Evolution at Multiple Loci

1
Evolution at Multiple Loci

• Linkage Equilibrium / Disequilibrium

2
The setting and terminology

• Deals with the consideration of two loci
  simultaneously
• The loci are physically linked on the same
  chromosome
• Locus A with alleles A, a and locus B with
  alleles B and b
• We track not only frequencies of alleles but also
  frequencies of chromosomes

3
More terminology

• Possible chromosome genotypes for this example
  are AB Ab aB ab
• These multi-locus genotypes of chromosomes (or
  gametes) are called haplotypes ( for haploid
  genotype)
• These haplotypes may occur in either Linkage
  Equilibrium or Linkage Disequilibrium

4
Loci which are linked together in Linkage
Equilibrium

• Have genotypes that are independent of one
  another.
• If you know the genotype at one locus (A) you
  cannot predict what the genotype will be at the
  other locus (B).
• Example Suppose that the gene which controls the
  length of toes in frogs (A) is linked to the gene
  that controls the amount of webbing between the
  toes (B).
• Populations that are in linkage equilibrium will
  show no correlation between toe length and the
  degree of webbing between them.

5
Loci which are in Linkage Disequilibrium

• Genotypes of the chromosomes (Haplotypes) exhibit
  a non random association between the linked
  genes.
• If you know the genotype at one locus (A) you
  have a clue about the genotype at the other locus
  (B).
• Example back to the gene which controls the
  length of toes in frogs which is linked to the
  gene that controls the amount of webbing between
  the toes.
• Populations that are in linkage disequilibrium
  will show a correlation between toe length and
  the degree of webbing between them.
• For instance we might observe that the shorter
  the toes the more webbing and the longer the toes
  the less webbing that occurs.

6
Comparing linkage equilibrium with linkage
disequilibrium
7
Predicting Haplotype frequencies
8
Linkage equilibrium

• If the frequencies of the haplotypes can be
  calculated by multiplying the frequencies of the
  two alleles involved, then they are in linkage
  equilibrium.
• Also, if the occurrence of B allele is equally
  likely on either the A or the a chromosome the
  alleles are in linkage equilibrium

9
Linkage Disequilibrium

• If the frequencies of the haplotypes cannot be
  calculated by multiplying the frequencies of the
  two alleles involved, then they are in linkage
  disequilibrium
• The occurrence of B allele is not equal on the
  A and the a chromosomes

10
Effects of selection
11
In Linkage Equilibrium

• If selection acts on one locus only....
• Selection for the A allele has no effect on the
  B allele frequency. See Figure 8.8b

A 5/25 .2 a .8
A 20/25 .8 a .2B 20/25 .8 b .2
B 20/25 .8 b .2
12
In Linkage Disequilibrium

• If selection acts on one locus only....
• Selection for the A allele changes the B allele
  frequencies also. As a chromosomes are lost they
  drag B alleles along in a disproportionate
  fashion. See Figure 8.8a

A 5/25 .2 a .8
A 20/25 .8 a .2B 17/25 .68 b .32
B 8/25 .32 b .68
13
Chromosome frequencies
14
Linkage equilibrium

• In linkage equilibrium chromosome (haplotype)
  frequencies do not change, they can still be
  predicted (calculated) from allele frequencies.
• B20/25.8 b5/25 .2 A20/25 .8
  a5/25 .2
• AB .64 Ab .16 aB .16 ab .04
• AB 16/25 .64 Ab 4/25 .16
• aB 4/25 .16 ab 1/25 .04

Calculated haplotype frequencies
15
Linkage disequilibrium

• In linkage disequilibrium chromosome frequencies
  change, they can not be predicted (calculated)
  from allele frequencies.
• B8/25 .32 b17/25 .68 A20/25 .8
  a5/25 .2
• AB.256 Ab .544 aB .064 ab .136
• AB 4/25 .16 Ab 16/25 .64
• aB 4/25 .16 ab 1/25 .04

calculated
16
Three tests for linkage Equilibrium

• The frequency of B on chromosomes carrying
  allele A is equal to the frequency of B on
  chromosomes carrying allele a.
• The frequency of any chromosome haplotypes can be
  calculated by multiplying the frequencies of the
  alleles which compose that haplotype
• The quantity D, (coefficient of disequilibrium)0
• D gABgab - gAbgaB
• g is the frequency of the various haplotypes

