06 random drift

Hardy - Weinberg Equilibrium random drift

1. Assignment
Subject : Crop Evolution GPB821
Presented by: Mr. Indranil Bhattacharjee
Student I.D. No.: 17PHGPB102
Presented to : Dr. G.M. Lal


Sam Higginbottom University of Agriculture, Technology &
Sciences
Allahabad-211007

2. Five Factors Drive Evolution
•Mutation

3. Venom-like proteins
first appeared about 200 million years ago

4. Venoms evolved from other proteins

5. Venoms were recruited from other functions

6. I. Natural Selection
Green mamba is arboreal
Its venom is most effective
against birds.
Black mamba is terrestrial
Its venom is most
effective against
mammals.

7. OVERPRODUCTION

8. HERITABLE VARIABILITY

9. COMPETITION

10. DIFFERENTIAL REPRODUCTION

11. II. GENETIC DRIFT
•The smaller the population, the less genetic
variety it has.
•In a very small population, alleles can be lost
from one generation to the next, simply by
random chance.
•When a population evolves only because of
this type of random sampling error, GENETIC
DRIFT is taking place.

12. FOUNDER EFFECT

13. BOTTLENECK EFFECT

14. AND IN 4.5 BILLION YEARS…
•The diversity of life on earth around us evolved.

15. Measuring Genetic Change
•The study of Population Genetics is the study
of how the genetic makeup of populations
changes from one generation to the next.
•Population geneticists study how genes/traits
–maintained
–lost
•…from a population’s gene pool.
–gene pool = all the genes at all the loci in all
members of the population

16. Let’s imagine
•A population of fruit flies with a gene we’ll call
“X”
•X codes for an important enzyme the fly needs
for survival.

17. Let’s imagine
•A mutation of the gene results in a mutant
allele we’ll call x
•X is dominant. x is recessive.
The recessive version of the gene
codes for a “broken” enzyme
that does not work.

18. Mate a heterozygous male with a
homozygous XX female
x

19. Predict offspring ratios with a Punnett
Square

20. What if two heterozygotes mated?
X

22. Inbreeding
•Mating between close relatives increases the
chance that recessive alleles will be expressed
(in homozygous individuals)

23. Outbreeding
•Mating between distantly related individuals decreases
the chance that recessive alleles will be expressed.
•Outbreeding increases heterozygosity at many gene loci.
•This results in….
•HYBRID VIGOR

24. Hardy-Weinberg Equilibrium
•If there are two alleles for a particular gene
•Then
•dominant alleles + recessive alleles = 100%
•100% can also also be represented as 1.0
•The proportion of each allele is also called its
FREQUENCY
•% = proportion = frequency

25. Hardy-Weinberg Equilibrium
With two alleles, there are
three possible genotypes:
XX
Xx
xx

26. Hardy-Weinberg Equlibrium
If a population is not evolving, then you should
have the same number of
XX , Xx, and xx individuals in every generation.
But if the proportions of XX, Xx, and xx change
from one generation to the next, then the
population is EVOLVING.

27. Hardy-Weinberg Equlibrium
•Let’s call the frequency of the dominant allele
(X)… p.
•Let’s call the frequency of the recessive allele
(x)… q.
•If only X and x alleles exist, then p + q = 1.0
•If you know q, you can figure out p.

But how do we figure out q?

28. Hardy-Weinberg Equilibrium
Every xx individual carries two recessive
alleles.
The frequency of the q allele in these
homozygotes is represented as q
2
Only homozygous recessives will show the
recessive trait.
To calculate q, take the square root of q
2

29. Hardy-Weinberg Equilibrium
•Since p + q = 1.0, then 1.0 – q = p
•Once you know both p and q, plug in to the
Hardy-Weinberg equation:
p
2
+ 2pq + q
2


–p2 is the proportion (frequency ) of XX homozygotes
–2pq is the proportion (frequency) of Xx heterozygotes
–q2 is the proportion (frequency) of xx homozygotes

30. Hardy-Weinberg Equilibrium
•If the relative frequencies of X and x change
from one generation to the next, then the
population is evolving.

•If the proportion of XX, Xx and xx individuals
in a population changes from one generation
to the next, then the population is evolving.

