Download Population Genetics

1 Thessalonians 5:21
21 Prove [test] all
things; hold fast
that which is good.
©2000 Timothy G. Standish
Evolution Of
Populations
Timothy G. Standish, Ph. D.
©2000 Timothy G. Standish
Macro and Micro Evolution
Macro evolution is the evolution of higher
taxonomic groups (formation of a new genus,
family etc.)
Micro evolution - Change in allele frequency
within a species or population of a species
Micro evolution is population genetics
Population genetics has been observed and this is
what is being talked about when scientists say that
evolution has been observed
Macro evolution has not been observed in any
definitive way
©2000 Timothy G. Standish
Speciation, Yes.
Natural Selection, ???
After The Origin of Species was published in
1859, the scientific community quickly
accepted that speciation occurred
Remember that speciation was not an entirely
new idea; it had been proposed by Lamarck
and Franz Unger (Mendel’s mentor) among
others
The mechanism for speciation proposed by
Darwin, natural selection, was not as quickly
accepted
©2000 Timothy G. Standish
Other Ideas
About Speciation
From Huxley’s book
Many believed that new species resulted from
hybridization between old species (not necessarily
untrue)
Orthogenesis (ortho = straight genesis = beginning)
- The idea that evolution was progressing along a
predictable path toward some ideal. Really a
throwback to Lamarckism
1920s After the rediscovery of Mendel's work, the
idea that evolution occurred in rapid leaps due to
mutations radically altering phenotype was popular
©2000 Timothy G. Standish
The Modern Synthesis
Darwin recognized that variation existed in
populations and suggested natural selection as a
mechanism for choosing some variants over others
resulting in survival of the fittest and gradual
changes in populations of organisms.
Without a mechanism for generation of new
variation, populations would be selected into a
corner where only one variation would survive and
new species could never arise.
The Modern Synthesis combines the mechanism of
DNA mutations generating variation with natural
selection of individuals in populations to produce
new species.
©2000 Timothy G. Standish
Where Speciation Occurs
Real acceptance of natural selection came
after it was realized that evolution occurs on
the level of populations, not individuals
Individuals that have more success at
reproducing than others are selected over
others in a population
If one type of individual is chosen (selected)
over another type, it will change the make up
of the population by passing on its genes to
more members of the next generation
Individuals are selected, populations evolve
©2000 Timothy G. Standish
What is a Population?
A group of individuals of the same species in
the same geographical area:
– Human population of Berrien Springs
– Chicken population of Hong Kong
– Human population of the United States
What is a species?
A group of populations that have the potential
to interbreed in nature
We’ll come back to this question
©2000 Timothy G. Standish
Population Genetics
Is mathematics
One definition:
Algebraic description of population's
genetic makeup including allelic
frequencies and genotypic frequencies
Emphasizes - Genetic variation within
populations (on which selection can occur)
Recognizes - The importance of
quantitative traits
©2000 Timothy G. Standish
History
1908 - G. H. Hardy, an English
mathematician, and W. Weinberg, a German
physician, simultaneously discovered an
equation that relates allelic and genotypic
frequencies in populations that meet certain
requirements commonly found in real
populations.
1920s - Developed very rapidly due to work
by R. A. Fisher, J. B. S. Haldane, and S.
Wright.
©2000 Timothy G. Standish
History Cont.
1960+ Has become a major area of
genetics due to:
Computers - Allowing rapid
computation on large data sets
Electrophoresis - Allows the rapid
gathering of large amounts of empirical
data
Newer techniques that allow the
analysis of relationships among species
©2000 Timothy G. Standish
The Hardy-Weinberg Theorem
The cornerstone of population genetics
“The frequency of alleles in a population will
remain constant over time if certain
conditions are met”
1 Infinite (or at least very large) population size
2 Isolation from other populations - No
migration
3 No net mutations
4 Random mating
5 No natural selection
©2000 Timothy G. Standish
The Equation
That Says it all
If we look at one gene in a population with 2
alleles, A and a, and we let:
p = f(A) q = f(a) -> f(A) + f(a) = p + q = 1 and
p = 1 - q and q = 1 - p
Probability of getting an individual with a given
genotype can be calculated on the basis of the
probability of getting parents with given
genotypes: (p + q)(p + q) = 1 x 1 = 1
(p + q)2 = 1 2
p2 + 2pq + q2 = 1
©2000 Timothy G. Standish
p2 + 2pq + q2 = 1
This equation allows us to predict
genotypic frequencies on the basis of
allelic frequencies and allelic
frequencies on the basis of genotypic
frequencies
f(AA) = f(A) x f(A) = p2
f(aa) = f(a) x f(a) = q2
f(Aa) =2 [f(A) x f(a)] = 2pq
©2000 Timothy G. Standish
Does This Equation Fit
With Mendelian Genetics?
