Download popgen2c1 - eweb.furman.edu

Deviations from HWE
I. Mutation
II. Migration
III. Non-Random Mating
IV. Genetic Drift
A. Sampling Error
Deviations from HWE
I. Mutation
II. Migration
III. Non-Random Mating
IV. Genetic Drift
A. Sampling Error
1. samples from a variable population may not represent the
population exactly. Deviation from the populational distribution is called
sampling error. This is a general statistical principle, measured by the
'variance' or 'standard deviation'.
Variance among samples drawn from one population = (pq/N)
Deviations from HWE
I. Mutation
II. Migration
III. Non-Random Mating
IV. Genetic Drift
A. Sampling Error
1. samples from a variable population may not represent the
population exactly. Deviation from the populational distribution is called
sampling error. This is a general statistical principle, measured by the
'variance' or 'standard deviation'.
Variance among samples drawn from one population = (pq/N)
- small samples deviate more, just by chance, from the original
population than large samples.
- small samples differ more from one another than large samples.
Deviations from HWE
I. Mutation
II. Migration
III. Non-Random Mating
IV. Genetic Drift
A. Sampling Error
1. samples from a variable population may not represent the
population exactly. Deviation from the populational distribution is called
sampling error. This is a general statistical principle, measured by the
'variance' or 'standard deviation'.
Variance among samples drawn from one population = (pq/N)
- small samples deviate more, just by chance, from the original
population than large samples.
- small samples differ more from one another than large samples.
2. This principle relates to biological populations because the
zygotes produced as an F1 generation represent a sample of the gametes
produced by the parental population - not all parents mate.
Deviations from HWE
I. Mutation
II. Migration
III. Non-Random Mating
IV. Genetic Drift
A. Sampling Error
2. This principle relates to biological populations because the
zygotes produced as an F1 generation represent a sample of the gametes
produced by the parental population - not all parents mate.
- causes of lower effective population size:
- only a fraction of parents mate
- skewed sex ratio
- selection (differential reproduction)
- generations overlap (increasing inbreeding/coalescence)
- Fluctuation in population size (bottlenecks)
Deviations from HWE
I. Mutation
II. Migration
III. Non-Random Mating
IV. Genetic Drift
A. Sampling Error
B. Coalescence
B. Coalescence
- Not all reproducing entities will leave a descendant. Over time,
most lineages will go extinct
B. Coalescence
- Not all reproducing entities will leave a descendant. Over time,
most lineages will go extinct
- After an elapsed time, many of the entities will be descendants of
the same successful lineage that, just by chance, has left a descendant in
each generation. So, over time, average relatedness among existing entities
increases.
B. Coalescence
- Not all reproducing entities will leave a descendant. Over time,
most lineages will go extinct
- After an elapsed time, many of the entities will be descendants of
the same successful lineage that, just by chance, has left a descendant in
each generation. So, over time, average relatedness among existing entities
increases.
- Eventually, all the entities that are present will trace their ancestry back to a
single ancestor; their genealogies 'coalesce' on a single ancestor
B. Coalescence
- Not all reproducing entities will leave a descendant. Over time,
most lineages will go extinct
- After an elapsed time, many of the entities will be descendants of
the same successful lineage that, just by chance, has left a descendant in
each generation. So, over time, average relatedness among existing entities
increases.
- Eventually, all the entities that are present will trace their ancestry
back to a single ancestor; their genealogies 'coalesce' on a single ancestor.
- If the entity is a single gene or a haploid genome, this means that
eventually, all the entities in the populations are the same - 'similar by
descent'... If this is an allele, the allele is now FIXED f = 1.0.
***When random change occurs, it will ultimately lead to
fixation and inbreeding***
Deviations from HWE
I. Mutation
II. Migration
III. Non-Random Mating
IV. Genetic Drift
A. Sampling Error
B. Coalescence
C. Evolution by Drift
C. Evolution by Drift
- So, by chance, one allele in the population will become fixed. The
probability = frequency in the population (p). Even one NEW allele with
frequency 1/2N, has that chance of eventually becoming fixed...
C. Evolution by Drift
- So, by chance, one allele in the population will become fixed. The
probability = frequency in the population (p). Even one NEW allele with
frequency 1/2N, has that chance of eventually becoming fixed...
- How long will fixation take? It depends on the population size.
Essentially, how long will it take for one gene to replace all the others, just by
chance? For a single newly formed allele to take over = 4N generations
C. Evolution by Drift
- So, by chance, one allele in the population will become fixed. The
probability = frequency in the population (p). Even one NEW allele with
frequency 1/2N, has that chance of eventually becoming fixed...
