SELECTION TOPICS

1
SELECTION TOPICS

• The life cycle
• Definitions and components
• Single-locus, 2-allele models
• General model
• Selection against recessive allele
• Selection against dominant allele
• Overdominance
• Underdominance
• Multiple alleles

2
SELECTION TOPICS

• Mutation-selection balance
• Multiple loci
• Frequency dependence
• Heterogeneous environments
• Density dependence
• Group selection / kin selection
• Fecundity selection
• The Fundamental Theorem
• Data

3
SELECTION Its real!

• Industrial melanism (Kettlewell)
• Ethanol resistance / ADH (Drosophila)
• In humans
• Sickle-cell anemia
• Huntington disease
• PKU
• Rh / Rh-
• MANY etc.s

4
SELECTION THE LIFE CYCLE

• Zygotes Adults

Viability Selection (Survival Probability)
Mating Cycle Selection (Fertility Selection,
Fecundity Selection, Gametic Selection)
5
SELECTION Definitions Components

• Viability probability of survival
• Fertility number of offspring
• Net fitness product of viability and fertility
• (These are usually means per genotype)

6
SELECTION Definitions Components

• Absolute fitness unscaled viability, fertility,
  or net fitness
• Relative fitness
• A measure of fitness, scaled so that a specific
  (usually the most fit) genotype has fitness 1
• Absolute fitness divided by the absolute fitness
  of a designated standard genotype (usually, but
  not always, the most fit)

7
SELECTION Definitions Components

• Genotype AiAj
• Viability eij (early selection)
• Fertility lij (late selection)
• Net fitness wij (eij)(lij)
• Selection
• coefficient sij 1 - wij
• (A lethal genotype has sij 1 and wij 0)

8
SELECTION COMPONENTSA Numerical Example

• Genotype A1A1 A1A2 A2A2
• Viability 1.0 0.8 0.6
• Fertility 0 5 10
• Net fitness 1.0(0) 0.8(5) 0.6(10)
• 0.0 4.0 6.0
• Relative
• fitness (wij) 0.0/6.0 4.0/6.0 6.0/6.0
• 0.00 0.67 1.00
• sij 1.00 0.33 0.00

9
SELECTION Analysis of Selection Models

• We begin by assuming
• All selection is viability selection
• One locus with two alleles

10
SELECTION1-locus, 2-allele models

• Genotype AA Aa aa
• Initial Frequency p2 2pq q2
• Relative Fitness wAA wAa waa
• Post-Selection
• Proportion p2wAA 2pqwAa q2waa
• Post-Selection p2wAA 2pqwAa q2waa
• Frequency w w w
• (Where w p2wAA 2pqwAa q2waa)

11
SELECTIONViability Estimation

• Simply reverse the steps in the previous slide
• i.e. divide post-selection frequencies by
  pre-selection frequencies
• This estimation procedure is
• valid for viabilities
• not valid in general, e.g., if selection acts
  during the reproductive cycle

12
SELECTION1-locus, 2-allele models

• Post-Selection p2wAA 2pqwAa q2waa
• Frequency w w w
• p p2wAA (1/2)2pqwAa p2wAA pqwAa
• w w
• ?p p - p p2wAA pqwAa - p
• w
• pq p(wAA - wAa) q(wAa - waa) / w

13
SELECTIONAgainst Recessive

• Genotype AA Aa aa
• Relative
• fitness 1 1 1-saa
• p (p2wAA pqwAa) / w (p2 pq) / w
• ?p pq p(wAA - wAa) q(wAa - waa) / w
• pq 0 q(saa) / w pq2saa / w
• NOTE ?p ? 0 (b/c saa, p, q, AND w ? 0)

14
SELECTIONAgainst Recessive

• ?p as a function of p

Direction of change in p
p
?p
0
0
1
-
15
SELECTIONAgainst Recessive

Direction of change in p
p
?p
0
0
1
Equilibrium _at_ p1 Equilibrium is Trivial Stable
-

• ?p as a function of p

16
SELECTIONAgainst Recessive

Direction of change in p
p
?p
0
0
1
Equilibrium _at_ p0 Equilibrium is Trivial Unstab
le
Equilibrium _at_ p1 Equilibrium is Trivial Stable
-

• ?p as a function of p

17
SELECTIONAgainst Recessive
Directional Selection

Direction of change in p
p
?p
0
0
1
Equilibrium _at_ p0 Equilibrium is Trivial Unstab
le
Equilibrium _at_ p1 Equilibrium is Trivial Stable
-

