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This presentation was originally prepared by
C. William Birky, Jr.
Department of Ecology and Evolutionary Biology
The University of Arizona
It may be used with or without modification for
educational purposes but not commercially or for profit.
The author does not guarantee accuracy and will not
update the lectures, which were written when the course
was given during the Spring 2007 semester.
Forces Determining Amount of Genetic Diversity
The following are major factors or forces that determine the amount of diversity
in a population. They also determine the rate and pattern of evolutionary base
substitution.
factor (parameter)
(1) mutation (rate)
(2) natural selection (kind and strength)
(3) random drift (effective population size)
Mutation
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Mutation is the ultimate source of genetic variation and differences between
species.
All other things being equal, the higher the mutation rate the greater the
genetic variance in the population and the larger the differences between
species.
u = mutation rate = probability that a particular base pair will undergo
mutation
u is very low, on the order of 10-8 to 10 -9 per base pair or
10-4 to 10 -6 per gene.
We are interested in the total number of mutations that enter the gene pool in
one generation.
In a diploid organism, if there are N individuals in the population, 2N gametes
must be produced each generation.
The total mutation rate in the population is the rate per base pair (or gene) per
gamete times the number of copies of the gene in the population. The number of
copies is the number of individuals (population size) N times 2 for a diploid
organism.
M = 2Nu
M = 2Nu
Mutations per gene = Number of gametes  mutations per gene per gamete
dimensional analysis:
mutations = gametes  mutations
genes
genes  gametes
M is usually very large:
If N is 10 5, the population will contain on the average of 2 new mutations in each
gene in each generation. Clearly most of th ese must be eliminated, otherwise
genetic variation will accumulate until species identity is lost.
If use DNA sequences to identify mutations, u is in mutations per bp per gamete
or mutations per site per gamete.
If N = 105 and u = 10-9 and th ere are 3 X 109 bp per human genome, will have
3 X 106 new mutations in gene pool in each generation.
3 X 106 new mutations
3 X 106 new and old mutations
Random genetic drift.
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Nondirectional force.
Acts equally to increase or decrease frequencies.
Eliminates or fixes new mutations.
Happens because different individuals have different numbers of offspring
by chance.
The probability that an al lele will be fixed by drift is equal to its frequency.
Why drift happens
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Not all individuals in a population produce the same number of offspring.
Not all genes leave the same number of offspring.
Some of difference due to selection, some to pure dumb luck.
E.g. Mutation happens in one of the 6 million primary oocytes in your germ line
when you were a fetus. Only a few hundred survive and ovulate. But you only
have two children. Probability that a child will have the mutation is about 2/6
million or 1/3 mi llion.
E.g. Three bdelloid rotifers belonging to same clone dry up and blow around.
Each one lands in a tiny pothole just after a rain and starts to reproduce. Each
one produces 5,000 offspring. A deer comes along and drinks the other pothole
dry, so that bdelloid has no offspring. Any allele of any gene carried by it only
leaves no offspring.
Eleplhant drinks all
Bad things can happ en even to good genes. (S--- happens.)
Drift leads to fixation or loss of alleles
Even in the absence of selection, allele frequencies are not constant: they undergo
random walks. If the frequency of an allele drifts to 0, it is lost; if it drifts to 1, it
is fixed and al l other alleles of that gene are lost.
Probability of fixation of an allele is equal to its frequency:
P(fix neutral allele of frequency x) = x
• Section 18 divided into 18a, b, c. 18a and b on web.
• Another homework assignment, on population and evolutionary genetics,
will be posted soon, hopefully on Friday.
Probability of fixation of an allele is equal to its frequency:
P(fix neutral allele of frequency x) = x
Random drift is much more likely to eliminate a new mutation than to fix it.
New mutation: x = 1/2N P(fix new mutation) = 1/2N
P(lose new mutation) = 1 - 1/2 N
e.g. N = 5,000
P(fix) = 1/10,000 = 0.0001
P(loss) = 0.9999
New mutation begins with frequency very close to 0 and very likely to hit 0 and
be lost. Conversely, it is very far from 1 and very unlikely to get there.
Proof that random drift actually occurs has been obtained repeatedly in
laboratory experiments. Done with very small population size to make it go fast.
Fig. 17.30 and adjacent text describe an experiment in Drosophila. Read it.
The strength of random drift depends on the population size; works faster in
smaller populations.
E.g. Haploid population with N = 5 or 10.
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What is important is the effective population size Ne.