- How long will fixation take? It depends on the population size.
Essentially, how long will it take for one gene to replace all the others, just by
chance? For a single newly formed allele to take over = 4N generations
***The time it takes for an allele to become fixed is
dependent on its initial frequency and the size of the
population***
IV. Genetic Drift
A. Sampling Error
B. Coalescence
C. Evolution by Drift
D. Effects on Variability
D. Effects on Variability
1. Heterozygosity is maximal when all alleles are at = frequency (if
two alleles, then p = q = 0.5).
D. Effects on Variability
1. Heterozygosity is maximal when all alleles are at = frequency (if
two alleles, then p = q = 0.5).
2. As genes drift from low to intermediate frequency (0.1  0.5),
variation (heterozygosity) increases. But, usually, rare alleles drift to 0 and
abundant alleles drift to 1, reducing heterozygosity and variation.
Ht = Ho [(1 - 1/2N)^t]
*** Drift, like inbreeding, leads to reduced heterozygosity
over time ***
E. Subdivided Populations
1. Wahlund Effect
Consider a population that is subdivided on two islands:
Island 1: p=0.3, q=0.7
Island 2: p=0.7, q=0.3
Subdivided populations will have lower heterozygosity than expected by
HWE when considering them as one fused population.
AA
Aa
aa
1
0.09
0.42
0.49
2
0.49
.042
0.09
mean
0.29
0.42
0.29
whole
0.25
0.5
0.25
E. Subdivided Populations
1. Subdivided populations will have lower heterozygosity than
expected by HWE when considering them as one fused population.
2. However, in a metapopulation consisting of separate populations
in which drift is fixing different alleles, drift increases the variance between
populations.
E. Subdivided Populations
1. Subdivided populations will have lower heterozygosity than
expected by HWE when considering them as one fused population.
2. However, in a metapopulation consisting of separate populations
which drift to fix different alleles, drift increases variance between
populations.
3. The rate of decline in heterozygosity at the metapop level depends
on the size of the demes (populations). Ht = Ho [(1 - 1/2N)^t], where:
Ho = initial heterozygosity,
N = mean deme size,
t = number of generations, and
Ht = Heterozygosity in generation t.
***Subdivision of populations will reduce heterozygosity
in the population as a function of the Wahlund Effect AND
increase variance due to drift. The rate depends on the
mean size of the demes***
IV. Genetic Drift
****F. Relationships Between Inbreeding and Drift****
IV. Genetic Drift
****F. Relationships Between Inbreeding and Drift****
1. In small populations, offspring have a higher probability of
receiving genes from a common source. For instance, if there is one gravid
female that founds a population, all individuals in the next generation will be
related by and average of 1/2 (full siblings).
IV. Genetic Drift
****F. Relationships Between Inbreeding and Drift****
1. In small populations, offspring have a higher probability of
receiving genes from a common source. For instance, if there is one gravid
female that founds a population, all individuals in the next generation will be
related by and average of 1/2 (full siblings).
2. Also, over time, coalescence is more rapid in a small population
than in a large population; so the population will sooner reach a point where
autozygosity is likely.
after t generations:
Ft = 1 - (1- (1/2N)^t)
Ht = (1- (1/2N)^t)Ho)
IV. Genetic Drift
****F. Relationships Between Inbreeding and Drift****
3. As we saw from the Wahlund Effect, a subdivided population will
decline in mean heterozygosity.
And we can measure this divergence as a proportional loss of
heterozygosity:
(2pq - H)/2pq
IV. Genetic Drift
****F. Relationships Between Inbreeding and Drift****
3. As we saw from the Wahlund Effect, a subdivided population will
decline in mean heterozygosity.
And we can measure this divergence as a proportional loss of
heterozygosity:
(2pq - H)/2pq
HEY!!! BUT THIS WAS THE FORMULA FOR INBREEDING, TOO!
F = (2pq - H)/2pq
This also equals = 1 - (1 - (1/2N)^t) with N = effective size of each deme.
IV. Genetic Drift
****F. Relationships Between Inbreeding and Drift****
1. In small populations, offspring have a higher probability of
receiving genes from a common source. For instance, if there is one gravid
female that founds a population, all individuals in the next generation will be
related by and average of 1/2 (full siblings).
2. Also, over time, coalescence is more rapid in a small population
than in a large population; so the population will sooner reach a point where
autozygosity is likely.
3. As we saw from the Wahlund Effect, a subdivided population will
decline in mean heterozygosity, and increase inbreeding.
*** SO! Drift causes a reduction in variability, an
increase in inbreeding, and a decrease in heterozygosity.
