Population Genetics

1
Population Genetics

• The study of Mendels laws and other genetic
  principles as they apply to entire populations of
  organisms
• Major theme the origin, maintenance and
  significance of genetic variation

2
Paradox of genetic variability

• It is to an individual organism's advantage to
  have the genetic make up best suited to the
  environment
• It is to a populations advantage to have genetic
  variability among its members in order to respond
  to changes in the environment

3
Paradox of genetic variability

• Genetic variability is necessary in order for
  populations to adapt to changing environments
• This adaptation is what many refer to as
  evolution
• Evolution is a populational phenomenon
  individuals cannot adapt in this sense

4
Kettlewells Moths

• Studied Biston betularia, the peppered moth, in a
  heavily industrialized area of England
• Two color morphs present
• peppered PP, Pp
• melanic pp

5
Kettlewells Moths

• By the time Kettlewell studied the moths in the
  1950s, most of the moths were homozygous
  recessive
• Natural selection
• More of the melanic moths survive
• therefore more of the melanic moths reproduce
• therefore more of the recessive alleles are
  passed on

6
Kettlewells Moths

• Today, the peppered variety is increasing in
  frequency.
• Anti-pollution laws are reducing soot emissions
• Lichen returning trees lightening
• Melanic form easier for birds to spot
• P increasing p decreasing

7
Definitions

• Polymorphism
• the presence of more than one allele at a locus
• generally, for a locus to be considered
  polymorphic the rare allele must be at a
  frequency of at least 5

8
Definitions

• Monomorphic loci
• loci where all individuals in a population have
  the same allele
• no genetic variation at these loci
• populations are said to be fixed for these
  alleles

9
Definitions

• Population
• a community of individuals of the same type
• Mendelian population
• a community of interbreeding, sexually
  reproducing individuals
• sometimes called a deme

10
Biological Species Concept

• A species is the most inclusive Mendelian
  population
• Biological Species Concept
• A species is a group of actually or potentially
  interbreeding individuals which are
  reproductively isolated from other such groups

11
Definitions

• Gene pool - all the alleles present in a
  population
• we generally consider only one locus at a time

12
Allele frequencies

• We use the frequencies of alleles as a measure of
  genetic change in a population
• Allele frequencies
• the percentage of a certain allele in a
  population
• Freq (A) A alleles / Total of alleles

13
Allele Frequencies...
Aa
aa
aa
Aa
aa
AA
AA
aa
AA
Aa
Aa
aa
AA
aa
Aa
Aa
Aa
15 Freq (A) ----------- 0.44 34
14
Allele Frequencies...

• Notice the frequency of the A allele plus the
  frequency of the a allele totals 1
• 0.44 0.56 1
• The allele frequencies must total 1 or 100

15
Allele Frequencies...

• In a two allele system, if we set the frequency
  of the A allele to sum number called p and the
  frequency of the a allele to q then
• p q 1
• For a three allele system, we would use p, q, and
  r
• p q r 1

16
Allele Frequencies...

• For example, ABO Blood grouping
• p freq. of A allele
• q freq. of B allele
• r freq. of O allele
• p q r 1
• there are no other alleles these percentages
  must total 1

17
Allele Frequencies...

• In the real world, we cannot see gene pools
  directly, we use the numbers of each phenotype to
  calculate allele frequencies
• Beta thalassaemia

TT Tt tt normal carrier(slight
anemia) anemic 400
75 25

18
TT Tt tt normal
carrier anemic 400 75
25
2(400) 1(75) freq (T) p
------------------------- 0.875 2(400
75 25)
19
Snails Brown Mottled White BB BW WW 150
500 350
20
Allele frequencies

• In the case of true dominance, we run into
  problems
• it is not possible to distinguish homozygous
  dominants from heterozygotes therefore we cannot
  directly calculate allele frequencies

21
The Hardy-Weinberg Equilibrium

• May be used to estimate allele frequencies if
  direct calculation is not possible
• Used to quantify changes in allele frequencies
• a way to measure evolution, in a way

22
The Hardy-Weinberg Equilibrium

• Relates allele frequencies and genotype
  frequencies
• Allows us to move back and forth between allele
  and genotype frequencies
• Allows us to see the effects of various outside
  forces on allele and genotype frequencies

23
The Hardy-Weinberg Equilibrium

• States In the absence of certain factors,
  genotype frequencies and allele frequencies
  remain constant from generation to generation
• In an ideal population, there will be no
  genetic change

24
The Hardy-Weinberg Equilibrium

• Five forces which may change allele frequencies
• mutation
• migration
• small population size
• non-random mating
• selection

25
Five forces changing H/W frequencies

• Mutation
• ultimate source of all variation
• with each mutation of one allele to another,
  their relative frequencies will change

• very s l o w change

26
Five forces changing H/W frequencies

• Migration
• gene flow - introduction of alleles from one
  population to another
• may be one way or two way exchange

27
Five forces changing H/W frequencies

• Small population size
• leads to random genetic drift
• allele frequencies change randomly
• most noticeable in populations smaller than
  around 2,000 individuals

28
Five forces changing H/W frequencies

• Non-random mating
• not all matings equally likely to occur
• positive assortative mating - like genotypes mate
• negative assortative mating - genotypes mate with
  other genotypes

29
Five forces changing H/W frequencies

• Selection
• Natural selection when one allele confers an
  advantage in survival
• If the presence of a certain allele enables
  individuals carrying that allele to better
  exploit the environment, that allele will
  increase in frequency
• remember the peppered moth!

