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Lectures for Week 9
Founder Effects, Inbreeding
and Hybrid Zones
Andrea Hatlen
Lecture Outline
1)  The Amish
2)  Inbreeding and Identity by Descent
3)  Allele Frequency Clines and the Formation of
Hybrid Zones
4)  Mini Revision Session
Lecture Outline
1)  The Amish
2)  Inbreeding and Identity by Descent
3)  Allele Frequency Clines and the Formation of
Hybrid Zones
4)  Mini Revision Session
The Amish

•  The Amish are an Anabaptist Christian denomination in the
United States and Ontario, Canada
•  Known for their plain dress and limited use of modern devices
such as automobiles and electricity
•  Most speak a German dialect known as Pennsylvania Dutch
The Amish
There are approximately 12,000 Amish in Lancaster county. They are
descended from about 400 founders originating from the Swiss German
border with very little recruitment from other populations. The few
converts are well documented.
The Amish
Over the generations the number of descendants of these few founders
has grown and the population has therefore expanded (although more
people leave the community than join).

•  excellent records

•  large family size
•  restricted population 
highly valuable for
genetic studies

1,225,366 names!

386,130 families!
The Genetics of Amish Populations
Alan	
  R	
  Shuldiner	
  M.D.
	
  

"Only about 200 Amish founders came from
Europe to the United States in the early
1700s," Shuldiner notes. "The Amish
population has grown to 30,000 in the
localized area of Lancaster County. While
diabetes does not occur more frequently in
the Amish than in other population groups,
the Amish are a closed population with a
fixed gene pool, have very large families, and
essentially complete genealogies dating back
14 generations. It's quite a unique situation to
be able to study a specific group of people
who have particularly good characteristics for
genetic research."
The Genetics of Amish Populations
The allele frequencies in the Amish population are atypical of the
communities from which they are descended in Europe because of… 
1. 

Founder events: the first
400 (or so) founders will
have, by chance, had an
atypical collection of genes

2. 

Further drift: the small
population size subsequent
to foundation will have lead
to further genetic drift.
The Genetics of Amish Populations
Six of the founders names are responsible for 3/4 of those seen today and a full
1/4 are called Stoltzfus!

 names are unlikely to
As
confer a selective advantage,
this change in the frequency
of names is most easily
explained as a random or
stochastic change. (Be
careful: they might be
associated with genes that
confer a selective advantage).
The same change would be predicted for Y chromosomes which are also
transmitted down the paternal line, and a similar change for mitochondrial DNA
which is passed down the maternal line.
The Genetics of Amish Populations
•  Wilma Bias (John Hopkins University) looked at 30-35 genetic systems
giving evidence about 100-150 loci from one blood sample. The loci
range from the well known blood groups to soluble enzymes.
•  It is important to remember that, by
chance some loci will have larger changes
in allele frequency, some smaller –
although those on the Y chromosome
and mitochondria would be expected to
show greater changes.
•  Like the names, some loci show dramatic
frequency changes since foundation
15%-25% in the case of Rh- blood.
The Genetics of Amish Populations
It is particularly important for expectant mothers to know their blood's Rh factor.
Occasionally, a baby will inherit an Rh positive blood type from its father while the
mother has a Rh negative blood type. 


The baby's life could be in danger if the Rh negative mother's immune system attacks
the baby's Rh positive blood. To prevent this, the mother is injected with anti-RhD
IgG immunoglobulin so that the Rh positive erythrocytes from the baby’s blood in
her system are destroyed before her immune system finds them.

Rh –ve is almost
certainly selected
against
The Genetics of Amish Populations
Questions

Q1) Why would we expect to see greater
genetic drift on the Y chromosome compared
with other parts of the genome?
A)  Smaller effective
population size
(Q1.2 How much smaller?)


Q2) How can Rh –ve have reached high
frequency when it is selected against?
A)  Drift acts on all loci,

Even those subject to selection
The Genetics of Amish Populations
Ellis-van Creveld syndrome (know colloquially as “Six fingered dwarfism”) is
a recessive trait: genealogical studies show that it is only expressed when an
individual carries two copies of the allele.