However, it INCREASES the variance BETWEEN
populations, reflected in increased divergence and a
decline in mean heterozygosity ***
IV. Genetic Drift
****F. Relationships Between Inbreeding and Drift****
SO SO SO!!! DRIFT CAUSES:
inbreeding
divergence
loss of heterozygosity in
metapopulation
Deviations from HWE
I. Mutation
II. Migration
III. Non-Random Mating
IV. Genetic Drift
V. The Neutral Theory
V. The Neutral Theory
A. Variation
1. Historically, all phenotypic variation was interpreted as adaptive.
- many studies confirmed that under one environmental
condition or another, there was a difference in fitness among variations.
- Mayr (1963) "it is altogether unlikely that two genes would
have identical selective value under all conditions under which they may
coexist in a population. Cases of neutral polymorphism do not exist."
V. The Neutral Theory
A. Variation
1. Historically, all phenotypic variation was interpreted as adaptive.
- many studies confirmed that under one environmental
condition or another, there was a difference in fitness among variations.
- Mayr (1963) "it is altogether unlikely that two genes would
have identical selective value under all conditions under which they may
coexist in a population. Cases of neutral polymorphism do not exist."
2. In the 1960's – electrophoresis revealed LOTS of variability.
- variability at the gene or protein level that did not
necessarily correlate with morphological variation.
- These are silent mutations in DNA, or even neutral
substitution mutations. This variation results in heterozygosity.
V. The Neutral Theory
A. Variation
1. Historically, all phenotypic variation was interpreted as adaptive.
2. In the 1960's – electrophoresis revealed LOTS of variability.
- variability at the gene or protein level that did not
necessarily correlate with morphological variation.
- These are silent mutations in DNA, or even neutral
substitution mutations. This variation results in heterozygosity.
3. Most populations showed mean heterozygosities across ALL loci
of about 10%. - And, about 20-30% of all loci are polymorphic (have at least 2
alleles with frequencies over 1%). Drosophila has 10,000 loci, so 3000 are
polymorphic. At these polymorphic loci, H = .33 - Conclusion - lots of
variation at a genetic level... is this also solely maintained by selection?
V. The Neutral Theory
A. Variation
B. Genetic Load
V. The Neutral Theory
A. Variation
B. Genetic Load
1. "HARD" Selection can 'cost' a population individuals:
V. The Neutral Theory
A. Variation
B. Genetic Load
1. "HARD" Selection can 'cost' a population individuals:
- those that die as a consequence of lower fitness
V. The Neutral Theory
A. Variation
B. Genetic Load
1. "HARD" Selection can 'cost' a population individuals:
- those that die as a consequence of lower fitness.
- the "breeding population" is smaller than the initial population.
V. The Neutral Theory
A. Variation
B. Genetic Load
1. "HARD" Selection can 'cost' a population individuals:
- those that die as a consequence of lower fitness.
- the "breeding population" is smaller than the initial population.
- Reproductive output must compensate for this loss of individuals if
the population is to persist in the face of this selective pressure.
V. The Neutral Theory
A. Variation
B. Genetic Load
1. "HARD" Selection can 'cost' a population individuals:
- those that die as a consequence of differential fitness values.
- the "breeding population" is smaller than the initial population.
- Reproductive output must compensate for this loss of individuals
- The stronger the "hard" selection, the more individuals are lost and
the higher the compensatory reproductive effort must be.
V. The Neutral Theory
A. Variation
B. Genetic Load
1. "HARD" Selection can 'cost' a population individuals:
- those that die as a consequence of differential fitness values.
- the "breeding population" is smaller than the initial population.
- Reproductive output must compensate for this loss of individuals
- The stronger the "hard" selection, the more individuals are lost and
the higher the compensatory reproductive effort must be.
- The 'cost' of replacing an allele with a new, adaptive allele =
"Genetic Load" (L)
L = (optimal fitness - mean fitness)/optimal fitness.
Essentially, this is a measure of the proportion of individuals that will die as a
consequence of this "hard" selection. The lower the mean fitness, the further
the population is from the optimum, and the more deaths there will be.
B. Genetic Load
1. "HARD" Selection can 'cost' a population individuals:
2. Why is this a problem?
B. Genetic Load
1. "HARD" Selection can 'cost' a population individuals:
2. Why is this a problem?
- If variation is maintained by selection, we are probably talking
about "heterosis" - selection for the heterozygote where the heterozygote
has the highest fitness (and both alleles are maintained).
