: 1. Viability; an individual’s ability to survive to reproduce 2. Fecundity; an individual’s reproductive output. A review of fitness Evolutionary fitness is symbolized with W Symbolism Genotype AA Aa aa Phenotype W AA W Aa W aa 1 1 0.76 2

A review of fitness: Directional selection 1 0.8 Fitness 0.6 W AA > W Aa > W aa 0.4 0.2 0 AA Aa aa Genotypes Directional selection occurs when selection favors the phenotype at an extreme of the range of phenotypes. • exerts pressure for FIXATION (frequency goes to 1) • imposes a direction on evolution A review of fitness: overdominat selection 1 0.8 W AA < W Aa > W aa Fitness 0.6 0.4 0.2 0 AA Aa aa Genotypes Overdominant selection occurs when the heterozygote has a greater fitness than either homozygote. • also called balancing selection or heterozygote advantage • maintains a stable polymorphism; acts against fixation 3

A review of fitness: Symbolism for generation 0 Genotype AA Aa aa 2 2 p 0 2 p 0 q 0 q 0 Frequency Phenotype W AA W Aa W aa W AA : W Aa : W aa Survival ratio: p 2 W AA : 2 pq W Aa : q 2 W aa Genotype ratio: Problem: the genotype ratios do not sum to 1. A review of fitness: Normalize by dividing by the grand total after selection: W = p 2 W AA + 2 pq W Aa + q 2 W aa W = AVERAGE FITNESS − 1 W Genetic load: 4

Fisher’s fundamental theorem of natural selection: FFTNS In words: The rate of increase in the average fitness of a population is equal to the genetic component of the variation in fitness Fisher’s fundamental theorem of natural selection: FFTNS FFTNS is based on the well known formula for the response of a population to phenotypic selection ( R ). R = h 2 × S h 2 : The proportion of total phenotypic variance that is predictably transmitted to next generation (i.e., additive genetic component of variance) S: SELECTION DIFFERENTIAL; the difference between the mean phenotype of those under selection and the mean phenotype of the population. 5

FFTNS ( ) V W = ∆ = a R W W The change in population fitness depends on just two parameters. W : The average fitness of the population V a ( W ): Additive component of the total variation in fitness Biological implications of FFTNS 1. Populations can’t adapt without genetic variance in fitness • Va ( W ) : zero or positive only • Va ( W ) = 0, then change in average fitness = 0 2. Rate of population evolution depends on mean fitness 3. Fitness always increases • Not as trivial as it seems. • populations only go to local maximum • populations cannot explore entire set of outcomes • selection can prevent further adaptation 6

Adaptive topography Adaptive topography; a surface of mean fitness for a population where peaks represent the highest values of mean fitness, and valleys the lowest values of mean fitness. Also called: Adaptive landscape Fitness topography Fitness landscape Adaptive topography The most simple case: 1 locus, 2 alleles, directional selection 1 W AA = 0.1 0.9 Ave fitness of popualtion W Aa = 0.75 0.8 W aa = 1 0.7 0.6 W = p 2 W AA + 2 pq W Aa + q 2 W aa 0.5 0.4 0.3 0.2 0.1 Directional selection 0 0 0.2 0.4 0.6 0.8 1 frequncey of allele "a" 7

Adaptive topography Another simple case: 1 locus, 2 alleles, overdominant selection 1 W AA = 0.5 0.9 W Aa = 1 Ave fitness of poplation 0.8 W aa = 0.1 0.7 W = p 2 W AA + 2 pq W Aa + q 2 W aa 0.6 0.5 0.4 0.3 0.2 0.1 0 0 0.2 0.4 0.6 0.8 1 freqeuncy of allele "a" Adaptive topography More complex case: 1 locus, 3 alleles, overdominant & directional selection …. we need a De Finetti diagram 8

Introduction to the De Finetti diagram: Allele 1 Indicates: Alleles 2 and 3 have freq =0 at this vertex Allele 1: freq = 0.35 Allele 2: freq = 0.15 Allele 3: freq = 0.50 0.5 0.15 Alleles 1 and 2have freq =0 at this vertex 0.35 Allele 2 Allele 3 Alleles 1 and 3 have freq =0 at this vertex Adaptive topography More complex case: 1 locus, 3 alleles, overdominant & directional selection Allele 1 Lowest mean fitness Lines: fitness contours where the frequencies of the three alleles yield the same population fitness Valley on the fitness landscape Local peak in mean fitness Global peak in mean fitness Allele 2 Allele 3 9

