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Evolution in Populations
(or How Natural Selection Works)
To take a step back:
We have talked about
1) Historical views of organic change
2) Darwin’s views of organic change
3) Evidence for change through time
(small and larger scale examples)
Next few lectures : HOW this change through time happens.
Definitions
Evolution (from previous slide show)
Changes over time of the proportion of individuals differing genetically in
one or more traits
**PATTERN**
Natural Selection
Differential success in the reproduction of different
phenotypes resulting from the interaction of
organisms with their environment.
**PROCESS**
A Little Basic Genetics
Gregor Mendel
(1822 - 1884)
A Little Basic Genetics
Imagine a very simple creature in which every cell has one chromosome -
A Little Basic Genetics
But every sexually reproducing creature has 2 of each chromosome
In you, there are 23 pairs of chromosomes for a total of 46
Each chromosome contains a series of genes but for now we’ll imagine
that there is just one on our chromosome
Gene A
Now assume that there are two versions of each gene - represented with a
capital and a small letter
Gene A
a
Another idea - Cell Division
There are 2 kinds of cell division
1. Mitosis - (duplication) - every cell makes a copy of itself
(this is how you grow and replace dead cells)
2. Meiosis - (reduction) - cells divide in such a way as to reduce the
number of chromosomes by 50%
Meiosis
In one of the stages of meiosis, the chromosomes line up on
the midline of the cell and are separated from each other
when the cell divides
A
A
a
A
a
a
Chromosomes line up
The cell divides
And just to inject a little bit of reality…….
A
A
a
These are
eggs or sperm
a
And a little arithmetic…….
What are the chances of getting each type of egg or sperm?
A
A
a
50% chance of each
a
A few more definitions and terms
Trait - any physical characteristic of an organism
(e.g. eye colour, hair colour, height)
(for now you can assume that gene = trait)
Allele - alternate versions of a gene or trait
(e.g. blue, brown, green, or hazel eyes)
Phenotype - the physical appearance of an organism
Genotype - the genetic makeup of an organism
In our simple creature
we have one trait A with two alleles of each
A - the dominant allele for trait A
a - the recessive allele for trait A
Probability of getting either a or A = 0.5
What about producing offspring? - all the possible
combinations of eggs and sperm
a
A
A
A
a
a
A
a
Or to put this a little more formally - A Punnett square
Female parent
A
(0.5)
Male
parent
A
(0.5)
a
(0.5)
a
(0.5)
AA
Aa
Aa
aa
The letters in each box are the GENOTYPE of the offspring
Or to put this a little more formally - A Punnett square
Female parent
A
(0.5)
Male
parent
A
(0.5)
a
(0.5)
a
(0.5)
AA
(.25)
Aa
(.25)
Aa
(.25)
aa
(.25)
The letters in each box are the GENOTYPE of the offspring
A
(0.5)
A
(0.5)
a
(0.5)
So we have 3 possible genotypes
AA
Ratio
1
Aa (x2)
2
aa
1
AA
(.25)
Aa
(.25)
a
(0.5)
Aa
(.25)
aa
(.25)
A
(0.5)
A
(0.5)
a
(0.5)
AA
(.25)
Aa
(.25)
a
(0.5)
Aa
(.25)
aa
(.25)
So we have 3 possible genotypes
AA
Ratio
1
Aa (x2)
2
aa
1
….and two possible phenotypes
Ratio
A_
aa
3
1
We can generalize this idea to be more inclusive
If you say that the frequency of the dominant allele is ‘p’
and the frequency of the recessive allele is ‘q’
In our example, p = 0.5 and q = 0.5
And p + q = 1
(p + q ALWAYS equals1)
And if you mate two organisms, you can mathematically
determine the expected proportion of offspring of each type
p+q
p+q
p2 + 2pq + q2
In our simple organism, p = q = 0.5
and p2 + 2pq + q2
= (0.5)(0.5) + 2 (0.5)(0.5) + (0.5)(0.5)
p2
2pq
q2
= .25 +.5 +.25
Which is back to our 1:2:1 genotypic ratio
This idea holds true for any value of p or q.
For example:
If p is very common - say 90% of the genes in the population
Then p = .9 and q = .1
And
p2 = .81 (the frequency of the AA genotype)
2pq = .18 (the frequency of the Aa genotype)
q2 = .01 (the frequency of the aa genotype)
In the early 1900’s, Hardy and Weinberg used this idea to
establish a fundamental idea in the genetic basis of natural
selection
The Hardy-Weinberg Equilibrium
Assume that p = .6 and q = 0.4
In Generation 1
p2 + 2pq + q2 = .36 + .48 + .16
In Generation 2
p2 + 2pq + q2 = .36 + .48 + .16
In Generation 3
p2 + 2pq + q2 = .36 + .48 + .16
In Generation 4
p2 + 2pq + q2 = .36 + .48 + .16
•
•
•
The Hardy-Weinberg Equilibrium
In any population, allelic and genotypic frequencies will
remain the same if Mendelian inheritance patterns are the
only factors at work
Requires:
1. Very large population size
2. No gene flow -no movement of genetic material
between populations
3. No mutations
4. Random mating
5. No natural selection
The Hardy-Weinberg Equilibrium
In any population, allelic and genotypic frequencies will
remain the same if Mendelian inheritance patterns are the
only factors at work
Requires:
1. Very large population size
2. No gene flow -no movement of genetic material
between populations
3. No mutations
4. Random mating
5. No natural selection
The Hardy-Weinberg Equilibrium
1. Large population sizes
What happens if the population isn’t ‘large’?
Genetic Drift - a statistic consequence of small populations
The Hardy-Weinberg Equilibrium
1. Large population sizes
What happens if the population isn’t ‘large’?
Genetic Drift - a statistic consequence of small populations
The Hardy-Weinberg Equilibrium
1. Large population sizes
http://darwin.eeb.uconn.edu/simulations/drift.html
The Hardy-Weinberg Equilibrium
1. Large population sizes
What happens if the population isn’t ‘large’?
Bottlenecks
The Hardy-Weinberg Equilibrium
1. Large population sizes
What happens if the population isn’t ‘large’?
Bottlenecks
Northern Elephant Seal
The Hardy-Weinberg Equilibrium
1. Large population sizes
What happens if the population isn’t ‘large’?
Bottlenecks
1700’s - ??
1890 - 20 est.
2009 - 135,000
Northern Elephant Seal
The Hardy-Weinberg Equilibrium
1. Large population sizes
What happens if the population isn’t ‘large’?
Bottlenecks
Assay of 16 genes in
159 individuals
0/16 had any variability
Northern Elephant Seal
The Hardy-Weinberg Equilibrium
1. Large population sizes
What happens if the population isn’t ‘large’?
Founder effect
The Hardy-Weinberg Equilibrium
1. Large population sizes
What happens if the population isn’t ‘large’?
Founder effect
1740’s
Amish
The Hardy-Weinberg Equilibrium
1. Large population sizes
What happens if the population isn’t ‘large’?
Founder effect
Ellis-Van Creveld Syndrome
-Polydactyly
-congenital heart defects
-pre-natal tooth eruption
-short-limbed dwarfism, short ribs
-cleft palate,
-malformation of the wrist bones
Amish
The Hardy-Weinberg Equilibrium
1. Large population sizes
What happens if the population isn’t ‘large’?
Founder effect
700
U.S.
Population
600
Incidence in
100,000
Births
500
500
400
300
200
100
0
Amish
1.4
`
The Hardy-Weinberg Equilibrium
2. Mutations - source of all new genetic variation
Rates of mutation - typically about .00001
(may be as low as .0000001)
OR 1 mutation/100,000 genes/generation
(1 mutation in 1000000/generation)
2. Mutations - source of all new genetic variation
How do we model this?
p 2 + 2pq + q 2
Frequency of aa
Frequency of AA
Frequency of Aa
Imagine that ‘A’ mutates to ‘a’ at a rate of m per generation