In the following cross:
– Aa x Aa
0.5 of alleles in gametes will be A
0.5 of alleles in gametes will be a
Therefore:
A
a
0.5 0.5
A AA Aa
0.5 0.25 0.25
a Aa aa
0.5 0.25 0.25
– f(A) = p = 0.5
A
a
0.1 0.9
– f(a) = q = 0.5
A AA Aa
p2 + 2pq + q2 = 1
0.1 0.01 0.09
a Aa aa
2
2
(0.5) + 2(0.5)(0.5) + (0.5) = 1
0.9 0.09 0.81
0.25 + 0.5 + 0.25 = 1
f(AA) = 0.25, f(Aa) = 0.5, f(aa) = 0.25
©2000 Timothy G. Standish
Problem 1
MN Blood Types in US. Whites
MN blood types are inherited in a
codominant fashion; thus heterozygous
individuals can easily be detected
In a sample of the U.S. white
population, blood types were
determined as follows:
–M (Genotype MM) = 1,787
–MN (Genotype MN) = 3,039
–N (Genotype NN) = 1,303
©2000 Timothy G. Standish
Problem 1 A
MN Blood Types in US. Whites
MM 1,787
MN 3,039
NN 1,303
A) What is the frequency of the M allele?
Answer - As each individual is heterozygous and there are a total
of 6,129 in the sample there should be 2(6,129) = 12,258 alleles
2 M alleles in each MM genotype = 2(1,787) = 3,574 alleles
1 M allele in each MN genotype = 3,039 alleles
Total M alleles/Total of all alleles = f(M) = p
+ (MN) 2(1, 787) + 3, 039 3, 574 + 3, 039
2(MM)
=
=
= 0.54
p=
2(Total )
2(6,129)
12, 258
or
+ 1/ 2(MN)
(MM)
p=
Total
©2000 Timothy G. Standish
Problem 1 B
MN Blood Types in US. Whites
MM 1,787
MN 3,039
NN 1,303
B) What is the frequency of the N allele?
Answer:
+ (MN)
2(NN
)
=
Or
p=
As p + q = 1
2(Total )
q=1-p
2(1, 303) + 3, 039 =
q = 1 - 0.54
2(6,129)
2, 606 + 3, 039 =
q = 0.46
0.46
12, 258
©2000 Timothy G. Standish
Problem 1 C
MN Blood Types in US. Whites
MM 1,787
MN 3,039
NN 1,303
C) Is this population described by the HardyWeinburg formula?
Answer: Predicted genotypic numbers in a population of this size =
– f(MM)(Total) = p2 (Total) = (0.54)2(6,129)
= 0.292 (6,129) = 1,787
– f(MN) (Total) = 2pq (Total) = 2(0.54)(0.46) (6,129) = 0.498 (6,129) = 3,045
– f(NN) (Total) = q2 (Total) = (0.46)2 (6,129)
= 0.212 (6,129) = 1,297
Quick math check:
– p2 + 2pq + q2 = 0.292 + 0.498 + 0.212 = 1.002(Close enough)
– 1,787 + 3,045 + 1,297 = 6,129 (Rounding errors go both ways!)
Do Chi square to decide
©2000 Timothy G. Standish
Problem 1 C Cont.
MN Blood Types in US. Whites
2
Chi Square:
d =
=
2


C
e
2
(Obs. Ex.)
Ex
MM
MN
Obs.
1,787
3,039
Ex.
1,787
3,045
O-E
0
-13
(O-E)2/E
0.000
0.0554
NN
1,303
1,297
4
0.0123
X2 =
0.0727
Degrees of freedom* = k - 1
=3-1=2
0.99 > p > 0.95
Yes, the population is probably
in a Hardy-Weinburg equilibrium
*Note that degrees of freedom are calculated
based on k - 1 - m where k = genotypic
classes and m = number of independent
allele frequencies estimated from the data.
In this case k = 3 (MM, MN and NN) and m
is zero as both allele frequencies were
determined directly from the data.
©2000 Timothy G. Standish
What if p2 + 2pq + q2 = 1
Did not Describe the Population?