31. Hardy-Weinberg Equilibrium
A population that is NOT
EVOLVING is said to be in Hardy-
Weinberg equilibrium.
We can use HW calculations to
measure microevolution in
populations.

32. MIGRATION
Movement of individuals from one subpopulation to
another followed by random mating.

Movement of gametes from one subpopulation to
another followed by fertilization.

Results in movement of alleles between populations
(GENE FLOW).

Can be a very local or a long-distance phenomenon.

33. CONTINENT-ISLAND MODEL OF MIGRATION
Alleles from the continent represent a large fraction of
the island gene pool.

Alleles from the island have negligible effect on gene
frequencies in the continent.
CONTINENT
ISLAND

34. THE HOMOGENIZING EFFECT OF MIGRATION IN A
CONTINENT-ISLAND SYSTEM
Let:
Frequency of A on island = p
I
Frequency of A on continent = p
C
Proportion of island population from the continent = m

Frequency of A on the island after migration:

p
I* = (1-m)p
I + mp
C

Change on island from one generation to the next:

p
I = p
I* - p
I = (1-m)p
I + mp
C –p
I

At equilibrium: p
I = p
C

36. Case Study: Lake Erie Water Snakes
FROM: King & Lawson (1995)
Distribution on islands in Lake Erie
Frequency of color patterns on mainland and
offshore islands.
Banded Form
Solid Form
Nerodia sipedon

37. MIGRATION – SELECTION BALANCE
If the migration rate (m) is << selection (s),

s
mp
p
C
iˆ
In King & Lawsons Water snakes,

p
c(Banded allele) = 1, s  0.16, and m  0.01

The equilibrium frequency is approximately, 94.0ˆ
,06.0ˆ


i
i
q
p

38. GENETIC DRIFT
Alteration of gene frequencies due to chance (stochastic)
effects.

Most important in small populations.

Tends to reduce genetic variation as the result of
extinction of alleles.

Generally does not produce a fit between organism and
environment; can, in fact, result in nonadaptive or
maladaptive changes.

39. Genetic drift results from random sampling
error
Sampling error is higher with smaller sample

40. Drift reduces genetic
variation in a population
•Alleles are lost at a faster rate in
small populations
–When all alternative alleles have been
lost, one allele becomes fixed in the
population

Time

41. COALESCENCE THEORY
We can trace the descendents of a gene
just like a haploid organism.
If we look back in time, all of the current
gene copies shared a single common
ancestor.
THE GENEALOGY OF THE PRESENT SEQUENCES COALESCES TO A
SINGLE COMMON ANCESTOR.
This process is due to the random extinction of lineages.
Eventually, in the absence of new mutation, coalescence will result in
the fixation of a single allele in the population.

42. GENETIC DRIFT IN REPLICATED POPULATIONS: SIMULATION
(N = 16)
NUMBER OF POPULATIONS

GENERATIONS NUMBER OF COPIES OF ALLELE 1

43. DISTRIBUTION OF ALLELES IN REPLICATED DROSOPHILA
POPULATIONS (107 POPS WITH N = 16)
FROM: Buri 1956

44. EFFECT OF GENETIC DRIFT ON GENETIC DIVERSITY
Genetic drift leads to a reduction in heterozygosity.
FROM: Buri 1956

45. LOSS OF HETEROZYGOSITY IN A RANDOM MATING
POPULATION OF N ADULTS
The rate of loss of heterozygosity per generation is equal to the
probability that a newborn contains two alleles at a locus that are
identical-by-descent from the previous generation,

= 1/(2N)

Heterozygosity after 1 generation at size N, 01 *
2
1
1 H
N
H








46. )2/(
00*
2
1
1
Nt
t
t eHH
N
H








 Heterozygosity after t generations at size N,
Example: After t = 6N generations, e
-t/(2N)
= 0.05,
implying that 95% of the original heterozygosity has
been lost. This is 60 generations for a population
size of 10 breeding adults.

47. LOSS OF HETEROZYGOSITY VS. POPULATION SIZE

48. Effective population size (N
e): the number of individuals in an ideal
population (in which every individual reproduces) in which the rate of
genetic drift would be the same as it is in the actual population.

The rate of genetic drift is highly influenced by the lowest population size
in a series of generations.

