Lecture 4 Pop Gen I F2017.ppt

POPULATION GENETICS:
The study of the rules governing the
maintenance and transmission of
genetic variation in natural populations.

DARWINIAN EVOLUTION BY NATURAL SELECTION
 Many more individuals are born than survive
(COMPETITION).
 Individuals within species are variable (VARIATION).
 Some of these variations are passed on to offspring
(HERITABILITY).
 Survival and reproduction are not random. There must be a
correlation between fitness and phenotype.

Gregor Mendel
The “rediscovery” of Mendel’s genetic
studies in 1902 by William Bateson
completed the missing model for the
inheritance of genetic factors.
 Mendel published his work in the
Transactions of the Brunn Society
of Natural History in 1866.

Mendel’s Laws:
 Segregation
 Independent assortment

SEXUAL REPRODUCTION CONTRIBUTES TO VARIATION
Example – A Line Cross Experiment
Consider 2 diploid individuals with 3 loci and 2 alleles,
Parents: aabbcc x AABBCC
F1 progeny: AaBbCc
F2 progeny:
AABBCC AABBCc AABBcc
AABbCC AABbCc AABbcc
AAbbCC AAbbCc AAbbcc
AaBBCC AaBBCc AaBBcc
AaBbCC AaBbCc AaBbcc
AabbCC AabbCc Aabbcc
aaBBCC aaBBCc aaBBcc
aaBbCC aaBbCc aaBbcc
aabbCC aabbCc aabbcc
27
COMBINIATIONS

Mechanisms of Evolution: Mendelian Genetics
in Populations
 Genetic variation is the raw material of evolutionary
change: how do we measure it?
 What are the forces that cause genetic changes within
populations? That is, what mechanisms cause
evolutionary change?

Population Genetics
 Evolution can be defined as a change in gene frequencies
through time.
 Population genetics tracks the fate, across generations, of
Mendelian genes in populations.
 Population genetics is concerned with whether a particular
allele or genotype will become more or less common over
time, and WHY.

A few things to keep in mind as we take an
excursion into population genetic theory:
“Make things as simple as possible, but no simpler.”
---Einstein
“All models are wrong, some are useful.”
---Box
“No theory should fit all the facts because some of the facts are
wrong.”
---Bohr
“Before I came here I was confused about this subject.
Having listened to your lecture I am still confused. But on a
higher level.”
---Fermi

Assumptions:
1) Diploid, autosomal locus with 2 alleles: A and a
2) Simple life cycle:
PARENTS GAMETES ZYGOTES
(DIPLIOD) (HAPLOID) (DIPLOID)
These parents produce a large gamete pool (Gene Pool) containing alleles
A and a.
a A A a
a A A a A a a
a A A a a A a A A
a a A A a a a
a A a a A A
A a A

Gamete (allele) Frequencies:
Freq(A) = p
Freq(a) = q
 p + q = 1
Genotype Frequencies of 3 Possible Zygotes:
AA Aa aa
Freq (AA) = pA x pA = pA
2
Freq (Aa) = (pA x qa) + (qa x pA) = 2pAqa
Freq (aa) = qa x qa = qa
2
 p2 + 2pq + q2 = 1

General Rule for Estimating Allele Frequencies
from Genotype Frequencies:
Genotypes: AA Aa aa
Frequency: p2 2pq q2
 Frequency of the A allele:
p = p2 + ½ (2pq)
 Frequency of the a allele:
q = q2 + ½ (2pq)

Sample Calculation: Allele Frequencies
Assume N = 200 indiv. in each of two populations 1 & 2
 Pop 1 : 90 AA 40 Aa 70 aa
 Pop 2 : 45 AA 130 Aa 25 aa
In Pop 1 :
 p = p2 + ½ (2pq) = 90/200 + ½ (40/200) = 0.45 + 0.10 = 0.55
 q = q2 + ½ (2pq) = 70/200 + ½ (40/200) = 0.35 + 0.10 = 0.45
In Pop 2 :
 p = p2 + ½ (2pq) = 45/200 + ½ (130/200) = 0.225 + 0.325 = 0.55
 q = q2 + ½ (2pq) = 25/200 + ½ (130/200) = 0.125 + 0.325 = 0.45

Main Points:
 p + q = 1 (more generally, the sum of the allele
frequencies equals one)
 p2 + 2pq +q2 = 1 (more generally, the sum of the
genotype frequencies equals one)
 Two populations with markedly different genotype
frequencies can have the same allele frequencies

The Hardy-Castle-Weinberg Law
 A single generation of random mating establishes H-W
equilibrium genotype frequencies, and neither these
frequencies nor the gene frequencies will change in
subsequent generations.
Hardy
p2 + 2pq + q2 = 1

H-W ASSUMPTIONS:
1) Mating is random (with respect to the locus).
2) The population is infinitely large. (no sampling error –
Random Genetic Drift)
3) Genes are not added from outside the population (no
gene flow or migration).
4) Genes do not change from one allelic state to another
(no mutation).
5) All individuals have equal probabilities of survival and
reproduction (no selection).