Ne depends on N but also on the sex ratio and other factors tha t determine
the variance in offspring number.
In nearly all cases, Ne < N. Often Ne << N.
e.g. elk harems
In diploids the important number is 2Ne because each individual has 2 genomes.
Play with a simple model of drift to understand it
Go to bottom of web site, then go either to URL for simulation or, better,
download stuff and do manual simulation. Best is to do both.
Another program ava ilable on web is PopG program which tracks changes in
gene frequencies under mutation, drift, and/or selection. We will use it later.
Combined effects of mutation and drift: neutral model
Drift always happens.
Mutation always happens. So add mutation to simulation:
This model is realistic: it fits many real situations in which most genetic
diversity is due to neutral alleles. Some people think that it fits the majority of
molecular data.
4Neu
H - 1 + 4N u - 4Neu =  Haploids and asexuals: substitute 2Neu
e
Animal mitochondrial genes: substitute Nfu
4Neu
 - 1 + 4N u - 4Neu = 
e
but now u is in mutations per site per gamete,
sometimes symbolized by 
Intuitive explanation for these equations:
Higher mutation rate: more mutations pumped into the population.
Larger Ne: drift is slower so mutations tend to linger in population longer.
Directional selection
If mutation and drift were all that happened, there would be no adaptation of
organisms to different habitats.
Differences in Ne and u can’t explain synonymous > nonsynonymous or introns
> exons, because all these are in same genome in same organism and have same
Ne and u.
Directional selection is a directional force that tends to increase frequencies of
advantageous alleles and decrease fre quencies of detrimental alleles.
By itself, directional selection will fix advantageous alleles and eliminate
detrimental alleles.
Directional selection is the basis for most cases of Darwinian adaptive evolution,
because it results in a phenotypic change that increases the fitness of the
organism.
Drosophila experimental results usually not as neat as those cases we use in
class.
Did three-factor cross in genetics lab course.
All mutant genotypes (e.g. white eye) present in fewer than the expected
numbers.
All visible mutants, all at least slightly detrimental.
If they were not detrimental, they would be more common in nature.
If they were advantageous, they would have become the wild type.
Adaptive Melanism in Lava Flow Mice
Hopi Hoekstra (now at Harvard), Michael Nachman (EEB), et al.
See Hopi’s web site:
http://www-biology.ucsd.edu/faculty/hoekstra.html
Follow the link to Projects.
Melanism seen in mice, lizards, and snakes living on desert lava flows.
Earlier work showed that melanism reduces owl predation on mice on dark lava
rock, and dark mice have reduced fitness on light rock.
Rock pocket mouse Chaeootdipus intermedius living in Arizona, New Mexico, and
northern Sonora
Hair color matches rock color.
Due to natural selection, act ing over < 500,000 years. Requires strong selection.
This is short-term evolution, within a species.
Mouse populations on lava are not completely isolated from mouse populations
on light rock in adjacent desert. Therefore selection must be very strong to
counteract effects of migration.
Melanism in Pinacate population in Arizona is due to a single point mutation in
the melanocolrtin-1 receptor gene (Mc1r) that is responsible for melanism.
Melanism in New Mexico populations due to different gene. • 2 independent
origins of adaptive melanism in pocket mice.
Selection intensit y is measured by relative fit nes s or by sele ction coe ffi cient s of mutant
all ele:
offspring number (relative fitness)
50
50
mutant
wild type
0
100
s
-1
----------------
0
lethal
detrim ental
neu tral
mutant
100
0
----------------
1
advan tageous
lethal
wild typle
The majority of mutan ts have selection coefficients with small
absolute values: |s| < 0.1.
Combined Effects of Selection and Drift
Probability of fixation of a new mutant allele with selection coefficient s in population
with effective size Ne is given by Kimura’s equation:
F = (1 – e-2Nes/N)/ (1 – e-4Nes)
Solving equation for various values of N, Ne, and s leads to the following conclusions:
• Even detrimental mutations can be fixed by drift.
• Even advantageous mutations can be lost by drift.
• Relative strength of selection and drift depends on the product Ne|s|:
Ne|s| >> 1
selection dominates
Ne|s| << 1
drift dominates (mutation is effectively neutral)
If Ne|s| >> 1, then either Ne is very large so drift works very slowly, or |s| is very large
so selection is very strong (or both).
If Ne|s| << 1, then either Ne is very small so drift is strong, or |s| is very small so
selection is very weak (or both).