The effective population size (N
e) over multiple generations is best
represented by the harmonic mean not the arithmetic mean.
RATE OF GENETIC DRIFT AND FLUCTUATIONS IN POPULATION SIZE 








110
11111
te NNNtN


49. RATE OF GENETIC DRIFT AND FLUCTUATIONS IN
POPULATION SIZE
Example:

Suppose a population went through a bottleneck as follows:


N
0 =1000, N
1 = 10, N
2 = 1000


What is the effective size (Ne) of this population across all three generations?

50. HARMONIC MEAN:

1/N
e = (1/3)(1/1000 + 1/10 + 1/1000) = 0.034

N
e = 29.4

ARITHMETIC MEAN:

N
e = (1/3)(1000 + 10+ 1000) = 670


RATE OF GENETIC DRIFT AND FLUCTUATIONS IN
POPULATION SIZE

51. GENETIC EFFECTIVE POPULATION SIZE (N
E)
The effective population size is often << than the actual census size

N
e << N
a

Consider a sexual population consisting of N
m males and N
f females

The actual size is, N
a = N
m + N
f but,

The effective size is,
fm
fm
e
NN
NN
N


4

52. Equal Sex Ratio
N
m = N
f = 50

For a population of N
a = 100

EFFECTIVE SIZE

PERCENT FEMALE

53. EFFECT OF GENETIC DRIFT ON GENETIC DIVERSITY
Genetic drift leads to a reduction in heterozygosity.
FROM: Buri 1956
N
e = 16
N
e = 9

54. Natural selection more powerful in large
populations
Drift weaker in large populations
Small advantages in fitness can lead to large changes
over the long term

55. GENETIC DRIFT
How can random genetic drift cause maladaptive evolution?

Since genetic drift can cause allele frequencies to increase, even
deleterious alleles can be advanced and fixed in populations. The result
is a decrease in mean population fitness.

Small populations are especially prone to this effect.

If s < 1/N
e

The effects of drift will dominate the dynamics of allele frequency
change from one generation to the next.

56. Genetic drift: evolution at random
• Random chance versus deterministic effect
• Random genetic drift versus adaptive evolution
• Genetic drift as sampling error

57. 10.1 A possible history of descent of
gene copies
•History of genetic lines
•Genealogy of genes coalesces to a single ancestor
•The smaller a population, the faster coalescence occurs

58. 10.1 A possible history of descent of
gene copies
•History of genetic lines
•Genealogy of genes coalesces to a single ancestor
•The smaller a population, the faster coalescence occurs
•H = 2p(1-p)
•Additional effects of mutation, gene flow and selection

59. 10.2 A “random walk” (or “drunkard’s walk”)
•Chance distribution due to neutral effects on fitness
•Allele frequencies show a random walk pattern
•Genetically identical subpopulations may develop strongly
differentiated genetic reservoirs as a result of chance effects

60. 10.3(1) Computer simulations of
random genetic drift in populations
•Computer simulation of random genetic drift in populations of 9 and
50 individuals during 20 generations
•Fluctuations are stronger and alleles become lost or fixed more
reapidly in small populations

61. 10.3(2) Computer simulations of
random genetic drift in populations
•Computer simulation of random genetic drift in populations of 9 and
50 individuals during 20 generations
•Fluctuations are stronger and alleles become lost or fixed more
reapidly in small populations

62. 10.4(1) Changes in the probability that an allele
will have various possible frequencies
•Distribution of allele frequencies among different populations of similar size
N and with identical initial allele frequencies
•After several generations, allele frequencies randomly drift towards 1
(fixation) or 0 (loss)

63. 10.4(2) Changes in the probability that an allele
will have various possible frequencies
•Proportion of populations with different allele frequencies after t = 2N
generations
•Proportion of populations in which allele is fixed or lost increases at a
rate of 1/4N per generation
•Each class of allele frequencies between 0 and 1 decreases at a rate of
1/2N per generation

64. 10.4(2) Changes in the probability that an
allele will have various possible
frequencies
•Allele or haplotype frequencies fluctuate randomly
•As a result, genetic variation at a locus decreases
•Genetic drift can be measured by the level of heterozygosity
•The probability of fixation of an allele is independent of previous shifts in its
frequency
•A proportion p of a set of populations with identical initial allele frequencies
p will be fixed for that particular allele
•A newly mutated allele with frequency p
t = 1/2N has a chance equal to its
initial frequency to become fixed; the probability of fixation increases with
decreasing N
•The average time to fixation for a new (neutral) allele is 4N generations
(diploid population)