B. Genetic Load
1. "HARD" Selection can 'cost' a population individuals:
2. Why is this a problem?
- If variation is maintained by selection, we are probably talking
about "heterosis" - selection for the heterozygote where the heterozygote
has the highest fitness (and both alleles are maintained).
- The problem is that load can be high in this situation, because lots
of homozygotes are produced each generation, just to die by selection.
B. Genetic Load
1. "HARD" Selection can 'cost' a population individuals:
2. Why is this a problem?
- If variation is maintained by selection, we are probably talking
about "heterosis" - selection for the heterozygote where the heterozygote
has the highest fitness (and both alleles are maintained).
- The problem is that load can be high in this situation, because lots
of homozygotes are produced each generation, just to die by selection.
3. Let's consider even a "best case" scenario:
B. Genetic Load
1. "HARD" Selection can 'cost' a population individuals:
2. Why is this a problem?
- If variation is maintained by selection, we are probably talking
about "heterosis" - selection for the heterozygote where the heterozygote
has the highest fitness (and both alleles are maintained).
- The problem is that load can be high in this situation, because lots
of homozygotes are produced each generation, just to die by selection.
3. Let's consider even a "best case" scenario:
- mean fitness = 1 - H((s+t)/2)
B. Genetic Load
1. "HARD" Selection can 'cost' a population individuals:
2. Why is this a problem?
- If variation is maintained by selection, we are probably talking
about "heterosis" - selection for the heterozygote where the heterozygote
has the highest fitness (and both alleles are maintained).
- The problem is that load can be high in this situation, because lots
of homozygotes are produced each generation, just to die by selection.
3. Let's consider even a "best case" scenario:
- mean fitness = 1 - H((s+t)/2)
- If s and t = .1 (very weak), and H = .33 (average for Drosophila),
then the mean fitness = 0.967.
B. Genetic Load
1. "HARD" Selection can 'cost' a population individuals:
2. Why is this a problem?
- If variation is maintained by selection, we are probably talking
about "heterosis" - selection for the heterozygote where the heterozygote
has the highest fitness (and both alleles are maintained).
- The problem is that load can be high in this situation, because lots
of homozygotes are produced each generation, just to die by selection.
3. Let's consider even a "best case" scenario:
- mean fitness = 1 - H((s+t)/2)
- If s and t = .1 (very weak), and H = .33 (average for Drosophila),
then the mean fitness = 0.967.
- Not bad; not much death due to selection at this one locus...
B. Genetic Load
1. "HARD" Selection can 'cost' a population individuals:
2. Why is this a problem?
- If variation is maintained by selection, we are probably talking
about "heterosis" - selection for the heterozygote where the heterozygote
has the highest fitness (and both alleles are maintained).
- The problem is that load can be high in this situation, because lots
of homozygotes are produced each generation, just to die by selection.
3. Let's consider even a "best case" scenario:
- mean fitness = 1 - H((s+t)/2)
- If s and t = .1 (very weak), and H = .33 (average for Drosophila),
then the mean fitness = 0.967.
- Not bad; not much death due to selection at this one locus...
- HOWEVER, there are 3000 polymorphic loci across the genome!!! So, if
selection is maintaining this variation, then mean fitness across the genome
= (0.967)^3000!
B. Genetic Load
1. "HARD" Selection can 'cost' a population individuals:
2. Why is this a problem?
- If variation is maintained by selection, we are probably talking
about "heterosis" - selection for the heterozygote where the heterozygote
has the highest fitness (and both alleles are maintained).
- The problem is that load can be high in this situation, because lots
of homozygotes are produced each generation, just to die by selection.
3. Let's consider even a "best case" scenario:
- mean fitness = 1 - H((s+t)/2)
- If s and t = .1 (very weak), and H = .33 (average for Drosophila),
then the mean fitness = 0.967.
- Not bad; not much death due to selection at this one locus...
HOWEVER, there are 3000 polymorphic loci across the genome!!! So, if
selection is maintaining this variation, then mean fitness across the genome
= (0.967)^3000!
- This is ridiculously LOW (.19 x 10^-44) relative to the best case
genome that is heterozygous at every one of the 3000 loci. So, some
individuals die because they are homozygous (and less fit) at A, others die
because they are homozygous (and less fit) at B, other die because they are
homozygous (and less fit) at C, and so forth... ALMOST EVERYBODY DIES!!!!
B. Genetic Load
1. "HARD" Selection can 'cost' a population individuals:
2. Why is this a problem?
- If variation is maintained by selection, we are probably talking
about "heterosis" - selection for the heterozygote where the heterozygote
has the highest fitness (and both alleles are maintained).
- The problem is that load can be high in this situation, because lots
of homozygotes are produced each generation, just to die by selection.