IMPLICATIONS OF THE H-W PRINCIPLE:
1) A random mating population with no external forces
acting on it will reach the equilibrium H-W frequencies
in a single generation, and these frequencies remain
constant there after.
2) Any perturbation of the gene frequencies leads to a
new equilibrium after random mating.
3) The amount of heterozygosity is maximized when the
gene frequencies are intermediate.
2pq has a maximum value of 0.5 when
p = q = 0.5

GENOTYPE VERSUS GENE FREQUENCIES
q2 (aa)
p2 (AA)
2pq (Aa)

FOUR PRIMARY USES OF THE H-W PRINCIPLE:
1) Enables us to compute genotype frequencies from
generation to generation, even with selection.
2) Serves as a null model in tests for natural selection,
nonrandom mating, etc., by comparing observed to
expected genotype frequencies.
3) Forensic analysis.
4) Expected heterozygosity provides a useful means of
summarizing the molecular genetic diversity in natural
populations.

Color Pattern dominula medionigra bimaculata Total
Genotype B1B1 B1B2 B2B2
Sample Size (Nij) 905 78 3 N = 986
Frequency (Pij) 0.918 0.079 0.003 1.000
Allele Frequencies:
p1 = p11 + ½ p12 = 0.918 + ½ (0.079) = 0.958
p2 = 1 – p1 = 0.041
Expectations (Nij) p1
2 N 2p1p2 N p2
2 N
905 79 2
Genotype frequencies for Wing-color Polymorphism in a Natural
Population of the Moth Panaxia dominula (Fisher & Ford, 1947)

EVOLUTIONARY THOUGHT AFTER DARWIN
 By the 1870s, most scientists accepted the historical reality of
evolution (and this has been true ever since).
 It would be at least 60 years after the publication of The Origin of
Species before natural selection would come to be widely accepted.
 People wanted life itself to be purposeful and creative, and
consequently did not find natural selection appealing.
 Neo-Lamarckism -- inheritance of acquired characteristics.
 Orthogenesis -- variation that arises is directed toward a goal.
 Mutationism -- discrete variations are all that matter.

MUTATIONISM AND THE IMPACT OF MENDEL
 Gregor Mendel’s research was published in 1866, but was not
noticed until 1900.
 NOTE: Darwin knew nothing about the mechanism of inheritance
when he conceived of natural selection.
 MUTATIONIST THEORIES (based on Mendel’s work):
 Emphasized the importance of DISCRETE VARIATION
 T. H. Morgan -- the founder of Drosophila genetics.
 R. Goldschmidt -- theory of “hopeful monsters”.
Mendelian genetics disproved Lamarckian and blending
inheritance theories. However, the emphasis on
discrete variation caused a rift between mutation and
natural selection that was initially damaging to the field.

THE MODERN SYNTHESIS OF EVOLUTIONARY
BIOLOGY
 The rift between genetics and natural selection was
resolved in the 1930s and 1940s.
 This synthesis was forged from the contributions of
geneticists, systematists, and paleontologists.

Sir R. A. Fisher
1890-1962
The Genetical Theory
of Natural Selection
1930
 Fisher united Mendelian
population genetics with
the inheritance of
continuous traits.
"The Correlation between Relatives on
the Supposition of Mendelian Inheritance"
Philosophical Transactions of the Royal
Society of Edinburgh in 1918, (volume 52,
pages 399–433).

J. B. S. Haldane
1892-1964
The Causes of Evolution
1932
 Developed the mathematical
theory of gene frequency
change under selection (and
many other interesting
applications).

Sewall Wright
On his 90th birthday
1889-1988
 Developed the mathematical
framework for understanding the
genetic consequences of
migration, effective population
size, population subdivision, and
conceived of the concept of
adaptive landscapes.

Outcomes of the “MODERN SYNTHESIS”
 Populations contain genetic variation that arises by random mutation.
 Populations evolve by changes in gene frequency.
 Gene frequencies change through random genetic drift, gene flow,
and natural selection.
 Most adaptive variants have small effects on the phenotype so
changes are typically gradual.
 Diversification comes about through speciation.