Extremely rare in the population at
large, however…

…estimates are that 1/7 of the
present day Amish population carry
the gene
Perhaps only 1 of the 400 founders carried the allele in the ancestral
population (in a single copy, hence the allele frequency would have been
1/800). The allele may have subsequently drifted to high frequency.
The Genetics of Amish Populations
This syndrome was described by Ellis and van Creveld in 1940. Very few
cases have been reported in the literature.
A follow up study was carried out by
McKusic et al. in 1964, which focussed on
the Amish population. Almost as many
affected individuals were found in this one
kindred as had been reported in all the
medical literature up to that time

McKusic et al. estimated that around 5 in
1000 Amish births resulted in EvC. From
this they estimated the frequency of
heterozygous carriers at around 13%.
The Genetics of Amish Populations
How did they arrive at these numbers?

First, lets remember Hardy-Weinberg 


Under random mating we expect to see Hardy-Weinberg
genotype frequencies:


p = allele frequency of one allele, q = allele frequency of the other



p2

2pq

q2



p2

2p(1-p)

(1-p)2
The Genetics of Amish Populations
How did they arrive at these numbers?

Let us call the EvC allele the ‘A’ allele and any non-EvC allele
the ‘B’ allele. We will use the symbol gAA to refer to the
homozygous (affected) genotype frequency. This genotype
frequency was estimated at gAA=0.005 from observed
individuals and historical records


Under Hardy Weinberg proportions we would expect to see p2
homozygotes of this sort, where p is the allele frequency of
the EvC allele. Thus, p2=0.005 and from this we can estimate
that p≈0.07


Again, assuming Hardy Weinberg proportions we would expect
the genotype frequency of heterozygotes to be gAB=2p(1-p),
which works out at around gAB≈0.13
The Genetics of Amish Populations
Notice that the proportion of carriers (gAB≈0.13) is much
larger than the proportion of affected individuals
(gAA=0.005 ).

Why might we generally expect to see this pattern in
recessive diseases?
The Genetics of Amish Populations
Brief summary…


•  The Amish are a text-book example of genetic drift.
•  A number of disadvantageous alleles have drifted to high frequency, in
spite of the action of selection against them. This reminds us that genetic
drift affects all loci, not just those that are evolving neutrally.
•  Detailed records combined with a polite culture open to conversation
with scientists means that we can investigate genotype and allele
frequencies for certain conditions that would otherwise be hidden from
view.
Lecture Outline
1)  The Amish
2)  Inbreeding and Identity by Descent
3)  Allele Frequency Clines and the Formation of
Hybrid Zones
4)  Mini Revision Session
Inbreeding and Identity by Descent
Genetic drift causes allele frequencies to change over time as a result of
sampling from a finite population. However, genotype frequencies are
expected to remain in Hardy Weinberg proportions every generation.

What can cause a deviation from these proportions is inbreeding: defined as
non-random mating of relatives leading to the increased probability of
identity by descent.

The Amish actually avoid cousin matings (and closer), so the population is
actually less inbred that you would expect from a random mating
population.
Inbreeding and Identity by Descent
Global distribution of marriages between couples related as second
cousins or closer
Inbreeding and Identity by Descent
The probability of identity by descent due to relatedness between parents
can be measured by the parameter f.


In simple terms, f is the chance that the two gene copies in a diploid
individual are descended from the same copy in an earlier generation.

The greatest possible amount of
inbreeding occurs in selffertilisation. 

In this case the two gene copies in
the offspring have a probability
f=1/2 of originating from the same
copy in the parent.
Inbreeding and Identity by Descent
Consider an infinitely large population of selfing diploids. Assume that every
individual in the starting population is a heterozygote.

Genotype frequencies change over generations until eventually we would be
left with only homozygotes. Notice that the allele frequencies have not
changed from the initial frequency of p=1/2.
Inbreeding and Identity by Descent
In more complex forms of inbreeding the coefficient f can still be worked out
by looking at pedigrees.

In this example the probability of identity by descent comes out at f=1/8.
Inbreeding and Identity by Descent
Word of caution: The word inbreeding is a bit “fuzzy”
Some people include genetic drift as a sort of inbreeding, others do not.
Better to contrast genetic drift against consanguinity.

Drift and consanguinity are similar in some ways, and complete opposites in
others!
•  Both occur due to a build up of shared ancestry within a population.
•  Drift occurs as a result of finite population size, whereas consanguinity
could technically occur even in an infinitely large population.
•  Drift results in a change in allele frequencies, but genotype frequencies
remain in HWE. Consanguinity results in a change in genotype
frequencies, but does not alter allele frequencies.