• ?p as a function of p

E.g., sickle-cell anemia in areas lacking malaria
18
SELECTIONAgainst Dominant

• Genotype AA Aa aa
• Relative
• fitness 1 1- s 1-s
• pp2wAA pqwAa/wp2 pq(1-s)/w
• NOTE p1 if the dominant is lethal (i.e. if
  s1)

19
SELECTIONAgainst Dominant

• Genotype AA Aa aa
• Relative
• fitness 1 1- s 1-s
• ?p pq p(wAA - wAa) q(wAa - waa) / w
• pq ps 0 / w p2qs / w
• NOTE
• ?p ? 0, because s, p, q, AND w are ? 0

20
SELECTIONAgainst Dominant
Directional Selection

p
?p
0
0
1
Equilibrium _at_ p0 Equilibrium is Trivial Unstab
le
Equilibrium _at_ p1 Equilibrium is Trivial Stable
-
Example Huntingtons disease (partially
dominant)
21
SELECTION Overdominance (Heterozygote Advantage)

• Genotype AA Aa aa
• Relative
• fitness 1-sAA 1 1-saa
• p p2wAA pqwAa/w
• p2 (1-sAA) pq/w

22
SELECTION Overdominance (Heterozygote Advantage)

• Genotype AA Aa aa
• Relative
• fitness 1-sAA 1 1-saa
• ?p pq p(wAA - wAa) q(wAa - waa) / w
• pq -psAA qsaa / w

23
SELECTION Overdominance (Heterozygote Advantage)

• Genotype AA Aa aa
• Relative
• fitness 1-sAA 1 1-saa
• ?p pq -psAA qsaa / w implies
• ?p 0 (an equilibrium) when
• p0, q0, or -psAAqsaa 0

24
SELECTION Overdominance (Heterozygote Advantage)

• Genotype AA Aa aa
• Relative
• fitness 1-sAA 1 1-saa
• -psAA qsaa 0
• -psAA (1-p)saa 0
• -psAA saa - psaa 0
• p(-sAA - saa) -saa
• p(e) saa / (sAAsaa)

25
SELECTION Overdominance
Equilibrium _at_ p(e) saa / (sAA
saa) Equilibrium is Polymorphic, Stable
Balancing Selection Stabilizing
Selection Protected Polymorphism Balanced
Polymorphism

p
1
?p
0
0
-
Equilibrium _at_ p0 Equilibrium is Trivial,
Unstable
Equilibrium _at_ p1 Equilibrium is Trivial,
Unstable
26
OVERDOMINANCE EXAMPLE (Sickle-Cell Anemia in
Locations with Malaria)

• Genotype AA Aa aa
• Relative
• fitness 0.85 1 0
• YOUR TURN! Please predict p(e) at the stable
  equilibrium. (This is teamwork -- please submit
  on paper.)

27
SELECTION Underdominance (Heterozygote
Disadvantage)

• Genotype AA Aa aa
• Relative
• fitness 1sAA 1 1saa
• p p2wAA pqwAa / w
• p2 (1sAA) pq / w

28
SELECTION Underdominance (Heterozygote
Disadvantage)

• Genotype AA Aa aa
• Relative
• fitness 1sAA 1 1saa
• ?p pq p(wAA - wAa) q(wAa - waa) / w
• pq psAA - qsaa / w
• ?p 0 (an equilibrium) when
• p0, q0, or psAA - qsaa 0

29
SELECTION Underdominance (Heterozygote
Disadvantage)

• Genotype AA Aa aa
• Relative
• fitness 1sAA 1 1saa
• psAA - qsaa 0
• psAA - (1-p)saa 0
• psAA - saa psaa 0
• p(sAA saa) saa
• p(e) saa / (sAA saa)

30
SELECTION Underdominance
Equilibrium _at_ p(e) saa / (sAA
saa) Equilibrium is Polymorphic, Unstable

p
0
?p
0
1
Disruptive Selection
-
Equilibrium _at_ p0 Equilibrium is Trivial, Stable
Equilibrium _at_ p1 Equilibrium is Trivial, Stable
31
SELECTION Multiple Alleles
Diploid Genotypic Viability Matrix
Freq(Ai) pi ?pi 1 wij ? fitness of AiAj
i
32
SELECTION Multiple Alleles
Diploid Genotypic Viability Matrix
Marginal Fitness of Ai wi ?wijpj Population
Mean Fitness w ?piwi ??wijpipj
j
i
i
j
33
SELECTION Multiple Alleles

• One can show pi pi( wi / w )
• Hence, pi increases over time if wi w
• Equilibria occur when pi - pi 0
• ? System of n linear equations
• ? Few general conclusions can be drawn
• ? Several specifics are known (next slide)