MUTATION SELECTION
DRIFT
MIGRATION
POPULATIONS
Phenotypic Evolution: Process
+
+/ —
—
—

MEASURING GENETIC VARIATION IN
NATURAL POPULATIONS
TWO COMMONLY USED MEASURES TO QUANTIFY GENETIC
VARIATION ARE:
P – the proportion of polymorphic loci (those that have 2 or
more alleles)
H – the average heterozygosity = proportion of loci at which
a randomly chosen individual is heterozygous.

SS FS FF
SS FS
FS FF
FF FS SS
Monomorphic locus: all individuals fixed for same allele
Polymorphic locus: 2 alleles
 Frequency of F allele, p = 10 / 20 = 0.5
 Frequency of S allele, q = 10 / 20 = 0.5
 H = 4 /10 = 0.4
* * * *

ALLOZYME VARIATION IN MAJOR TAXA
In F. J. Ayala (ed.) 1976. Molecular Evolution. Sinauer Assoc.

ALLOZYME VARIATION
WITHIN MAJOR TAXA

ALLOZYME VARIATION AMONG Drosophlia spp.
In F. J. Ayala (ed.) 1976. Molecular Evolution. Sinauer Assoc.

3 MICROSATELLITE
LOCI, SHOWING
HIGH LEVELS OF
POLYMORPHISM
WITHIN A
POPULATION.

SEQUENCE DATA
 The definitive source of information regarding genetic
variation.
 Usually obtained by PCR and direct sequencing of a
particular gene of interest.
 Sequence-level variation can also be assessed using
restriction enzymes (RFLPs).
 More on sequences when we get to “molecular evolution”.

THE EXTENSION OF H-W TO LOCI WITH MANY ALLELES
 Regardless of the number of alleles per locus, the H-W
principle still applies as long as the organisms are diploid.
 Assume that you have a locus with n alleles (A1, A2, … , An),
and the allele frequencies are given by p1, p2, p3, … , pn.
 The expected frequency of any homozygote is just the
square of the allele frequency.
F (A1A1) = p1
2, F (A6A6) = p6
2, etc.
 The expected frequency of any heterozygote is 2 times the
product of the respective allele frequencies.
F (A1A3) = 2p1p3, F (A3A5) = 2p3p5, etc.
 Expected heterozygosity is 1 – Σ(pi
2).

With the recognition… that the… genome is replete with
DNA sequence polymorphisms such as RFLP’s, it was
only a small leap to imagine that DNA could, in
principle, provide the ultimate identifier.
E. S. Lander, 1991
DNA analysis will be to the end of the 20th century what
fingerprinting was to the 19th.
Melson, 1990
DNA POLYMORPHISM AS A TOOL FOR FORENSICS???

APPLICATIONS OF H-W TO FORENSICS
Example:
Defendant Genotype Tissue Sample From
Crime Scene
A14A27 A14A27
Question:
 What is the probability of this match being a false
positive???
 In other words what is the probability that this match
occurred simply by chance?

PROBABILITY OF A FALSE POSITIVE
Frequency of A14 in population = p14
Frequency of A27 in population = p27
 Expected fraction of random individuals in the population
with the same genotype as the defendant = 2 p14 p27
PRODUCT RULE:
 With multiple loci, the probability of a false positive is
simply equal to the product of the locus-specific
probabilities.
 As this probability becomes small, we become more
confident that the match is real.

Highly repetitive blocks of DNA ( ) found
through out the genome.
DNA is cut with restriction enzymes ( ),
labeled with 32P and run through a gel to
reveal a characteristic banding pattern
INDIVIDUAL
A B C
VNTR Loci:

FROM: Balazs et al. 1989. Am. J. Hum. Genet. 44:182-190.
Balazs et al. 1992. Genetics 131:191-198
Genetic diversity of VNTR Loci in
Human Populations
Average heterozygosity of 6 VNTR
loci in ethnic groups:
Caucasian 0.89
Chinese 0.84
Cambodian 0.80
Melanesian 0.76
Australian aborigine 0.77
American
Blacks
Caucasians
Hispanics

Some Definitions:
 Population: A freely interbreeding group of individuals.
 Gene Pool: The sum total of genetic information present in a
population at any given point in time.
 Phenotype: A morphological, physiological, biochemical, or
behavioral characteristic of an individual organism.
 Genotype: The genetic constitution of an individual organism.
 Locus: A site on a chromosome, or the gene that occupies the site.
 Gene: A nucleic acid sequence that encodes a product with a distinct
function in the organism.
 Allele: A particular form of a gene.
 Gene (Allele) Frequency: The relative proportion of a particular
allele at a single locus in a population (a number between 0 and 1).
 Genotype Frequency: The relative proportion of a particular
genotype in a population (a number between 0 and 1).

Lecture 4 Pop Gen I F2017.ppt

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