Verify
17
What causes linkage disequilibrium

• selection on multilocus genotypes
• genetic drift
• population admixture

18
Selection on multilocus genotypes

• If we use the population from figure 8.2 (p. 283)
  to provide gametes to the next generation which
  is now undergoing multilocus selection we have a
  possibility of the following haplotypes in each
  gamete
• AB Ab aB or aB
• The frequencies of the possible zygotes formed by
  this population in the next generation are given
  by

19
View punnett square
AABB (.2034) AABb (.0576) AaBB (.1536)
AaBb (.0384)   AABb (.0576) AAbb (.0144)
AaBb (.0384) Aabb (.0096)   AaBB (.1536)
AaBb (.0384) aaBB (.1024) aaBb
(.0256)   AaBb (.0384) Aabb (.0096) aaBb
(.0256) aabb (.0064)
This population is in Linkage equilibrium until.
See Figure 8.3 pg 287
20
Differential selection now acts on this
population such that.
All individuals which are smaller than 13 units
in size (indicted by individuals with less than 3
dominant alleles) are eaten by predators and
eliminated from the population, Leaving
21
A population that is now in disequilibrium
How can we verify that this population is in
linkage disequilibrium?
22
Test 1 Frequency of B alleles on A and a
chromosomes is the same

• Looking at the last figure we can count the
  frequency of B on A and on a

B on A
.88
B on a
1.0
23
Test 2 the frequency of any haplotype can be
calculated by multiplying the frequencies of
constituent alleles

• a
• b

• ab frequency should be .02 but it is actually 0

24
Finally we test to determine if the linkage
equilibrium value for D is equal to zero

• D gABgab - gAbgaB
• gab 0
• so D a negative value and D is not 0

25
Lets try another scenario using these same
chromosomes

• Lets look at problem 3 on page 313. Work with
  the people at your table to answer part a.

26
We have just examined how selection on multilocus
genes can lead to linkage disequilibrium

• Genetic drift and population admixture also
  disrupt linkage equilibrium
• We will not be doing examples of these. If you
  are interested please refer to your text on pages
  288-289.

27
Why and when does disequilibrium matter

• If populations are in linkage disequilibrium,
  single locus models (Hardy Weinberg) may yield
  inaccurate predictions about the population. WHY?

28
Stop here on day one
29
We will now investigate the role of sexual
reproduction in the behavior of linked genes
30
First we will investigate the basic concepts of
sexual reproduction as it relates to the
distribution of alleles in offspring.
31
Why sexual reproduction leads to genetic
diversity ?

• Get genetic recombination due to
• Meiosis and crossing over
• Random mating between unrelated individuals
• Millions of different gametes produced by each
  parent
• Billions of possible combinations of gametes
  for each mating
• In every generation alleles which are part of a
  multilocus genotype will appear in different
  combinations
• An example from a highly simplified example
  using eye color and hair color alleles.

32
Which haplotypes are possible in the gametes from
this parent?
Haplotypes possible are rb or RB only
33
(No Transcript)
34
Eye color
Hair color
Now we have all four haplotypes rb RB Rb and
rB
Genetic recombination shuffles genotypes for
multilocus genes and will reduce genetic
disequilibrium
35
Sexual reproduction reduces linkage
disequilibrium

• Because of crossing-over and outbreeding, Sexual
  reproduction reduces linkage disequilibrium
• Meiosis and sexual reproduction lead to genetic
  recombinations of genes linked on the same
  chromosome
• Genetic recombination tends to randomize
  genotypes at one locus with respect to genotypes
  at another locus on the same chromosome
• The result is a reduction in linkage
  disequilibrium
• The greater the rate of crossing over between two
  loci, the faster linkage disequilibrium will be
  eliminated by sexual reproduction

36
An experiment on the effects of sexual mating and
equilibrium at two loci

• Fruit fly experiments of Michael Clegg
• Started with two populations both in total
  linkage disequilibrium and at the opposite ends
  of the disequilibrium scale
• Within 50 generations of sexual reproduction, all
  of the populations were approaching linkage
  equilibrium

37
Figure 8.7 pg 291
38
The adaptive significance of sex A closer look
at the importance of the role of reproductive
strategies in the survival and evolution of
species
39

• Sexual reproduction

• The cost is too high
• Many potential barriers to successful
  reproduction
• What are some of them?
• finding a mate cooperation between mates
  sexual diseases mating may prove infertile and
  result in no offspring
• Asexual Reproduction
• Asexual reproduction is so much more efficient
  and produces so many more offspring
• The offspring of the original parent are clones
  so they may be better adapted to the environment
  and survive and reproduce more