34
SELECTION Multiple Alleles

• n trivial equilibria exist (corresponding to
  fixation of each of the n alleles)
• May be other equilibria, depending on viability
  matrices
• Heterozygote advantage (wii wjj), for all
  i, j, does NOT assure a complete polymorphism
• Complete polymorphism is stable if BOTH of the
  following inequalities hold
• 1. wij
• 2. wij (wii wjj) / 2

35
SELECTION Multiple Alleles

• Complete polymorphism is stable if BOTH of the
  following inequalities hold
• 1. wij
• 2. wij (wii wjj) / 2
• How often are these conditions met?
• Hardly ever!
• R. Lewontin coworkers generated and analyzed
  many random viability matrices (all of which
  included heterozygote advantage)
• E.g. for a locus with 7 alleles, only 0.1 of
  the viability matrices met the above 2 conditions
• CONCLUSION SELECTION IS UNLIKELY TO MAINTAIN
  MORE THAN A FEW ALLELES AT A LOCUS! . . . So . .
  . Do you think selection is important at DNA
  forensic loci?

36
SELECTIONBalance with Point Mutation

• With both selection and mutation, we suspect a
  polymorphic equilibrium

1
Directional Selection
q
q(e)
Point Mutation
0
Time
37
Selection Against Dominant Allele, With Mutation
From before, gain of A1 by selection ?p p2qs
/ w BUT, loss of A1 by mutation ?p
-up Overall ?p -up (p2qs / w ) At
equilibrium ?p -up (p2qs / w ) 0 At
equilibrium, q is small, so p ? 1 and w ?
1 Thus -u(1) (12qs / 1) ? 0 q(e) ? u / s
38
Selection Against Recessive Allele, With Mutation
From before, gain of A1 by selection ?p
pq2saa / w BUT, loss of A1 by mutation ?p
-up Overall ?p -up (pq2saa / w ) At
equilibrium ?p -up (pq2saa / w ) 0 At
equilibrium, q is small, so p ? 1 and w ?
1 Thus -u(1) (1q2saa / 1) ? 0 q(e) ? (u
/ saa)1/2
39
SELECTIONBalance with Mutation

• So what?
• Phenotypic frequencies should be
• With dominant allele ? 2u / s
• With recessive allele ? u / saa
• So, with selection-mutation equilibrium, we can
  use phenotypic frequencies to
• Estimate u (if we know selection coefficient)
• Estimate selection coefficient (if we know u)

40
SELECTION Multiple Loci

• Consider this gametic fitness matrix

wi. fitness effect of Ai w.i fitness effect
of Bi
The fitnesses in this matrix are ADDITIVE.
41
SELECTION Multiple Loci

• Consider this gametic fitness matrix

wi. fitness effect of Ai w.i fitness effect
of Bi
The fitnesses in this matrix are MULTIPLICATIVE.
42
SELECTION Multiple Loci

• Consider this gametic fitness matrix

Fitnesses in this matrix are epistatic.
Selection is epistatic when the fitness effect of
an allele of one locus depends on the alleles of
another locus.
43
SELECTION Multiple Loci

• Remember disequilibrium (D)????
• Epistatic selection can lead to non-zero D
• In the example above, D increases because
• A1B1 A2B2 tend to increase in frequency
• A1B2 A2B1 tend to decrease in frequency
• The population will forever remain polymorphic at
  both loci
• D ? 0 permanently

44
SELECTION Multiple Loci

• Remember disequilibrium (D)????
• Other selection can cause non-zero D
• Hitch-hiking selection
• Target of selection is one locus
• Causes allele-frequency changes at neutral loci
  (and temporary non-zero D), IF
• D ? 0 initially between selected and neutral loci
• Selected and neutral loci are linked or are in
  inbreeders

45
Epistatic Selection orHitch-hiking Selection?

• Its usually difficult to discern cause of
  disequilibrium
• Consider an example composite-cross
  cultivated barley populations
• Mixtures/hybrids of many varieties
• Established in 1920s - 1940s
• Grown each year ever since
• Now in generations 60 - 80

46
Epistatic Selection or Hitch-hiking Selection?

• Isoenzyme genetic markers
• We focus on 4 loci (each with 2 alleles)
• Esterase A
• Esterase B
• Esterase C
• Esterase D
• All 4 loci were studied in barley in
• Many generations of two composite crosses
• USDAs world collection of barley

47
Epistatic Selection or Hitch-hiking Selection?

• Observations in Composite Crosses
• Of the 16 possible 4-locus gametic combinations,
  two increased in frequency over time (i.e. D
  increased)
• 1221 increased in frequency
• 2112 increased in frequency
• This result occurred in both composite crosses
  studied
• Clegg, M.T., R.W. Allard and A.L. Kahler. 1972.
  Is the gene the unit of selection? Evidence from
  two experimental plant populations. Proc. Natl.
  Acad. Sci. USA 692474-2478.