Analogy: selection is signal, drift is noise.
Balancing Selection
Balancing selection is any kind of selection that maintains two or more alleles
in a population.
Sickle-cell anemia
Sickle-cell gene has been maintained in fairly high frequency even though it is
detrimental.
Heterozygotes are more resistant to malaria than homozygous normal.
Heterozygotes have selective advantage where malaria is endemic.
HbA HbA
HbA HbS
HbS HbS
anemia
none
mild
severe
effects of
malaria
severe
less severe
?
Example of overdominance = heterozygotes are more fit than either
homozygote.
There are a number of other kinds of balancing selection.
e.g. different alleles are adapted to different habitats.
Deer mice in western U.S. live from sea level to 14,000 feet.
Polymorphic for two variants of -globin protein, one more efficient at binding
oxygen at high altitude and the other at low altitude.
Only a few cases of balancing selection have been clearly demonstrated.
Probably less important than directional selection, but this is still being debated.
Balancing selection delays the fixation or loss of alleles, which increases
heterozygosity.
Combined Effects of Mutation, Drift, and Selection: Simple Models
of Extreme Cases
Each dot represents a gene.
Time goes left to right.
Each vertical column of dots represents the genes in one generation.
Directional selection reduces genetic variability relative to neut ral
case by accelerating the fixation or loss of mutations.
Balancing selection increases genetic variability relative to neut ral
case.
Directional Selection
Mutations stay in population average
neutral
- 4Ne generations
detrimental
pushed to loss
< 4Ne generations
advantageous
pushed to fixation
< 4Ne generations
balanced
maintained
> 4Ne generations
H or 
- 4Neu
< 4Neu
< 4Neu
> 4Neu
Balancing selection is not very common. Therefore if we look at a large
segment of DNA, we will find that H < 4Neu.
A few genes have H > 4Neu showing balancing selection.
Analogy:
Gene pool is bathtub with water molecules as alleles.
Mutation is faucet.
Drift is drain.
Directional selection is pump.
Balancing selection is 2 (or more) rubber duckies which can’t fit out the drain
or pump.
Evidence for directional and balancing selection from population
genetics of Drolsophila Adh
Directional selection:
(1) There is more polymorphism in introns than in exons.
(2) In the exons, there is much more polymorphism in DNA sequence than in
amino acid sequence.
(4) The left end of exon 4 is an exception. The F/S site is polymorphic, and
regions close to it on both sides have a higher polymorphism than other exons.
The F/S difference is maintained by balancing selection. This selection also tends
to maintain heterozygosity for mutations closely linked to F or S. Further away,
recombination tends to separate new mutations from F or S and d irectional
selection acts to reduce polymorphism.
Explaining patterns/phenomena:
Different species have different diversities
Could be due to differences in u, Ne, or s.
Why are cheetahs so uniform?
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No reason to believe mutation rate different from other animals.
Some markers probably nearly neutral so probably not due to very strong selection.
Probably mainly small N and Ne; lingering effects of population bottleneck.
Different genomes have different diversities.
Hominids: mitochondrial gene diversity > nuclear gene diversity
2Nfum > 4Neun
we know 2Nf < 4Ne
therefore um > un
where Nf = number of females
Mitochondria have different DNA polymerase, less effective repair systems, and more
exposure to mutagens.
Different genes or regions of genome have different diversity.
E.g. fibrinopep tides > -globin
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All nu clear gene s in same species, so diff erence not due to Ne or to u.
Is due to selection ; fibrinopep tides work with a wide range of ami no acid sequence s so new
mutations are only sli ghtly de trim ental; globin mutations more detrim ental.
Why are conserved sequences lower in variation than others?
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Not low u, which is same on average for all segments of a genome.
Not N and Ne, which are same for all genes in an organism.
Conserved sequences have arge negative s: on av erage, larger proportion of
mutations are detrimental, fewer are neutral.
Why are VNTRs so useful for forensic work?
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Ne is same for VNTRs and other genes.
Most nearly neutral, so high variation partly due to lack of directional selection.
Mutation rate u is high (due to replication slippage and changes in repeat numbers,
not to single-base mutations)
One Implication for Conservation
Endangered species have small N. This means small Ne and Ne|s|, which
means less effective selection, which includes more accumulation of
detrimental mutations, leading to reduced fitness and further reduction in
N.
Vicious circle:
smaller N
smaller Ne and Ne|s|
reduced fitness
less effective
selection