65. •Effective population size N
e refers to the size of an ideal population (in
which all individuals reproduce equally) which shows a similar degree
of random genetic drift (measured as loss of heterozygosity) as the
census population size

10.5 Effective population size among northern
elephant seals is much lower than the census
size

66. •Variation in number of offspring reduces N
e
•Deviation from 1:1 sex ratio reduces N
e
•Natural selection reduces N
e
•Strong overlap between generations reduces N
e
•Fluctuations in population size reduce N
e
10.5 Effective population size among northern
elephant seals is much lower than the census size

67. 10.6 Effects of a bottleneck in population size on
genetic variation, as measured by heterozygosity
•Effect of bottleneck in population size on genetic variation
•H decreases more rapidly with decreasing number of founders
•H decreases more rapidly with decreasing increase in population size
•Mutations create new genetic variation

68. 10.7 Random genetic drift in 107 experimental
populations of Drosophila melanogaster
•Random genetic drift in 107 experimental Drosophila melanogaster populations
(8 males + 8 females; heterozygote for bw/bw
75
)
•Populations already start to vary in allele frequencies after 1 generation
•First loss of allele bw
75
after six generations
•After 19 generations increasing loss/fixation of allele bw
75

69. 10.7 Random genetic drift in natural
populations
•Patterns of genetic variation in natural populations often match
predictions made under the assumption of genetic drift
•Differently-sized populations often show comparable mean allele
frequencies, but variation mostly increases with decreasing size

70. 10.8(1) Aggression and genetic similarity
between Argentine ants
•Aggression and genetic similarity between Argentine ants in relation to distance
between colonies
•Introduced populations in California show little aggression between colonies
•Colonies in California show higher genetic similarity than those in Argentinia
because the population is genetically more uniform due to founder effect

71. 10.8(2) Aggression and genetic similarity
between Argentine ants
•Aggression and genetic similarity between Argentine ants in relation to distance
between colonies
•Introduced populations in California show little aggression between colonies
•Colonies in California show higher genetic similarity than those in Argentinia
because the population is genetically more uniform due to founder effect

72. •Adaptive versus selective neutral genetic variation
•High proportions of enzyme loci are polymorphic (Lewontin & Hubby 1966)
•Neutral theory of molecular evolution (Motto Kimura 1968)
•Although small minority of mutations in DNA are advantageous and are fixed
by natural selection, and although many are disadvantageous and eliminated,
great majority of fixed mutations are neutral with respect to fitness and fixed
by genetic drift
•Evolutionary substitutions proceed at roughly constant rate
Principles of neutral theory

73. Principles of neutral theory
• Constant mutation rate u
T (per gamete/generation) of which f
0
selective neutral
• u
0 = f
0u
T < u
T (functional constraint)
• Number of fixed neutral mutations per generation 2N
eu
0 x 1/(2N
e) =
u
0
• Fixation rate of mutations is constant and approximates the neutral
mutation rate (4N
e generations to fixation)
• number of base pairs difference: D = 2u
0t

74. 10.10 Number of base pair differences per site
between mDNA of pairs of mammalian taxa
•Number of base pair differences between mDNA of pairs of mammalian taxa in
relation to divergence time
•Difference increases linearly (5-10 mil year) before reaching an asymptote
•Mutation rate calculated from linear part of curve (0.01 mut/base
pair/lineage/year ( 10
-8
/year)

75. 10.11 Equilibrium level heterozygosity at a locus
increases as a function of the product of N
e & u
0
•While the allelic composition continues to change, an equilibrium in allelic
variation is eventually reached
• At equilibrium:


Allozymen: u
0 = 10
-6
/gameet; H = 0.004 (N
e =1000) en H = 0.50 (N
e =
250.000) 14
4
0
0


uN
uN
H
e
e

76. •Rate at which a population drifts to fixation of an allele is inversely related to
its effective population size
•Genetic drift is neutralized by gene flow (with rate m)
•At equilibrium:
•Nm refers to the number of immigrants per generation: if m=1/N then Nm=1
and F
ST= 0.20
•Estimation of gene flow:
•Assumes neutrality and hence equally affects all loci
•Assumes equilibrium between gene flow and genetic drift
Geneflow and drift 14
1