3. Let's consider even a "best case" scenario:
- mean fitness = 1 - H((s+t)/2)
- If s and t = .1 (very weak), and H = .33 (average for Drosophila,
above), then the mean fitness = 0.967.
- across the genome, there is a huge genetic load
In this case, the load is SO GREAT across the genome that almost NOBODY
lives to reproduce. And those that do can not possibly produce enough
offspring to compensate for this amount of death.
So, hard selection can not be SOLELY responsible for the
variation we observe... a population could not sustain
itself under this amount of genetic load...
B. Genetic Load
1. "HARD" Selection can 'cost' a population individuals:
2. Why is this a problem?
3. Scenario
4. Solutions
a. Selectionists
- Not all selection is "hard", imposing additional deaths above
background mortality.
B. Genetic Load
1. "HARD" Selection can 'cost' a population individuals:
2. Why is this a problem?
3. Scenario
4. Solutions
a. Selectionists
- Not all selection is "hard", imposing additional deaths above
background mortality.
- There is also "soft" selection, in which the death due to selection
occurs as a component of background mortality, not in addition to it.
B. Genetic Load
1. "HARD" Selection can 'cost' a population individuals:
2. Why is this a problem?
3. Scenario
4. Solutions
a. Selectionists
- Not all selection is "hard", imposing additional deaths above
background mortality.
- There is also "soft" selection, in which the death due to selection
occurs as a component of background mortality, not in addition to it.
- For instance, consider territoriality or competition for a resource.
Suppose there is only enough food or space to support 50 individuals, but 60
offspring are produced each generation. Well, each generation there are 10
deaths and there are 50 "winners".
B. Genetic Load
1. "HARD" Selection can 'cost' a population individuals:
2. Why is this a problem?
3. Scenario
4. Solutions
a. Selectionists
- Suppose we have a population of aa homozygotes initially. All the
territories are occupied by aa individuals and 10 individuals die.
B. Genetic Load
1. "HARD" Selection can 'cost' a population individuals:
2. Why is this a problem?
3. Scenario
4. Solutions
a. Selectionists
- Suppose we have a population of aa homozygotes initially. All the
territories are occupied by aa individuals and 10 individuals die.
- Well, If an 'A' allele is produce by mutation and heterozygotes have
the highest relative fitness (probability of acquiring a territory), then the allele
"A" increase in frequency to equilibrium....
B. Genetic Load
1. "HARD" Selection can 'cost' a population individuals:
2. Why is this a problem?
3. Scenario
4. Solutions
a. Selectionists
- Suppose we have a population of aa homozygotes initially. All the
territories are occupied by aa individuals and 10 individuals die.
- Well, If an 'A' allele is produce by mutation and heterozygotes have
the highest relative fitness (probability of acquiring a territory), then the allele
"A" increase in frequency to equilibrium....
- Selection occurs, BUT THERE ARE STILL ONLY 10 DEATHS PER
GENERATION.
B. Genetic Load
1. "HARD" Selection can 'cost' a population individuals:
2. Why is this a problem?
3. Scenario
4. Solutions
a. Selectionists
- Suppose we have a population of aa homozygotes initially. All the
territories are occupied by aa individuals and 10 individuals die.
- Well, If an 'A' allele is produce by mutation and heterozygotes have
the highest relative fitness (probability of acquiring a territory), then the allele
"A" increase in frequency to equilibrium....
- Selection occurs, BUT THERE ARE STILL ONLY 10 DEATHS PER
GENERATION.
- In this case there is NO genetic load, as selection is NOT causing
ADDITIONAL mortality. It is just changing the probability of who dies.
B. Genetic Load
1. "HARD" Selection can 'cost' a population individuals:
2. Why is this a problem?
3. Scenario
4. Solutions
a. Selectionists
- Suppose we have a population of aa homozygotes initially. All the
territories are occupied by aa individuals and 10 individuals die.
- Well, If an 'A' allele is produce by mutation and heterozygotes have
the highest relative fitness (probability of acquiring a territory), then the allele
"A" increase in frequency to equilibrium....
- Selection occurs, BUT THERE ARE STILL ONLY 10 DEATHS PER
GENERATION.
- In this case there is NO genetic load, as selection is NOT causing
ADDITIONAL mortality. It is just changing the probability of who dies.
- So, selection across lots of loci does not NECCESSARILY lead to
impossible loads.... as long as it is SOFT SELECTION
B. Genetic Load
1. "HARD" Selection can 'cost' a population individuals:
2. Why is this a problem?
3. Scenario
4. Solutions
a. Selectionists
b. Neutralists