These two processes have different implications
for eg. disease
Inbreeding and Identity by Descent

Bottleneck
Those deleterious recessive alleles that
drift up produce increased incidence of
the disorder. This is then reduced by
selection over subsequent generations.

Consanguinity
The incidence of each disorder is
increased, but selection reduces the
incidence rapidly.
Questions?
Lecture Outline
1)  The Amish
2)  Inbreeding and Identity by Descent
3)  Allele Frequency Clines and the Formation of
Hybrid Zones
4)  Mini Revision Session
Allele Frequency Clines
•  Biston betularia (the Peppered
Moth) exists in melanic and
wild-type phenotypes

•  As the melanic (A) allele is
dominant: both AA and AB
individuals express the black
colouration – hence wAA = wAB
•  Industrial melanism
hypothesis: selection in favour
of the melanic form post
industrial revolution
Allele Frequency Clines
Selection in favour of a dominant allele…
Allele Frequency Clines
Some evidence to support this: Mark recapture experiments found
that the fitness of the melanic morph is higher in areas where they
are prevalent.
Allele Frequency Clines
•  The industrial revolution did not lead to
the blackening of all trees. The Delamere
Forest near Manchester and Liverpool is
relatively unaffected but the peppered
moths are predominantly melanic there.
•  On the other hand the Gonodontis bidentata
(Scalloped Hazel), which are also melanic
right in the heart of the major industrial
centres, are predominantly non-melanic in
Delamere forest.
•  The difference between the two species
may be explained by their dispersal rates.
HOW?
Allele Frequency Clines
Lecture Outline
1)  The Amish
2)  Inbreeding and Identity by Descent
3)  Allele Frequency Clines and the Formation of
Hybrid Zones
4)  Mini Revision Session
Hybrid Zones
Meiotic combinations
•  Fused:Fused

•  Unfused : Unfused


•  Hybrid

?
Hybrid Zones

The existence of this frequency cline can be explained by the reduced fitness of
heterozygotes.
HOW?
Hybrid Zones
Hybrid Zones
Hybrid Zones

Gene flow never gets far into the other population due to the
reduced fitness of heterozygotes
Questions?
A Complete(ish) Picture
We can start to build up a picture of what
evolution really looks like…
•  First and foremost there is genetic drift
•  There may also be some selection
acting
•  Gene flow homogenises allele
frequencies between populations
•  Mutation introduces new
genetic variation into
populations that may have lost it
due to drift or selection
•  There are still many processes
missing from this picture!
Lecture Outline
1)  The Amish
2)  Inbreeding and Identity by Descent
3)  Allele Frequency Clines and the Formation of
Hybrid Zones
4)  Mini Revision Session
Inbreeding and Identity by Descent

Bottleneck
Those deleterious recessive alleles that
drift up produce increased incidence of
the disorder. This is then reduced by
selection over subsequent generations.

Consanguinity
The incidence of each disorder is
increased, but selection reduces the
incidence rapidly.
Mini Revision Session

What is

the probability of identity by descent (f) of
an offspring of full sib parents (parents are brother
and sister with the same mother and father)?
Mini Revision Session
First things first; we need to draw a pedigree
of the offspring of full sib parents.
One thing that was confusing people is that
the question did not specify the genotypes of
either the parents or the offspring.
Remember that we are trying to work out the
probability of identity by descent – in
other words, the probability that the two
genes in the offspring are descended from the
same gene copy in an earlier generation. We
do not need to know any genotypes to work
this out! To make this point clear, I have
drawn genes in the grandparents as dots,
rather than letters.
Mini Revision Session
1.  We know that one gene copy in the
offspring came from the father, and one
from the mother. The question is; where
did each of these come from in the
grandparental generation?
Mini Revision Session
1.  We know that one gene copy in the
offspring came from the father, and one
from the mother. The question is; where
did each of these come from in the
grandparental generation?
2.  Looking just at the paternal side, there is
an equal chance that this gene came from
any of the 4 gene copies in the
grandparents. Thus, we can say that the
probability of each of these events is ¼.
Mini Revision Session
1.  We know that one gene copy in the
offspring came from the father, and one
from the mother. The question is; where
did each of these come from in the
grandparental generation?
2.  Looking just at the paternal side, there is
an equal chance that this gene came from
any of the 4 gene copies in the
grandparents. Thus, we can say that the
probability of each of these events is ¼.
3.  The same is true of the maternal side. The
probability of this gene descending from
each of the genes in the grandparents is
¼.
Mini Revision Session
4.  Combining this knowledge, we can work
out the probability that both offspring
genes are descended from the same copy.
Looking at the first grandparental gene (ie.
the first black dot), we know that the
probability of both the maternal and
paternal genes coming from here is
¼ × ¼ = 1/16.
Mini Revision Session
4.  Combining this knowledge, we can work
out the probability that both offspring
genes are descended from the same copy.
Looking at the first grandparental gene (ie.
the first black dot), we know that the
probability of both the maternal and
paternal genes coming from here is
¼ × ¼ = 1/16.
5.  The same is true of the second
grandparental gene (second black dot). In
fact, this is true of any of the 4
grandparental genes.
Mini Revision Session
6.  In summary; there are 4 ways that the
offspring genes could be descended from
the same gene copy. Each of these has
probability 1/16. Thus, the overall
probability of identity by descent is…
1/16 + 1/16 + 1/16 + 1/16 = 4/16