Nm
F
ST  
4
1/1 

STF
Nm

77. 10.14 Geographic variation in allele
frequencies at two electrophoretic loci
in the pocket gopher
•Geographic variation in allele frequencies at two electrophoretic loci in the
pocket gopher
•Large variation also between close locations (south-west VS and Mexico: F
ST
= 0.412, Nm = 0.36)
•Suggests low degree of gene flow

78. 10.16 Homo erectus spread from Africa to Europe and
Asia and evolved into H. neanderthalensis
•Homo erectus dispersed ca. 1.8 mil years ago from Africa to Europe and Asia
•Homo sapiens (other species) also originated in Africa and dispersed ca
100.000 year
•This colonization involved a small N
e only (possibly < 12.000)

79. Random Genetic Drift : Chance as
an Evolutionary Force
•Random Genetic Drift is the random change in allele
frequencies from one generation to the next that is
caused by the finite size of the breeding population
of parents.

•By chance, some parents have more offspring than
other parents.

•By chance, some parents have fewer offspring or no
offspring at all.

80. •Random Genetic Drift occurs in ALL countable, finite
populations.

•RGD is STRONGER in Small Populations (0 < N < 500).

•RGD is WEAKER in Large Populations (500 < N).

•The Strength of RGD is proportional to (1/2N) in a
diploid population and to (1/N) in a haploid population.

81. 1) WITHIN populations RGD DECREASES GENETIC VARIATION ::
Random Genetic Drift makes a population less genetically
less variable and makes the individuals in the population
more Homozygous.
The ultimate outcome: ALL HERITABLE VARIATION IS LOST!!
The population becomes either p* = 0.0 (allele is lost) or p* =
1.0 (allele is FIXED).

2) BETWEEN populations RGD INCREASES GENETIC VARIATION:
Random Genetic Drift makes two populations become
genetically different from one another.
RGD and its Evolutionary
Consequences

82. 5
5
5
Generation 1 Generation 2
7
4
4
No Chance Events
5
5
5
Chance Events
Random Genetic
Drift
5
5
5
Frequencies
Stay Exactly
the Same

83. 5
5
5
Generation 1
Generation 2
Different
Chance Events
Lead to
Different Outcomes
One Starting Point
Many Possible Outcomes
7
4
4
6
4
5
6
6
3
Random Genetic Drift

84. RGD for A Few
Generations
With NO
Migration
START: All Populations Genetically
Identical
END: Populations Genetically
Different from one another
RGD INCREASES Variation AMONG Populations

85. 5
5
5
Generation 1 Generation 2
Average of MANY
Independent
Chance Events
5
5
5
Average Effect of
Random Genetic Drift
On Allele Frequencies = ZERO
Average P = 0
On AVERAGE
Frequencies
Stay the Same

86. 5
5
5
Generation 1 Generation 2
5
5
5
No Chance Events
5
5
5
Random Genetic
Drift
5
5
5
Frequencies
Stay Exactly
the Same
On AVERAGE
Frequencies
Stay the Same

87. RGD for A Few
Generations
With NO
Migration
START: All Populations Genetically
Identical
END: Populations Genetically
Different from one another
RGD INCREASES Variation AMONG Populations

88. RGD for Many
Generations
With NO
Migration
All Populations Genetically
Identical
Populations Genetically
Different from one another
RGD DECREASES Variation WITHIN Populations

89. RGD and Migration
for Many
Generations
All Populations Genetically
Identical
Populations Somewhat
Genetically Different
Migration OPPOSES RGD and LIMITS its effects

90. Random Genetic Drift : Effects
1. On average WITHIN one population, RGD DECREASES genetic variation:
A) Random Genetic Drift makes INDIVIDUALS more homozygous, more
genetically similar.
B) the POPULATION becomes genetically less variable.
C) RGD causes ALLELES to become FIXED (P
a = 1) or LOST (P
a = 0).
D) RGD diminishes the heritable variation within a population, which
limits NATURAL SELECTION.
2. On average AMONG a group of populations, RGD INCREASES genetic
variation:
A) RGD makes different populations genetically more
different from one another.
3. GENETIC FIXITY of SPECIES is NOT possible as long as there are a lot of
populations, because RGD will do something different in each
population. There is continual change of allele frequencies in finite
populations by chance, RGD.

