Download Evolution without Selection

Population genetics and
Hardy-Weinberg equilibrium
Mendelian-Darwinian SynthesisPopulation Genetics
• Although Mendel’s and Darwin’s work were published
within 5 years of each other, a synthesis of their ideas
was not truly met until 1930’s
• Recognition that the relative abundance of traits in a
population is tied to the relative abundance of alleles
that influence them
• Under what circumstances will the relative abundance
of alleles change within a population (i.e. the
population evolves)?
Population genetics integrates Darwin’s evolution by
natural selection with Mendelian genetics
Evolution is change in allele frequency across
generations
Population genetics begins with a model of what
happens to allele and genotype frequencies in an
idealized population
Suppose that in a population there are two
alleles, A and A at a locus of interest.
There are three possible genotypes.
AA
Homozygous, A
AA
Heterozygous
AA
Homozygous, A
AA
AA
AA
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
If gametes join at random…
a
A
will meet with a
half the time , and with a
A
A
the other half the time.
Similarly, a
A
will join with the two egg
types at a 50:50 ratio.
Half of all eggs have A and half have A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
Half of all sperm have A
and half have A
A
A
A
Zygotes
AA
AA
AA
AA
AA
AA
AA
AA
AA
AA
AA
AA
p = freq. of the A allele = 0.5 AA
q = freq. of the A allele = 0.5
AA
AA
AA
AA
AA
AA
AA
AA
AA
AA
AA
Homozygous, A
freq. = 0.25 = p2
Heterozygous
freq = 0.5 = 2pq
Homozygous, A
freq. = 0.25 = q2
Regardless of allele frequencies - no matter
what the values of p and q - genotype
frequencies will go to, and remain at…
2
p
+ 2pq +
2
q
= 1
Hardy-Weinberg equilibrium equation
How are different alleles inherited? - Law of
Segregation
each diploid individual carries 2 non-blending copies of each
gene
• each gamete (sperm/egg) receives only one of these genes
• each gene is segregated randomly – there is no way of knowing
which copy of the gene a specific gamete will receive
• different forms (alleles) of the gene are thus also segregated
randomly amongst the gametes
How are allele frequencies and genotypes
related in a population?
For a simple 2 allele (A1 and A2) locus, possible genotypes
are A1 A1, A1 A2 and A2 A2
If we know the relative frequencies of A1 and A2, we can
predict the relative frequencies of each genotype
In a hypothetical 2 allele closed population
frequency of A1 in gene pool = p
frequency of A2 in gene pool = q
Since there are only 2 alleles
in the population:
p + q= 1
A1
Sperm
A2
A1
A 1A1
A 1A2
A2
A1 A2
A2 A2
Eggs
A1
Sperm
A2
A1
A 1A1
A 1A2
A2
A1 A2
A2 A2
Eggs
A1
Sperm
A2
A1
A 1A1
A 1A2
A2
A1 A2
A2 A2
Eggs
Genotypic Outcome Probabilities
A1A1 Homozygotes = p x p = p2
A1A2 Heterozygotes = (p x q) + (p x q) = 2pq
A2A2 Homozygotes = q x q = q2
p2 + 2pq + q2 = 1
Yule’s Numerical Example:
The Simplest Case
•If the frequency of each of 2 alleles in the population is
exactly equal, the frequency of each allele = 0.5
•i.e. A1 = 0.5, A2 = 0.5
•Since any 2 gametes in a randomly mixed “gene lottery”
will have an equal chance of being picked, the probability of
a sperm having the A1 allele = 0.5
Conclusion 1: allele frequencies in a population will
not change, generation after generation
Conclusion 2: if allele frequencies are given by p & q,
the genotype frequencies are p2, 2pq, q2
5 Assumptions for H-W Principle
1) no selection
2) no mutation
3) no migration to or from population
4) no random events that cause some individuals to pass on
more of their genes than others
5) random mating
So what is the value of this null model with
entirely unrealistic assumptions?
1) We can quantify what will happen if there is
selection on an allele
2) Likewise if there are mutations
3) etc.
5 Assumptions for H-W Principle
1) no selection
2) no mutation
3) no migration to or from population
4) no random events that cause some individuals to pass on
more of their genes than others
5) random mating
When individuals with some genotypes survive at
higher rates than individuals with other genotypes,
allele frequencies can change from one generation
to the next.
ie. natural selection causes evolution
Violation of no-selection assumption violates
Conclusion 1: allele frequencies in a population will
not change, generation after generation
Persistent selection can cause substantial changes in
allele frequencies over time
5 Assumptions for H-W Principle
1) no selection
2) no mutation
3) no migration to or from population
4) no random events that cause some individuals to pass on
more of their genes than others
5) random mating
Mutation can cause appreciable changes in allele
frequencies over very long periods of time
Mutation is a weak force of evolution
Nonetheless it provides the raw material upon which
natural selection acts
Mutation - selection balance
5 Assumptions for H-W Principle
1) no selection
2) no mutation
3) no migration to or from population
4) no random events that cause some individuals to pass on
more of their genes than others
5) random mating
Migration is a potent force in evolution
Migration is a potent force in evolution
Migration is most important in preventing populations
from diverging
Violation of no-migration assumption violates
Conclusion 2: if allele frequencies are given by p & q,
the genotype frequencies are p2, 2pq, q2
5 Assumptions for H-W Principle
1) no selection
2) no mutation
3) no migration to or from population
4) no random events that cause some individuals to pass on
more of their genes than others
5) random mating
In populations of finite size, chance events - in the
form of sampling error in drawing gametes from the
gene pool - can cause evolution
Selection is differential reproductive success that
happens for a reason; genetic drift is differential
reproductive success that just happens
Genetic drift is most important in small populations
Frequency of allele A1
Average heterozygosity
Popln = 4
Generation
Popln = 40
Popln = 400
Generation
As alleles drift to fixation or loss, the frequency of
heterozygotes in the population declines
Violation of no-drift assumption violates both
Conclusion 1: allele frequencies in a population will
not change, generation after generation
Conclusion 2: if allele frequencies are given by p & q,
the genotype frequencies are p2, 2pq, q2
5 Assumptions for H-W Principle
1) no selection
2) no mutation
3) no migration to or from population
4) no random events that cause some individuals to pass on
more of their genes than others
5) random mating
Coral releasing gametes into the water
Violation of random mating assumption violates
Conclusion 2: if allele frequencies are given by p & q,
the genotype frequencies are p2, 2pq, q2
Inbreeding:
decreases the frequency of heterozygotes and
increases the frequency homozygotes.
Inbreeding can lead to
“Inbreeding Depression”
• Most mutations are deleterious when
homozygous, but not when heterozygous
• Close relatives are likely to have inherited
the same deleterious mutations from their
ancestors, and carry them in the
heterozygous state.
• When close relatives mate, they produce
homozygotes for the mutation.
Inbreeding increases the chance that deleterious
homozygotes are produced
PP
PP
Pp
PP
Pp
Pp
PP
Pp
Pp
pp
Assortative Mating by Height in Humans
200
195
r = 0.49
Father's Height
190
185
180
175
170
165
160
155
135
140
145
150
155
160
165
Mother's Height
170
175
180
How do you know if a population is in H-W?
• Look at observed genotype frequencies in the
population…
• From these, calculate allele frequencies..
• From allele frequencies, calculate the genotype
frequencies predicted by H-W…
• Compare observed genotype frequencies to
predicted
Wild flower population
AA, n = 44
Aa, n = 46
aa, n = 10