Functional divergence 1: FFTNS and Shifting balance theory

Transcription

1 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

2 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 Genotype Phenotype Symbolism AA Aa W AA W Aa 1 1 aa W aa

3 A review of fitness: Directional selection Fitness AA Aa aa Genotypes W AA > W Aa > W aa 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 Fitness AA Aa aa W AA < W Aa > W 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

4 A review of fitness: Symbolism for generation 0 Genotype AA Aa aa Frequency 2 p 0 2p 0 q 0 2 q 0 Phenotype W AA W Aa W aa Survival ratio: W AA : W Aa : W aa Genotype ratio: p 2 W AA : 2pqW Aa : q 2 W aa 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 + 2pqW Aa + q 2 W aa W = AVERAGE FITNESS Genetic load: 1 W 4

5 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

6 FFTNS R = W = Va 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

7 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 W = p 2 W AA + 2pqW Aa + q 2 W aa Ave fitness of popualtion W AA =0.1 W Aa = 0.75 W aa = 1 Directional selection frequncey of allele "a" 7

8 Adaptive topography Another simple case: 1 locus, 2 alleles, overdominant selection W = p 2 W AA + 2pqW Aa + q 2 W aa Ave fitness of poplation W AA = 0.5 W Aa = 1 W aa = freqeuncy of allele "a" Adaptive topography More complex case: 1 locus, 3 alleles, overdominant & directional selection. we need a De Finetti diagram 8

9 Introduction to the De Finetti diagram: Indicates: Allele 1: freq = 0.35 Allele 2: freq = 0.15 Allele 3: freq = 0.50 Allele 1 Alleles 2 and 3 have freq =0 at this vertex Alleles 1 and 2have freq =0 at this vertex 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 Lines: fitness contours where the frequencies of the three alleles yield the same population fitness Allele 1 Lowest mean fitness Local peak in mean fitness Valley on the fitness landscape Global peak in mean fitness Allele 2 Allele 3 9

10 Adaptive topography More complex case: 1 locus, 3 alleles, overdominant & directional selection start here end here start here end 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

11 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 = q) W a = q(w aa ) + p(w Aa ) Allele A (freq = p) Allele a (freq = q) Allele c (freq = r) 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

12 Adaptation in human populations: sickle cell haemoglobin 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

13 Sickle cell crisis and anemia have profound clinical consequences S-RBC lifespan: 20 days (verses 120) 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 plasmodium infected cells: direct destruction [?] 2. High oxygen radical production by sickle-cells kills parasites [?] 3. Promotes immune system attack 13

14 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 * : Fitness and mortality are estimated as an average over 72 west African populations of humans. Data from Cavalli-Sforza and Bodmer (1971). * Cerebral anemia is not fun 14

15 A and S allele polymorphism is classic example of overdominant selection Ave fitness of poplation freqeuncy of allele "S" As before, the fitness of the population can only go uphill. Marginal fitness calculations verify this result. Initial freq of S = 0.01: W S = 0.99 and W = 0.89 W S - W = 0.11; the S allele will increase Initial freq of S = 0.25: W S = 0.8 and W = 0.89 W S - W = ; the S allele will decrease 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

16 A and C allele polymorphism is classic example of directional selection Genotypes AA AC Blood Phenotype Normal Normal Fitness 0.89 * 0.89 * Data from Cavalli-Sforza and Bodmer (1971). CC Resistant 1 * Cerebral anemia is not fun A and C allele polymorphism is classic example of directional selection Ave fitness of popualtion frequncey of allele "a" c As before, the fitness of the population can only go uphill. Marginal fitness calculations verify this result. Initial freq of C = 0.01: W C = and W = W C - W = ; the C allele will slowly increase Initial freq of C = 0.25: W C = and W = 0.90 W C - W= +0.02; the C allele will increase Peak in average fitness of population Natural selection arrives at a solution that protects about 100% of the population 16

17 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 Frequency p 2 2pq q 2 2pr 2qr r 2 Fitness 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

18 Let s consider a population with A, S and C alleles Population close to balanced A/S polymorphism: Frequency of A = = p Frequency of S = = q Frequency of C = = r W = W S = q(w SS ) + p(w AS ) + r(w SC ) W S = 0.12(0.2) (1) (0.71) W S = W C = r(w CC ) + p(w AC ) + q(w SC ) W C = 0.001(1.31) (0.89) (0.71) W C = Importance of historical effects 2. Natural selection can prevent adaptation Let s consider a population with A, S and C alleles Assume both S and C are rare: Frequency of A = = p Frequency of S = 0.05 = q Frequency of C = 0.01 = r W S = W C = W = W S - W= 0.06; The S allele invades! W C - W = -0.01; the C allele cannot invade! 18

19 Adaptive topography for three allele case [same as before] S allele In this region the C allele only needs to be a littler more than 10% The C allele has to start with a high frequency in order for it to invade A allele C allele Let s consider a population with A, S and C alleles Assume both S and C are rare: Frequency of A = 0.64 = p Frequency of S = 0.25 = q Frequency of C = 0.11 = r W S = W C = W = W S - W = -0.10; The S allele is a gonner! W C - W = +0.01; the C allele invades! 19

20 Adaptive topography for three allele case Natural selection cannot move population across the valley! Two other population genetic forces can: 1. Strong genetic drift: increase C > 10% 2. Inbreeding: does not change allele frequencies reduce frequency of AS heterozygote Increase frequency of CC homozygote Sewall Wright: shifting balance theory (SBT) of evolution The problem as I see it is that of a mechanism by which species may continually find its way from lower to higher peaks 20

21 SBT: assumptions Assumption 1: Large amount of polymorphism in equilibrium. Variation must be relevant to fitness Fitness variation is relevant to minor factors Assumption 2: Each gene has many phenotypic effects [pleiotropy] Assumption 3: Complex adaptive topography Assumption 4: Multiple, partially isolated populations 21

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24 SBT: Three phases 1. Phase of genetic Drift [exploration] 2. Phase of Mass selection 3. Phase of inter-population selection 24

25 Difficulties with SBT 1. Species never get stuck on peaks; there is always a way off. 2. N e of natural populations too large for drift to move them around to the degree required by SBT SBT has been controversial since the beginning 25

26 Modern difficulties with SBT 1. Requires: low migration rates for exploration and transition [phases 1 and 2]; and higher migration rates for phase Population structures typical of natural populations seem to be too small for phase 1 3. Group selection is a weak force for evolution, and hence unlikely to result in a shift in equilibrium: an extremely high amount of migration is required among sub-populations for phase 3 to work. 4. Alternatives seem more likely. Wright suggested some alternatives 1. Change in environment.. 2. Mutation.. 3. Change in strength of selection.. It seems that SBT and the alternatives require some waiting 26

27 SBT and FFTNS are important theories Their status and role are quite different from that of the neutral theory 27