91. 5
5
5
Generation 1
Generation 2
Many
Different
Chance Events
One Starting Point
Three Equally Possible Outcomes
15
0
0
15
15
0
0
0
0
Random Genetic Drift

92. Migration as an Evolutionary Force
•Migration is the Movement of Individuals between
populations.
•When individuals move from one population to
another and then breed with the residents of the
new population, ‘Gene Flow’ can change frequency
of alleles in the new population.
–immigration
•movement of individuals INTO a population
–emigration
•movement of individuals OUT OF a population

93. Evolutionary Consequences of Migration
(Gene Flow)
1) Gene Flow between populations reduces the genetic differences
between the populations.

2) Gene Flow can be a constraint on evolution when immigrants carry
genes into a population that are not adapted for the ecological
conditions of the population.
•alleles that are good in one population may be bad in another
population

3) Gene Flow can accelerate evolution when immigrants carry genes into a
population that are adapted for the conditions of the population.
•beneficial alleles from other populations can be brought in
faster by migration than they can arise by mutation.
Migration does NOT create new genetic variation; it moves around already
existing variation.

94. p
Green = 1.00
p
RED = 0.00
Population 1 Population 2
Exchange Migrants
M = 0.20
p
Green = 0.00
p
RED = 1.00
The two Populations
are genetically very
Different BEFORE
GENE FLOW
The two Populations
are genetically more
similar AFTER
GENE FLOW

95. p’
Green
= (1 – M)p
GREEN,1 + (M)p
GREEN,2
= 0.80*(1.00) + 0.20*(0.00) = 0.80
Δp
GREEN,1 = M (p
2 – p
1) < 0, Green DECREASED
What is Allele Frequency AFTER Migration in
Population 1?
p
Green = 1.00
p
RED = 0.00
p’
Green = ???
p’
RED = ???
Population 1 Population 1

96. Δp
GREEN,2 = M (p
1 – p
2) > 0, GREEN INCREASED
What is Allele Frequency AFTER Migration in
Population 2?
p
Green,2 = 0.00
p
RED,2 = 1.00
p’
Green = ???
p’
RED = ???
p’
Green,2
= (1 – M)p
GREEN,2 + (M)p
GREEN,1
= 0.80*(0.00) + 0.20*(1.00) = 0.20
Population 2 Population 2

97. Random Genetic Drift versus Migration
•RGD makes populations genetically different.
•Migration makes populations genetically
similar.
•Together, RGD and Migration place a limit on
the degree of genetic differences between
populations.
•Where is the limit or Balance between these
two evolutionary forces?

98. RGD and Migration
for Many
Generations
All Populations Genetically
Identical
Populations Somewhat
Genetically Different
Migration opposes RGD and LIMITS its effects

99. RGD for Many
Generations

All Populations Genetically
Identical
Populations Genetically
Different from one another
Could this happen with Migration? Answer: ????

100. Random Genetic Drift and Migration:
Effects
1. On average WITHIN one population, RGD DECREASES genetic variation,
Migration INCREASES genetic variation:

A) RGD makes INDIVIDUALS more homozygous, Migration makes
INDIVIDUALS more heterozygous.
B) the POPULATION reaches a STABLE LEVEL of genetic variation where
RGD and Migration are balanced.
C) Migration PREVENTS RGD from making ALLELES become FIXED (P
a =
1) or LOST (P
a = 0).
D) Migration can replenish the heritable variation within a population
lost by RGD.

2. On average AMONG a group of populations, RGD INCREASES genetic
variation, Migration DECREASES genetic variation.

101. References
Briggs, D and Walters, S.M. 1986. Plant Variation and
Evolution
Charles W., Jason B. Wolf. edited by 2005Evolutionary
genetics: Concepts and case studies. Oxford Unisrrsity
Press.
Christopher Cumo. Plants and People: Origin and
Development of Human--Plant Science Relationships,
CRC Press Taylor & Francis Group

102. Thank You