40
Which reproductive mode is better for survival ?

• John Maynard Smith (1978) developed a null model
  to explore the evolutionary fate of a population
  under sexual reproduction versus asexual
  reproduction.
• Involves two assumptions
• If both of these assumptions are met then one
  form of reproduction will not be favored over
  the other
• 1. A females reproductive mode does not affect
  the number of offspring she can produce.
• 2. A females reproductive mode does not
  affect the probability that her offspring will
  survive

41
As figure 8.17 shows, assumption 1 is not met.
Asexual parthenogenetic females will produce
larger numbers offspring than sexual reproducers
(16 of 24 are asexual)
Pg 304

• The asexuals will constitute an increasingly
  larger percentage of the population in each
  generation and should completely take over

42
What are the potential consequences?

• Just a single mutation in a sexually reproducing
  population that produces an asexual female will
  lead to inevitable takeover by asexuals
• This is not what happens in reality and sexual
  and asexual forms of many species coexist just
  fine
• For sexual species to coexist means they must
  confer some benefit for survival
• This benefit could lie in violation of either or
  both assumptions

43
There would be a violation of Assumption 1 if.
A females reproductive mode does affect the
number of offspring she can produce

• ...for instance when paternal care of the young
  is required
• Sexual populations would leave more young because
  asexuals could not take care of their young and
  not as many would survive.
• Not may species fall into this category.

44
A violation of assumption 2 is more likely
This would be violated if a females reproductive
mode does affect the probability that her
offspring will survive

• A study with flour beetles
• Dunbrack and colleagues set up a study that
  compared asexual populations and sexual
  populations of flour beetles and compared the
  ability of the two population to respond to an
  environmental stress, namely the application of
  an insecticide to their food.
• Figure 8.18 shows the results

45
The control alone, would supports assumption 1
that if there is an advantage in the number of
offspring produced then that type of reproduction
should be favored
10
20
30
Looking at this experimental population and
comparing it to the control shown above, we see
that there appears to be a definite advantage to
sexual reproduction. The sexually reproducing
population eventually eliminated the asexual
population when exposed to selection stress.
Why is this?
Figure 8.18 pg 306
10
20
30
46
Sexual strains can evolve, asexual strains cannot
47
Same experiment but with the black beetle being
given the sexual role. We see essentially the
same results
We can conclude that assumption 2 is incorrect
10
20
30
48
At the level of population genetics, reduction of
linkage disequilibrium is the only consequence of
sex

• Therefore if a population is already in linkage
  equilibrium there is no advantage to sexual
  reproduction
• Population-genetic Models which propose
  evolutionary benefits for sex must include two
  things
• 1. A mechanism to produce linkage disequilibrium
  
• 2. An explanation for why genes that tend to
  reduce disequilibrium are favored

49
Theories dealing with the advantages of sexual
reproduction

• There are two categories of models based on the
  source of linkage disequilibrium
• 1. Those that propose genetic drift
• 2. Those that propose selection on multilocus
  genotypes.

50
Pairs of genes most likely to show
disequilibrium are those that are situated so
closely together on the chromosome that crossing
over between them is rare.

• Linkage disequilibrium is most often a problem in
  asexual populations since sexual reproduction
  tends to eliminate linkage disequilibrium
• In freely mating populations most pairs of loci
  should be in linkage equilibrium and single-locus
  models will work well most of the time

51
Mullers Ratchet Genetic Drift plus Mutation
can make sex beneficial

• Works in populations which are small, where drift
  is a potent mechanism
• As mutations occur in asexual populations, they
  are passed on to all offspring of the asexual
  parent
• Over time several mutations can be accumulated in
  a population (the frequency of each individual
  mutant allele is a balance between mutation rate,
  the strength of selection and genetic drift)
• Asexual populations are doomed to accumulate
  deleterious mutations which are passed on to all
  offspring
• Asexual populations cannot get rid of the
  mutations which are accumulating until the
  population is eliminated

52
Asexual Sub-populations are separate and
reproductively isolated from one another. These
sub-populations will have different mutations and
differing numbers of mutations

• The fittest of the sub-populations are those with
  the fewest mutations
• However, drift can eliminate any of these
  populations by chance
• Figure 8.20 pg 308 shows how this works

53
Each bar represents an asexual sub-population.
Sub populations will differ in the number of
mutations they contain. The sub-population with
the fewest deleterious mutations will be the
fittest.
If the 0 mutation group is lost by drift then the
fittest group now becomes the population with
only one mutation
If drift then takes the1-mutation sub-
population, the fittest is the one with 2
mutations etc
54

• Over time as the populations age the shift is
  toward the accumulation of more and more
  mutations

• Genetic load increases, the populations are less
  and less fit and ultimately the population
  becomes extinct
• Genetic Load the accumulation of deleterious
  alleles, the more harmful mutations there are in
  a population the greater the genetic load.