48
Epistatic Selection or Hitch-hiking Selection?

• Observations in USDA world collection
• D large
• Two 4-locus gametic combinations are in excess of
  expectation
• 1221 frequency expected if D0
• 2112 frequency expected if D0
• These are the same combinations that increased in
  frequency in composite crosses!
• Kahler, A.L. and R.W. Allard. 1981. Worldwide
  patterns of genetic variation among four esterase
  loci in barley (Hordeum vulgare L.). Theoret.
  Applied Genet. 59101-111.

49
Epistatic Selection or Hitch-hiking Selection?

• Why are 1221 2112 favored?
• Epistatic selection? In principle, a possible
  cause
• Hitch-hiking? Plausible because
• 1221 2112 are common in parents of composite
  crosses
• 1221 2112 may have been common at origin of
  cultivated barley
• s0.99 in cultivated barley
• A, B, C loci are tightly linked

50
Epistatic Selection or Hitch-hiking Selection?

• How to distinguish between the two causes?
• Answer initiate populations that lack 1221 and
  2112 combinations
• E.g., begin with 1111 X 2222 cross
• Actual Result 1221 2112 increased faster than
  expected (in 8 different populations)
• Conclusion hitch-hiking rejected as cause of
  disequilibrium observed in barley

51
What locus is the target of selection?

• In barley example, selection could be acting on
• 1. The 4 esterase loci themselves
• OR
• 2. Other loci tightly linked to each of the 4
  esterase loci
• How to distinguish 1 vs. 2?
• Randomize esterase alleles within genetic
  background
• Study mechanism of selection

52
What locus is the target of selection?

• Consider example of apparent selection on PGI
  alleles in Colias butterflies
• Observations (population dynamics)
• Certain genotypes have high fitnesses at low
  temperatures (high altitude Colorado)
• At high temperatures other PGI genotypes are most
  fit (mediterranean California)
• Two possible explanations
• 1. Selection acts on PGI genotypes directly
• 2. PGI alleles hitch-hike due to selection on
  some unknown locus linked to PGI

53
What locus is the target of selection?

• Does selection act directly on PGI genotypes in
  Colias?
• If so . . . biochemical characteristics of PGI
  from favored genotypes should be superior to
  those of disfavored genotypes

54
What locus is the target of selection?

• Does selection act directly on PGI genotypes in
  Colias?
• Experimental Results
• PGI of genotypes with higher fitnesses at low
  temps had superior kinetic properties (based on
  Vmax Km) at low temps
• PGI of genotypes with higher fitnesses at high
  temps had superior kinetic properties at high
  temps

55
What locus is the target of selection?

• Does selection act directly on PGI genotypes in
  Colias?
• Conclusion
• Selection acts on PGI directly, rather than via
  hitch-hiking.
• Watt, W.B., R.C. Cassin and M.S. Swan. 1983.
  Adaptation at specific loci. III. Field
  behavior and survivorship differences among
  Colias PGI genotypes are predictable from in
  vitro biochemistry. Genetics 103725-739.

56
SELECTION Multiple Loci

• Remember disequilibrium (D)????
• Other selection can cause non-zero D
• Directional selection, additively for multiple
  loci, causes temporary non-zero D

57
SELECTION Multiple Loci

• Consider this additive viability matrix
  (selection is directional for each of two loci)

• Assume
• 1. p1 p2 q1 q2 0.5 initially
• 2. Each locus is in H-W genotypic proportions
  initially
• 3. D0 initially
• What are D and D after one round of selection?

58
SELECTION Multiple Loci

• Punchlines for multiple loci
• 1. Permanent non-zero D requires epistatic
  selection
• 2. For D to be large permanently, epistasis
  must overcome tendency of recombination to
  reform disfavored genotypes, so . . .
• Epistasis must be strong (relative to inbreeding
  linkage), i.e.
• Inbreeding linkage must be weak (relative to
  strength of epistasis)
• 3. When we observe D ? 0 or D increasing, we
  should not assume epistasis!