Or

f = 1/4
Mini Revision Session

In

a random mating population, there is a disease
that is encoded by a dominant allele. About 50 out
of 1000 individuals have this disease. Calculate the
genotype frequencies for AA, Aa, and aa.



p2

2pq

q2



p2

2p(1-p)

(1-p)2
Mini Revision Session
+


gAA + gAa = 50/1000 = 0.05

gaa = (1 - 0.05) = 0.95
p2 = 0.95
p ≈ 0.974679

gAa = 2p(1-p) ≈ 0.04936

0.05
gAA = (1-p)2 ≈ 0.00064

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Evolution lectures WK9

  • 1. Lectures for Week 9 Founder Effects, Inbreeding and Hybrid Zones Andrea Hatlen
  • 2. Lecture Outline 1)  The Amish 2)  Inbreeding and Identity by Descent 3)  Allele Frequency Clines and the Formation of Hybrid Zones 4)  Mini Revision Session
  • 3. Lecture Outline 1)  The Amish 2)  Inbreeding and Identity by Descent 3)  Allele Frequency Clines and the Formation of Hybrid Zones 4)  Mini Revision Session
  • 4. The Amish •  The Amish are an Anabaptist Christian denomination in the United States and Ontario, Canada •  Known for their plain dress and limited use of modern devices such as automobiles and electricity •  Most speak a German dialect known as Pennsylvania Dutch
  • 5. The Amish There are approximately 12,000 Amish in Lancaster county. They are descended from about 400 founders originating from the Swiss German border with very little recruitment from other populations. The few converts are well documented.
  • 6. The Amish Over the generations the number of descendants of these few founders has grown and the population has therefore expanded (although more people leave the community than join). •  excellent records •  large family size •  restricted population highly valuable for genetic studies 1,225,366 names! 386,130 families!
  • 7. The Genetics of Amish Populations Alan  R  Shuldiner  M.D.   "Only about 200 Amish founders came from Europe to the United States in the early 1700s," Shuldiner notes. "The Amish population has grown to 30,000 in the localized area of Lancaster County. While diabetes does not occur more frequently in the Amish than in other population groups, the Amish are a closed population with a fixed gene pool, have very large families, and essentially complete genealogies dating back 14 generations. It's quite a unique situation to be able to study a specific group of people who have particularly good characteristics for genetic research."
  • 8. The Genetics of Amish Populations The allele frequencies in the Amish population are atypical of the communities from which they are descended in Europe because of… 1.  Founder events: the first 400 (or so) founders will have, by chance, had an atypical collection of genes 2.  Further drift: the small population size subsequent to foundation will have lead to further genetic drift.
  • 9. The Genetics of Amish Populations Six of the founders names are responsible for 3/4 of those seen today and a full 1/4 are called Stoltzfus! names are unlikely to As confer a selective advantage, this change in the frequency of names is most easily explained as a random or stochastic change. (Be careful: they might be associated with genes that confer a selective advantage). The same change would be predicted for Y chromosomes which are also transmitted down the paternal line, and a similar change for mitochondrial DNA which is passed down the maternal line.
  • 10. The Genetics of Amish Populations •  Wilma Bias (John Hopkins University) looked at 30-35 genetic systems giving evidence about 100-150 loci from one blood sample. The loci range from the well known blood groups to soluble enzymes. •  It is important to remember that, by chance some loci will have larger changes in allele frequency, some smaller – although those on the Y chromosome and mitochondria would be expected to show greater changes. •  Like the names, some loci show dramatic frequency changes since foundation 15%-25% in the case of Rh- blood.
  • 11. The Genetics of Amish Populations It is particularly important for expectant mothers to know their blood's Rh factor. Occasionally, a baby will inherit an Rh positive blood type from its father while the mother has a Rh negative blood type. The baby's life could be in danger if the Rh negative mother's immune system attacks the baby's Rh positive blood. To prevent this, the mother is injected with anti-RhD IgG immunoglobulin so that the Rh positive erythrocytes from the baby’s blood in her system are destroyed before her immune system finds them. Rh –ve is almost certainly selected against
