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Population Genetics. The study of Mendel’s laws and other genetic principles as they apply to entire populations of organisms Major theme: the origin, maintenance and significance of genetic variation. Paradox of genetic variability.

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population genetics
Population Genetics
  • The study of Mendel’s laws and other genetic principles as they apply to entire populations of organisms
  • Major theme: the origin, maintenance and significance of genetic variation
paradox of genetic variability
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 population’s advantage to have genetic variability among its members in order to respond to changes in the environment
paradox of genetic variability1
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
kettlewell s moths
Kettlewell’s Moths
  • Studied Biston betularia, the peppered moth, in a heavily industrialized area of England
  • Two color morphs present:
    • peppered; PP, Pp
    • melanic; pp
kettlewell s moths1
Kettlewell’s Moths
  • By the time Kettlewell studied the moths in the 1950’s, 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
kettlewell s moths2
Kettlewell’s 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
definitions
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%
definitions1
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
definitions2
Definitions
  • Population
    • a community of individuals of the same type
  • Mendelian population
    • a community of interbreeding, sexually reproducing individuals
    • sometimes called a deme
biological species concept
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
definitions3
Definitions
  • Gene pool - all the alleles present in a population
    • we generally consider only one locus at a time
allele frequencies
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
allele frequencies1
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

allele frequencies2
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%
allele frequencies3
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
allele frequencies4
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
allele frequencies5
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

# :

slide18

TT Tt tt

normal carrier anemic

400 75 25

2(400) + 1(75)

freq (T) = p = ------------------------- = 0.875

2(400 + 75 + 25)

slide19

Snails:

Brown Mottled White

BB BW WW

150 500 350

allele frequencies6
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
the hardy weinberg equilibrium
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
the hardy weinberg equilibrium1
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
the hardy weinberg equilibrium2
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
the hardy weinberg equilibrium3
The Hardy-Weinberg Equilibrium
  • Five forces which may change allele frequencies:
    • mutation
    • migration
    • small population size
    • non-random mating
    • selection
five forces changing h w frequencies
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
five forces changing h w frequencies1
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
five forces changing h w frequencies2
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
five forces changing h w frequencies3
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
five forces changing h w frequencies4
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!
five forces changing h w frequencies5
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

hardy weinberg equilibrium
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
relationship between allele and genotype frequencies
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

relationship between allele and genotype frequencies1
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

relationship between allele and genotype frequencies2
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

slide35

genotypes: AA AB BB

frequencies: p2 2pq q2

Are there any other possible genotypes with these two

alleles?

No! Therefore:

p2 + 2pq + q2 = 1

three or more alleles
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

relationship between allele genotype frequencies and equilibrium
Relationship between allele/genotype frequencies and equilibrium

p = q = .5

A B

p

q

A p2 pq

B pq q2

p q

relationship between allele genotype frequencies and equilibrium1
Relationship between allele/genotype frequencies and equilibrium

p = .70

q = .30

A B

A

B

p

q

p2

pq

pq

q2

p q

using the hardy weinberg equations
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)
testing for equilibrium
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

testing for equilibrium1
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?

slide42

genotypes: AA AB BB

obs. #’s: 100 100 100

exp. #’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 < 0.01

testing for equilibrium2
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
testing for equilibrium3
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

estimating allele genotype frequencies
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)
estimating allele genotype frequencies1
Estimating allele/genotype frequencies

Tay-Sachs Disease:

autosomal recessive, lack of hexosaminidase A --> build-up of

gangliosides

TT Tttt

8777 1223

assume q2 = 1223/10000

q = 0.35

p = 0.65

estimating allele genotype frequencies2
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