30
Five forces changing H/W frequencies

• Any one of these forces (alone or in combination)
  may change allele genotype frequencies
• some are more efficient than others
• In the absence of these factors, there will be NO
  CHANGE in frequencies

equilibrium
31
Hardy - Weinberg Equilibrium

• Equilibrium means there is no change in allele
  frequencies
• Equilibrium DOES NOT mean there are equal numbers
  of each allele
• equilibrium is possible if p q 0.5
• equilibrium is possible at any other values of p
  and q also

32
Relationship between allele and genotype
frequencies
p freq (A) q freq (B)
Since gametes are haploid, the allele frequencies
are equal to the frequencies of the gametes
carrying each allele.
If the frequency of an allele is p, the frequency
of gametes carrying that allele will also be p
33
Relationship between allele and genotype
frequencies
If mating is random, we can construct a Punnett
square
eggs
A B
p q
A B
AA AB
p q
p2
pq
sperm
AB BB
pq
q2
34
Relationship between allele and genotype
frequencies
A B
p q
AA AB
A B
p q
p2
pq
AB BB
pq
q2
genotypes AA AB BB
frequencies p2 2pq q2
35
genotypes AA AB BB
frequencies p2 2pq q2
Are there any other possible genotypes with these
two alleles?
No! Therefore
p2 2pq q2 1
36
Three or more alleles

• freq (A) p freq (B) q freq (C) r
• p q r 1
• genotype frequencies

AA AB AC BB
BC CC p2 2pq 2pr
q2 2qr r2
p2 2pq 2pr q2 2qr r2
1
37
Relationship between allele/genotype frequencies
and equilibrium
p q .5
A B
p q
A p2 pq B pq
q2
p q
38
Relationship between allele/genotype frequencies
and equilibrium
p .70 q .30
A B
A B
p q
p2
pq
pq
q2
p q
39
Using the Hardy-Weinberg Equations

• To test for equilibrium
• used when numbers of each genotype is known
• To estimate allele and genotype frequencies
• used in cases of true dominance
• must assume equilibrium
• (really, really cheating)

40
Testing for equilibrium
genotypes AA AB BB numbers 100 100 100
Is this population in equilibrium? i.e. do the
genotype frequencies p2, 2pq, and q2?
200 100 p --------------- 0.5 600
q 0.5
41
Testing for equilibrium
genotypes AA AB BB numbers 100 100 100
exp. freqs (.5)2
2(.5)(.5) (.5)2 0.25
0.50 0.25
exp. s 0.25(300) 0.50(300)
0.25(300) 75 150 75
So, do the observed s match the expected s?
42
genotypes AA AB BB obs. s 100 100 100 ex
p. s 75 150
75
(100 - 75)2 (100 - 150)2 (100
- 75)2 c2 ------------- --------------
------------ 75 150
75 33.27 d.f. classes
- 1 - independent variables calculated from
data 3 - 1 - 1 1 p lt 0.01
43
Testing for equilibrium

• If a population is not in equilibrium, one or
  more of those five factors is at work
• it is generally not possible to tell which one
• Once all five conditions are met, it will take
  only one generation to return to equilibrium

44
Testing for equilibrium
Congenital adrenal hyperplasia neonatal death if
untreated treatment w/ cortisones leads to
normal lifespan, health and fertility. Carriers
detectable w/ RFLP analysis. Frequency of HH
1/20,000 in general U.S. population. 1/500 in
Yupik Eskimos.
HH Hh hh 1520 464 16
45
Estimating allele/genotype frequencies

• If there is true dominance, we cannot distinguish
  homozygous dominants from heterozygotes
• therefore, we cannot calculate allele frequencies
• therefore, we cannot test for equilibrium
• We must ASSUME equilibrium and estimate p and q
• (generally not a valid assumption)

46
Estimating allele/genotype frequencies
Tay-Sachs Disease autosomal recessive, lack of
hexosaminidase A --gt build-up of gangliosides
TT Tt tt 8777 1223
assume q2 1223/10000 q 0.35 p
0.65
47
Estimating allele/genotype frequencies
So, how many of the normal individuals are
expected to be carriers?
expected frequency 2pq 2(0.65)(0.35)
0.455
expected s 0.455 (10000) 4550