Frequency of A after one generation of mutation
p1 = p0 - mp0 = p0 (1 - m)
Frequency of A after a second generation of mutation


p2 = p1 - mp1 = p1(1 - m)
Imagine that ‘A’ mutates to ‘a’ at a rate of m per generation
Frequency of A after one generation of mutation
p1 = p0 - mp0 = p0 (1 - m)
Frequency of A after a second generation of mutation

Substitute
p2 = p1 - mp1 = p1(1 - m)
p2 = p1 - mp1 = p0 (1 - m)(1 - m)

p 2 = p1 - mp1 = p 0 (1 - m) 2
For any number of generations (x)

p 2 = p 0 (1 - m) x
The Hardy-Weinberg Equilibrium
3. Random mating
This assumes no preferences in mates
Humans: Preferences
Height - we tend to mate with people closer to
our own height
The Hardy-Weinberg Equilibrium
3. Random mating
1.0
.1
Probability
of mating
Humans - distance from home
.01
.001
.0001
Distance from ‘home’
The Hardy-Weinberg Equilibrium
3. Random mating
1.0
.1
Probability
of mating
.01
Humans - distance from home
40 km
.001
.0001
Distance from ‘home’
The Hardy-Weinberg Equilibrium
3. Natural Selection
-depends on variability that is heritable
-differences must be passed to the offspring
Key idea :
Fitness: The contribution an individual makes to the gene pool of
the next generation relative to other individuals
The Hardy-Weinberg Equilibrium
3. Natural Selection
-depends on variability that is heritable
-differences must be passed to the offspring
Key idea :
Fitness: The contribution an individual makes to the gene pool of
the next generation relative to other individuals
Lower fitness
Higher fitness
Types of Natural Selection
Most traits have a normal (or bell curve distribution)
Types of Natural Selection
Most traits have a normal (or bell curve distribution)
Types of Natural Selection
1. STABILIZING SELECTION
Types of Natural Selection
1. STABILIZING SELECTION
Human birth weight
Types of Natural Selection
2. DIRECTIONAL SELECTION
Types of Natural Selection
2. DIRECTIONAL SELECTION
Salmon fishing - largest fish are taken every year
Types of Natural Selection
3. DISRUPTIVE SELECTION
Types of Natural Selection
3. DISRUPTIVE SELECTION
Breed together
Selection of positively and
negatively geotactic
Drosophila
• •
• •
• ••
Negatively geotactic •
•
Positively geotactic
Breed together
•
• •
••
• •
• ••
• •
•
Artificial Selection - Drosophila geotaxis
• •
•
Types of Natural Selection
3. DISRUPTIVE SELECTION
Selection for bristle
number in Drosophila
Modelling Natural Selection
Select against recessive homozygote - aa
AA
Aa
aa
Total
Initial Frequency
p2
2pq
q2
1
Fitness
1
1
1-s
Next Generation
1
1
q2(1 – s)
p2
1- sq 2
Normalized

q 2 (1 - s)
1- sq 2
2pq
1 - sq 2


1 – sq2