Specific Cases of Selection

1. Specific Cases of Selection • Advantageous dominant allele + Disadvantageous recessive allele W11 = W12 > W22 p2(1) + 2pq (1) + q2(1-S) =1-sq2 So... ∆ p = spq2 / (1-sq2) ∆ q = -spq2 / (1-sq2)

2. Selection Example 1 SINCE: ∆ p = Spq2 / (1-Sq2) ∆ q = -Spq2 / (1-Sq2) THEN ∆ p = -∆ q We call this Purifying Selection!

3. Selection Example 2 • Fitness of heterozygote is greater than either homozygote W11 < W12> W22 Substitute 1-s, 1, 1-t for W11, W12, W22 So... ∆ p = pq(-Sp+tq) 1-Sp2 – tq2 Therefore... the freq. of A1 is proportional to the relative strength of selection against A2A2

4. Selection Example 3 • Heterozygote is intermediate between the 2 homozygotes ∆ p = (1/2)Spq / (1-sq)

5. If we look carefully... ∆ p = (1/2)Spq / (1-sq) We see that (1-Sq) is actually W [remember W = average relative fitness] This is because 1-p=q so ∆ p = -∆ q

6. ∆ p = -∆ q The rate of decline of the disadvantageous allele is given by the negative value of increase of the positively selected allele (and vice versa)

7. ∆ q = -spq / W This expression (derived from ∆ p = (1/2)spq / (1-sq)) describes the rate that purifying selection reduces the frequency of the deleterious allele So, if p=1, you have a stable equilibrium as the rate of increase is proportional to p & q and the coefficient of selection S

8. ∆ q = -spq / W • What does all this mean? • It tells us that ∆ p, the rate of evolutionary change, increases as the variation at the locus increases • When selection is weak, ∆ p, is approx. proportional to the product of pq • Also, ∆ p is positive as long as s is greater than zero, even if s is very small!

9. Power of Natural Selection As long as no other evolutionary factors intervene, a characteristic with even a minuscule advantage will be fixed by natural selection This explains the extraordinary apparent “perfection” of some adaptations we see in nature!

10. Dominant & Recessive Traits Whether a trait (or allele) is Dominant or Recessive influences the rate of allele frequency change, but not its qualitative outcome! ∆ p = spq2 / 1-sq2 A1 increases to fixation max rate p=0.25 q=0.75

11. Generations to Fixation Depends on: • Initial allele frequencies • Selection coefficient • Degree of dominance

12. Generations to Fixation Example: (without dominance) p (A1) = 0.75 and q (A2) = 0.25 Fitness: A1A1=1 A1A2=0.99 A2A2=0.98 Requires 110 generations for A1 freq. to go from 0.75  0.90 Requires ANOTHER 240 generations for A1 freq. to go from 0.90  0.99

13. Generations to Fixation Example: (WITH Dominance) p (A1) = 0.75 and q (A2) = 0.25 Fitness: A1A1=1 A1A2=1 A2A2=0.99 Requires 710 generations for A1 freq. to go from 0.75  0.90 Requires ANOTHER 9,240generations for A1 freq. to go from 0.90  0.99

14. Generations to Fixation A rare recessive allele occurs mostly in heterozygous form, thus, deleterious recessive alleles should exist in very low frequencies at many loci This is because (as we have seen in the last slide) it takes SOOOOO long to remove these alleles from the population... perhaps as long as it would take for mutation to make new forms!

15. Generations to Fixation If we have an advantageous mutation which is initially rare, it increases rapidly if expressed in the heterozygote (especially if dominant or partially dominant) than if it is recessive!

16. Directional Selection If a locus has experienced consistent directional selection for a long time, the advantageous allele should be near fixation!

17. Persistence of Deleterious Alleles Advantageous alleles should be fixed by directional selection. However, deleterious alleles often persist because they are repeatedly introduced, by mutation, or by gene flow

18. Persistence of Deleterious Alleles What happens if a stable equilibrium (a balance) is reached between the rate at which a deleterious allele is introduced by mutation or gene flow? p = 1-q A2 is recessive up = spq2 / w

19. up = spq2 / w What does this equation tell us?  The equilibrium rate for introduction of deleterious alleles into a population is proportional to the mutation rate!!!!!