Remember that the Hardy-Weinburg theorem is
true only if certain conditions are met:
1 Infinite (or at least very large) population size
2 Isolation from other populations - No migration
3 No net mutations
4 Random mating
5 No natural selection
If the Hardy-Weinburg equation does not
describe the population, it is probably evolving
due to violation of one of these conditions
©2000 Timothy G. Standish
Infinite Population Size
This same assumption is made in most descriptive statistics
Small population sizes can lead to sampling error so that the next
generation is not an accurate representation of the previous
generation
– Genetic drift - With each generation each allele has a fixed
probability of not being passed on; in small populations this
probability is significant
– Founder effect - A small number of individuals from a large
population populate an area. Only the alleles of the few founders
are represented in their descendants, not the entire population
from which they came (i.e., the human population of Finland)
– Bottleneck effect - A large population is reduced to a very small
number then recovers, but only those alleles that made it through
the bottleneck are in the recovered population (i.e., cheetahs in
Southern Africa)
©2000 Timothy G. Standish
Isolation From Other Populations
If members of another population with different allelic
frequencies are migrating in, the population being studied
will not be in equilibrium
Example: Two populations of 100 individuals:
– 1 p1 = 0.1 q1 = 0.9 AA=1, Aa=18, aa=81
– 2 p2 = 0.9 q2 = 0.1 AA=81, Aa=18, aa=1
Combined together: p1+2 = 0.5 q1+2 = 0.5
Predicted genotypic frequency:
– f(AA) = p2 = 0.25 or 50/200 (actual 0.41 or 82/200)
– f(Aa) = 2pq = 0.50 or 100/200 (actual 0.18 or 36/200)
– f(aa) = q2 = 0.25 or 50/200 (actual 0.41 or 82/200)
©2000 Timothy G. Standish
No Net Mutations
In reality, heritable mutations are very rare events.
Remember that most mutations are not a good thing for
the organism, so it is in the best interest of all living
things to avoid damage to their DNA
Even if mutation was common, an equilibrium would be
reached:
Let A and a be alleles for a given gene, mutation from A
to a =  and mutation from a to A = 
A


a
©2000 Timothy G. Standish
Random Mating
If mates are chosen on the basis of a genetic trait,
then that trait or allele will be passed to the next
generation at higher frequencies than alternative
alleles; thus allelic frequencies will change over time,
and the population will not be in equilibrium
Sexual Selection - Choosing a mate on the basis of
their genotype
Hi there
sweetie!
©2000 Timothy G. Standish
Natural Selection
Natural selection is thought to be the most
common cause of changes in allelic frequencies
and thus populations being out of equilibrium
It is important to note that for the effect of natural
selection to be detected on the basis of violation
of Hardy-Weinburg, selection would have to be
fairly stringent at the point in time data was
collected
Hardy-Weinburg can be used to compare
populations of the same species and may infer that
selection has occurred assuming the other factors
previously mentioned are not at play
©2000 Timothy G. Standish
Natural Selection
p= 0.1
q= 0.9
©2000 Timothy G. Standish
Natural Selection
p= 0.1
q= 0.9
If selection (s)
is 0.5 against aa
and fitness = W=1-s
©2000 Timothy G. Standish
Natural Selection
Second Generation
p= 0.17
q= 0.83
AA=2
Aa =30
aa =68
©2000 Timothy G. Standish
Natural Selection
Third Generation
p= 0.25
q= 0.75
AA=3
Aa =46
aa =51
©2000 Timothy G. Standish
Natural Selection
Fourth Generation
p= 0.34
q= 0.66
AA=3
Aa =62
aa =35
©2000 Timothy G. Standish
Natural Selection
Fifth Generation
p= 0.42
q= 0.58
AA=4
Aa =75
aa =21
©2000 Timothy G. Standish
Natural Selection
Sixth Generation
p= 0.46
q= 0.54
AA=5
Aa =83
aa =12
©2000 Timothy G. Standish
Natural Selection
Sixth Generation
After 6 generations, the population is not in
equilibrium:
p= 0.46 q= 0.54
p2 + 2pq + q2 = 0.212 + 0.497 + 0.292 =1.001
Expected genotype numbers:
AA = 21 (Actual =5)
Aa = 50 (Actual = 83)
aa = 29 (Actual = 12)
No need to do a Chi square on this one!
©2000 Timothy G. Standish
Rate of Change With
Selection
Even with heavy selection (s=0.5) the rate of
change in allele frequency declines rapidly
after a few generations
Frequency
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
1
q
2
3
4
5
6
p
7
Generations
8
9
Alleles
10
©2000 Timothy G. Standish
Rate of Change With Selection
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
1
2
3
q
4
5
6
7
8
Generations
p
9
10
Alleles
Frequency
Frequency
The heavier the selection, the faster the
change and the quicker the decline in
rate of change.
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
1
s = 0.9
q
2
3
4
5
6
p
7
8
Generations
s = 0.1
9
Alleles
10
©2000 Timothy G. Standish
Types of Selection
Selection
Selection
Frequency
Frequency
Stabilizing
Selection
Frequency
Pseudopterix
pleiorostrum
(many beaked
fake bird)
Directional
Diversifying
©2000 Timothy G. Standish
When the Data Speaks
“For example, researchers have calculated that
‘mitochondrial Eve’--the woman whose
mtDNA was ancestral to that in all living
people--lived 100,000 to 200,000 years ago in
Africa. Using the new clock, she would be a
mere 6,000 years old.
No one thinks that's the case, but at what point
should models switch from one mtDNA time
zone to the other?”
Gibbons, A. 1998. Calibrating the mitochondrial
clock. Science 279:28-29
©2000 Timothy G. Standish
©2000 Timothy G. Standish