59
SELECTIONComplications due to Reality

• FREQUENCY DEPENDENCE tends to maintain variation

High
E.g., gametophytic self-incompatibility in
plants rare male advantage in Drosophila
Fitness
wAa
wAA
waa
Low
1
0
p1
60
SELECTIONComplications due to Reality

• HETEROGENEOUS ENVIRONMENTS can maintain variation
• Environmental heterogeneity over space
  (geographical variation)
• Maintains high FST
• Environmental heterogeneity over time within
  subpopulations
• Maintains variation within subpopulations

61
SELECTIONComplications due to Reality

• DENSITY DEPENDENCE
• Two extreme situations to consider
• 1. Populations at carrying capacity
• k-selection
• Fitness of AiAj depends on its carrying capacity
  (kij)
• 2. Colonizing populations, rapid population
  growth
• r-selection
• Fitness of AiAj depends on intrinsic rate of
  increase (rij)
• The genotype(s) favored by r-selection may differ
  from the genotype(s) favored by k-selection!

62
SELECTIONComplications due to Reality

• GROUP SELECTION
• Altruism alleles that benefit group at expense
  of individual should increase in frequency, due
  to success of cooperative group
• BUT . . . non-cooperative mutant, when it occurs,
  should increase in frequency within group
  eliminate altruism alleles
• This paradox can be resolved by kin selection, in
  which altruism benefits relatives (e.g., in
  social insects),
• so . . .

63
SELECTIONComplications due to Reality
Because of kin selection . . . . . .
evolutionarily speaking . . . . . . you should
be willing to lay down your life for 1 twin, 2
full-siblings, 8 first cousins (and so on . .
.)! Inclusive fitness more important than
individual fitness in kin selection models . . .
64
SELECTIONComplications due to Reality

• FERTILITY, FECUNDITY GAMETIC SELECTION
• Thus far, we have considered viability selection
• BUT Selection can operate in the mating cycle!
• Fertility selection varying average numbers of
  offspring produced by different diploid genotypes
• Gametic selection varying average fertilization
  success of different gametic (haploid) genotypes
• Fecundity selection varying average numbers of
  offspring produced by mating pairs

65
SELECTIONComplications due to Reality
Selection Components in Slender Wild Oat
Clegg, M.T. and R.W. Allard. 1973. Viability
versus fecundity selection in the slender wild
oat, Avena barbata L. Science 181667-668.
66
SELECTIONComplications due to Reality

• FERTILITY, FECUNDITY GAMETIC SELECTION
• These topics could occupy you for a long time . .
  .
• We will not delve into them deeply, but . . .
• We will consider one result, which you may find
  surprising . . .

67
FECUNDITY SELECTION

• Consider this fecundity matrix (cell entries are
  the average numbers of offspring produced by the
  mating pairs)

• Assume these initial conditions
• 1. p1 0.9
• 2. H-W genotypic proportions
• 3. No viability selection
• Compute mean fecundity for this and the next 2
  generations.

68
FECUNDITY SELECTION

• In this fecundity matrix, selection decreases the
  populations mean fitness!!!!

But we have all been taught that natural
selection increases mean fitness . . . ! (Even
Sir R. A. Fisher believed it to be true!)
69
THE FUNDAMENTAL THEOREM OF NATURAL SELECTION

• The rate of increase of mean fitness is equal
  to the genetic variance in fitness (Sir R. A.
  Fisher 1930)
• If the Fundamental Theorem is true
• Evolution by selection requires genetic variation
  in fitness
• Selection never causes mean fitness to decrease

70
THE FUNDAMENTAL THEOREM OF NATURAL SELECTION

• The Fundamental Theorem is true only for certain
  types of selection, such as single-locus
  viability selection

71
THE FUNDAMENTAL THEOREM OF NATURAL SELECTION
Mean Fitness vs. Allele Frequency with
Directional Viability Selection
1
Mean Fitness
0
0
1
Allele Frequency
72
THE FUNDAMENTAL THEOREM OF NATURAL SELECTION
Mean Fitness vs. Allele Frequency with Viability
Overdominance
1
Mean Fitness
0
pe
0
1
Allele Frequency
73
THE FUNDAMENTAL THEOREM OF NATURAL SELECTION
Mean Fitness vs. Allele Frequency with Viability
Underdominance
1
Mean Fitness
0
pe
0
1
Allele Frequency
74
THE FUNDAMENTAL THEOREM OF NATURAL SELECTION
Adaptive Topography for 2-Locus Viability
Selection
1
(Contours represent mean fitness)
Allele Frequency
0
0
1
Allele Frequency
75
THE FUNDAMENTAL THEOREM OF NATURAL SELECTION

• The Fundamental Theorem
• Its NOT fundamental
• Its NOT a theorem!
• You have demonstrated its shortcoming by your
  work on fecundity selection!