Adaptive topography More complex case: 1 locus, 3 alleles, overdominant & directional selection start here end here end here start here Difficult assumptions of FFTNS 1. Constant fitness through time 2. Complete linkage equilibrium 3. Fitness must be the phenotype 4. No genetic drift • not useful as a general model over long periods of time • very useful for examining specific aspects of the evolutionary process 10

A new term: the marginal fitness of an allele Marginal fitness: the average fitness of all individuals in a population that bear a certain allele. Also called: average affect of an allele Notation for “ a ” allele: W a marginal fitness Allele A (freq = p ) Allele A (freq = p ) Allele a (freq = q ) Allele a (freq = q ) Allele c (freq = r ) W a = q ( W aa ) + p ( W Aa ) W a = q ( W aa ) + p ( W Aa ) + r ( W ac ) W a - W = 0; no change in frequency of a W a - W > 0; the a allele increases in frequency W a - W < 0; the a allele decreases in frequency 11

Adaptation in hum an populations: sickle cell haem oglobin Sickle morphology of RBCs leads to a “crisis” Sickle morphology is triggered by extreme deoxygenating event (0.1 to 1 second). Crisis leads to anemia 12

Sickle cell ”crisis” and anemia have profound clinical consequences S-RBC lifespan: 2 0 days ( verses 1 2 0 ) The genetics you probably already know A allele: normal hemoglobin S allele: single amino acid substitution at position 6 (GLU → Val) Genotypes AA AS SS Blood Phenotype Normal 40% sickling of RBCs Sickle cell anaemia AS phenotyoe: 1 . Selective sickling of plasm odium infected cells: direct destruction [ ?] 2 . High oxygen radical production by sickle-cells kills parasites [ ?] 3 . Prom otes im m une system attack 13

S allele is maintained in human populations by natural selection A and S allele polymorphism is classic example of overdominant selection Genotypes AA AS SS Blood Phenotype Normal 40% sickling of RBCs Sickle cell anaemia Mortality 1 moderate Low very high Fitness 1 0.89 * 1 0.2 1: Fitness and mortality are estimated as an average over 72 west African populations of humans. Data from Cavalli-Sforza and Bodmer (1971). * Cerebral anem ia is not fun 14

A and S allele polymorphism is classic example of overdominant selection 1 As before, the fitness of the 0.9 Ave fitness of poplation population can only go “uphill”. 0.8 Marginal fitness calculations verify 0.7 this result. 0.6 I nitial freq of S = 0 .0 1 : 0.5 W S = 0.99 and = 0.89 W 0.4 W S - = 0.11; the S allele will increase W 0.3 0.2 I nitial freq of S = 0 .2 5 : W S = 0.8 and = 0.89 0.1 W W S - W = -0.088; the S allele will decrease 0 0 0.2 0.4 0.6 0.8 1 freqeuncy of allele "S" Peak in average fitness of population Natural selection arrives at a solution that protects about 20% of the population There is another allele called C 15

A and C allele polymorphism is classic example of directional selection Genotypes AA AC CC Blood Phenotype Normal Normal Resistant Fitness 0.89 * 0.89 * 1 Data from Cavalli-Sforza and Bodmer (1971). * Cerebral anem ia is not fun A and C allele polymorphism is classic example of directional selection 1 As before, the fitness of the 0.9 Ave fitness of popualtion population can only go “uphill”. 0.8 Marginal fitness calculations verify 0.7 this result. 0.6 I nitial freq of C = 0 .0 1 : 0.5 W C = 0.891 and = 0.890 W 0.4 W C - = + 0.001; the C allele will slowly W 0.3 increase 0.2 0.1 I nitial freq of C = 0 .2 5 : W C = 0.917 and = 0.90 0 W W C - W = + 0.02; the C allele will increase 0 0.2 0.4 0.6 0.8 1 frequncey of allele "a" “c” Peak in average fitness of population Natural selection arrives at a solution that protects about 100% of the population 16

Most human populations have adapted by going to a balanced A/S polymorphism Let’s consider a population with A, S and C alleles Frequency of A = p Frequency of S = q Frequency of C = r Genotypes AA AS SS AC SC CC p 2 q 2 r 2 Frequency 2 pq 2 pr 2 qr Fitness 0.89 1 .2 .89 .71 1.31 Mortality 1 moderate low Very high moderate moderate low Anaemia none some severe none some none 1: Fitness and mortality are estimated as an average over 72 west African populations of humans. Data from Cavalli-Sforza and Bodmer (1971). 17