55
Summary of Mullers Ratchet

• The milder the deleterious mutations, the quicker
  the ratchet works. If mutations are too serious,
  selection will eliminate them before drift can
  carry them to fixation
• There are examples from laboratory experiments
  and in nature that show that mutation and drift
  could indeed be a mechanism to favor sexual
  reproduction
• However this mechanism works very slowly over a
  long period of time

56
Sexual reproduction breaks the ratchet

• In the case of sexually reproducing species,
  groups which are lost by chance can be
  reconstituted by outcrossing and recombination
• Example if the 0 mutation group has been lost
  and two individuals each with just 1 mutation
  mate, then 1/4 of their offspring will be
  mutation-free
• Sex reduces linkage disequilibrium by recreating
  the missing genotypes

57
Selection Caused by a changing environment

• In general constant environments favor asexual
  reproducers that are well adapted to the current
  environment
• When the environment changes they are at a
  disadvantage
• The changing environment theories for the
  advantage of sex assume trade-offs such that
• genotypes that do well in one type of environment
  necessarily do more poorly in others

58
Population Genetic Model of varying selection

• Basically involves alternating between a
  selection regime which favors selection of
  particular multilocus genotypes at one point in
  time and then later selection is for a different
  set of multilocus genotypes
• Sex can recreate the genotypes that were
  recently eliminated but have now become favored
• Differences in fitness may be caused by either
  physical changes in the environment or by changes
  in biotic interactions ( Elderflower example)

59
The Red Queen Hypothesis

• Red Queen hypothesis, refers to the huffy chess
  piece in Lewis Carroll's Through the Looking
  Glass. In Looking Glass Land, the Queen tells
  Alice, "It takes all the running you can do, to
  keep in the same place."
• According to the Red Queen hypothesis, sexual
  reproduction persists because it enables many
  species to rapidly evolve new genetic defenses
  against parasites that attempt to live off of
  them.

60
PBS evolution video segment

• You may click the button below to review the main
  points of the video.
• As the parasites adapt to new genotypes In the
  fish, if they are asexual they are susceptible
• Meanwhile the sexuals can continue to recombine
  and present resistant genotypes on a regular
  basis

61
Figure8.22 page 311
I
62
Summary of the advantage of Sex

• In the context of population genetics, the
  advantage of sex is to reduce linkage
  disequilibrium
• population-genetic model for the adaptive value
  of sex has two parts
• 1. A mechanism for the creation of linkage
  disequilibrium
• 2. a reason why selection favors traits that
  tend to reduce linkage disequilibrium

63
There are two classes of models

• Those that credit genetic drift with introducing
  disequilibrium by creating high fitness genotypes
  that can be lost by drift
• natural selection patterns which continuously
  alter the currently best-adapted genotype. Sex
  allows lost genotypes to be reclaimed that were
  formerly selected against

64
The End
65
Fig. 8.2a pg 283
66
Figure 8.2b pg 283
Go to conditions
67
Figure 8.3a pg 287
68
of chromosomes that are A .2304 .0576
.0576 .1536 .4992/.6528 76
of chromosomes that are a .1536/.6528 24
B on A .2304 .0576 .1536 / .4992 88
B on a .1536/.1536 1.0
b on A .0576 / .4992 12
69
View punnett square
AABB (.2034) AABb (.0576) AaBB (.1536)
AaBb (.0384)   AABb (.0576) AAbb (.0144)
AaBb (.0384) Aabb (.0096)   AaBB (.1536)
AaBb (.0384) aaBB (.1024) aaBb
(.0256)   AaBb (.0384) Aabb (.0096) aaBb
(.0256) aabb (.0064)
70
(No Transcript)
71
.2304 ½ (.0576) ½ (.0576) ½ (.1536) ½
(.1536) .2304 .0576 .0576 ½ (.1536) ½
(.1536)
.2304.0576.1536 .2304.0576.0576.1536
.4416 .4992

0.88