20. Selection and Gene flow • Directional selection fixes different alleles among different populations of a species • Thus, in the absence of gene flow: q  1 in some populations q  0 in other populations

21. Selection and Gene flow • Gene flow among populations can introduce each allele into population where it is absent (remember how gene flow can homogenize allele frequencies!) q = balance between gene flow and selection

22. Selection and Gene flow If m (=gene flow) is less than s (=selection) then: q is approx. = mqm/s (where qm = freq. of allele q in immigrants)

23. Selection and Gene flow • What if a series of populations are distributed along an environmental gradient where selective pressures change along this gradient? • In the absence of gene flow, we would expect an abrupt shift in allele freq. (stepped cline) at the point where selection favors different alleles

24. Selection and Gene flow • What about if there was gene flow between these populations along this cline of selection pressure? • We would expect to, instead, see a smooth cline in allele freq. as we look along this gradient

25. Mytilus edulis (blue mussel) • Examined the frequency of the ap94 allele of amino peptidase I locus • ap94 freq. increases from 0.12  0.55 with as salinity increases from E – W • ap94 genotypes have higher intercellular amino acid levels making the allele favored for life in more saline waters (towards the W) • However, high enzyme activity is less advantageous in low salinity environments...

26. Mytilus edulis (blue mussel)

27. Maintenance of Polymorphism • We know that natural selection can only operate on variation which is, essentially, the same as saying Polymorphism • Given the importance of variation, hypotheses that explain how variation is maintained in populations are critical to our understanding of evolution • However, these hypotheses remain among the most debated topics in evolutionary theory • Now, based on what we have learned about selection, lets identify some mechanisms which may maintain polymorphism in populations...

28. Maintaining Polymorphism • Recurrent mutation produces deleterious alleles, subject to weak selection • Gene flow of locally deleterious alleles from other populations in which they are favored by selection • Selective neutrality (i.e. genetic drift) • Maintenance of polymorphism by natural selection

29. Heterozygote Advantage(Overdominance or Heterosis) ∆ p = pq(-Sp+tq) 1-Sp2 – tq2 p = t/s+t q = s/s+t where p & q are the equil. freqs. of A1 & A2

30. Single Locus Heterozygote Advantage • beta-Hemoglobin • 1 allele at this locus (S) is the sickle cell version of the beta subunit • It is distinguished by only a single amino acid replacement from the normal allele (A)

31. Single Locus Heterozygote Advantage • At low oxygen concentrations, the S form of hemoglobin forms large polymers (all sticks together) • This polymerization causes the RBCs to collapse (sickle) which can kill RBCs, prevent O2 transport, and produce serious problems with blood circulation! • Hetozygotes (AS) suffer only slight anemia, whereas homozygotes (SS) suffer tremendous pain, medical complications, cannot withstand moderate exertion, and may face death resulting their condition (USUALLY BEFORE REPRODUCING!)

32. Single Locus Heterozygote Advantage • If RBCs of heterozygotes are infected with Malaria (Plasmodium felciparum) the infected RBCs rapidly sickle, preventing the malaria protozoan from reproducing and continuing its infectious life cycle • Thus, carriers of the S allele are offered a degree of immunity to malaria! • In Africa where malaria can be very common, the frequency of the S allele is high because heterozygotes survive at higher rates than either homozygotes

33. Opposing Selection • In the example of sickle cell anemia, we see an interesting example of opposing forces of selection... • Antagonistic Selection – only because the heterozygote happens to have highest fitness (e.g. sickle cell anemia)

34. Varying Selection • fluctuating env. may favor different genotypes at different times; different genotypes may be fittest in different habitats or microhabitats  not true mathematically... a variable env. does not necessarily maintain genetic variation; it does so only under special circumstances

35. Varying Selection • Temporal fluctuations in the environment may slow down the rate of fixation • However, it does not usually preserve both of the two alleles indefinitely unless fitness of the heterozygote exceeds that of the homozygote

36. Spatial Variation • More likely to maintain polymorphism • Coarse Grained – individual experiences only 1 or the other state of env. during its lifetime • Fine Grained – multiple environmental states per lifetime of individual

37. Hard vs. Soft Selection • Hard Selection – likelihood of survival depends on how well its genotype equips it for the micro-environment in which it settles • Soft Selection – occurs when the # of survivors is determined by competition for a limited factor such as food

38. So... What seems to maintain polymorphism? Models indicate Course Grained environmental variation and Soft Selection are more likely to maintain genetic polymorphism than Fine Grained, Hard Selection

39. Interaction of Selection and Drift • In a finite population allele freq. are simultaneously affected by both selection and drift • Thus the Ne and s both affect changes in allele freq.

40. Interaction of Selection and Drift • The effect of drift is negligible if selection is strong relative to Ne (if s is greater than 1/4Ne) • Conversely if s is much less than 1/4Ne than allele freq. change is mainly due to drift

41. Pop size and selection • The effect of population size on the efficacy of selection has several important consequences • Population may not reach stable equilibrium, wander around due to drift • A slightly advantageous mut. is less likely to be fixed in a small pop. than in a large pop. • Population bottlenecks provide temp condition that drift may sufficiently counteract selection, so that a deleterious mutation may increase in freq.