  • 12. The Genetics of Amish Populations Questions Q1) Why would we expect to see greater genetic drift on the Y chromosome compared with other parts of the genome? A)  Smaller effective population size (Q1.2 How much smaller?) Q2) How can Rh –ve have reached high frequency when it is selected against? A)  Drift acts on all loci, Even those subject to selection
  • 13. The Genetics of Amish Populations Ellis-van Creveld syndrome (know colloquially as “Six fingered dwarfism”) is a recessive trait: genealogical studies show that it is only expressed when an individual carries two copies of the allele. Extremely rare in the population at large, however… …estimates are that 1/7 of the present day Amish population carry the gene Perhaps only 1 of the 400 founders carried the allele in the ancestral population (in a single copy, hence the allele frequency would have been 1/800). The allele may have subsequently drifted to high frequency.
  • 14. The Genetics of Amish Populations This syndrome was described by Ellis and van Creveld in 1940. Very few cases have been reported in the literature. A follow up study was carried out by McKusic et al. in 1964, which focussed on the Amish population. Almost as many affected individuals were found in this one kindred as had been reported in all the medical literature up to that time McKusic et al. estimated that around 5 in 1000 Amish births resulted in EvC. From this they estimated the frequency of heterozygous carriers at around 13%.
  • 15. The Genetics of Amish Populations How did they arrive at these numbers? First, lets remember Hardy-Weinberg Under random mating we expect to see Hardy-Weinberg genotype frequencies: p = allele frequency of one allele, q = allele frequency of the other p2 2pq q2 p2 2p(1-p) (1-p)2
  • 16. The Genetics of Amish Populations How did they arrive at these numbers? Let us call the EvC allele the ‘A’ allele and any non-EvC allele the ‘B’ allele. We will use the symbol gAA to refer to the homozygous (affected) genotype frequency. This genotype frequency was estimated at gAA=0.005 from observed individuals and historical records Under Hardy Weinberg proportions we would expect to see p2 homozygotes of this sort, where p is the allele frequency of the EvC allele. Thus, p2=0.005 and from this we can estimate that p≈0.07 Again, assuming Hardy Weinberg proportions we would expect the genotype frequency of heterozygotes to be gAB=2p(1-p), which works out at around gAB≈0.13
  • 17. The Genetics of Amish Populations Notice that the proportion of carriers (gAB≈0.13) is much larger than the proportion of affected individuals (gAA=0.005 ). Why might we generally expect to see this pattern in recessive diseases?
  • 18. The Genetics of Amish Populations Brief summary… •  The Amish are a text-book example of genetic drift. •  A number of disadvantageous alleles have drifted to high frequency, in spite of the action of selection against them. This reminds us that genetic drift affects all loci, not just those that are evolving neutrally. •  Detailed records combined with a polite culture open to conversation with scientists means that we can investigate genotype and allele frequencies for certain conditions that would otherwise be hidden from view.
  • 19. Lecture Outline 1)  The Amish 2)  Inbreeding and Identity by Descent 3)  Allele Frequency Clines and the Formation of Hybrid Zones 4)  Mini Revision Session
  • 20. Inbreeding and Identity by Descent Genetic drift causes allele frequencies to change over time as a result of sampling from a finite population. However, genotype frequencies are expected to remain in Hardy Weinberg proportions every generation. What can cause a deviation from these proportions is inbreeding: defined as non-random mating of relatives leading to the increased probability of identity by descent. The Amish actually avoid cousin matings (and closer), so the population is actually less inbred that you would expect from a random mating population.
  • 21. Inbreeding and Identity by Descent Global distribution of marriages between couples related as second cousins or closer
  • 22. Inbreeding and Identity by Descent The probability of identity by descent due to relatedness between parents can be measured by the parameter f. In simple terms, f is the chance that the two gene copies in a diploid individual are descended from the same copy in an earlier generation. The greatest possible amount of inbreeding occurs in selffertilisation. In this case the two gene copies in the offspring have a probability f=1/2 of originating from the same copy in the parent.
  • 23. Inbreeding and Identity by Descent Consider an infinitely large population of selfing diploids. Assume that every individual in the starting population is a heterozygote. Genotype frequencies change over generations until eventually we would be left with only homozygotes. Notice that the allele frequencies have not changed from the initial frequency of p=1/2.
  • 24. Inbreeding and Identity by Descent In more complex forms of inbreeding the coefficient f can still be worked out by looking at pedigrees. In this example the probability of identity by descent comes out at f=1/8.
  • 25. Inbreeding and Identity by Descent Word of caution: The word inbreeding is a bit “fuzzy” Some people include genetic drift as a sort of inbreeding, others do not. Better to contrast genetic drift against consanguinity. Drift and consanguinity are similar in some ways, and complete opposites in others! •  Both occur due to a build up of shared ancestry within a population. •  Drift occurs as a result of finite population size, whereas consanguinity could technically occur even in an infinitely large population. •  Drift results in a change in allele frequencies, but genotype frequencies remain in HWE. Consanguinity results in a change in genotype frequencies, but does not alter allele frequencies. These two processes have different implications for eg. disease
  • 26. Inbreeding and Identity by Descent Bottleneck Those deleterious recessive alleles that drift up produce increased incidence of the disorder. This is then reduced by selection over subsequent generations. Consanguinity The incidence of each disorder is increased, but selection reduces the incidence rapidly.
  • 28. Lecture Outline 1)  The Amish 2)  Inbreeding and Identity by Descent 3)  Allele Frequency Clines and the Formation of Hybrid Zones 4)  Mini Revision Session
  • 29. Allele Frequency Clines •  Biston betularia (the Peppered Moth) exists in melanic and wild-type phenotypes •  As the melanic (A) allele is dominant: both AA and AB individuals express the black colouration – hence wAA = wAB •  Industrial melanism hypothesis: selection in favour of the melanic form post industrial revolution
  • 30. Allele Frequency Clines Selection in favour of a dominant allele…
  • 31. Allele Frequency Clines Some evidence to support this: Mark recapture experiments found that the fitness of the melanic morph is higher in areas where they are prevalent.
  • 32. Allele Frequency Clines •  The industrial revolution did not lead to the blackening of all trees. The Delamere Forest near Manchester and Liverpool is relatively unaffected but the peppered moths are predominantly melanic there. •  On the other hand the Gonodontis bidentata (Scalloped Hazel), which are also melanic right in the heart of the major industrial centres, are predominantly non-melanic in Delamere forest. •  The difference between the two species may be explained by their dispersal rates. HOW?
  • 34. Lecture Outline 1)  The Amish 2)  Inbreeding and Identity by Descent 3)  Allele Frequency Clines and the Formation of Hybrid Zones 4)  Mini Revision Session
  • 36. Meiotic combinations •  Fused:Fused •  Unfused : Unfused •  Hybrid ?
  • 37. Hybrid Zones The existence of this frequency cline can be explained by the reduced fitness of heterozygotes. HOW?
  • 40. Hybrid Zones Gene flow never gets far into the other population due to the reduced fitness of heterozygotes
  • 42. A Complete(ish) Picture We can start to build up a picture of what evolution really looks like… •  First and foremost there is genetic drift •  There may also be some selection acting •  Gene flow homogenises allele frequencies between populations •  Mutation introduces new genetic variation into populations that may have lost it due to drift or selection •  There are still many processes missing from this picture!
  • 43. Lecture Outline 1)  The Amish 2)  Inbreeding and Identity by Descent 3)  Allele Frequency Clines and the Formation of Hybrid Zones 4)  Mini Revision Session
  • 44. Inbreeding and Identity by Descent Bottleneck Those deleterious recessive alleles that drift up produce increased incidence of the disorder. This is then reduced by selection over subsequent generations. Consanguinity The incidence of each disorder is increased, but selection reduces the incidence rapidly.
  • 45. Mini Revision Session What is the probability of identity by descent (f) of an offspring of full sib parents (parents are brother and sister with the same mother and father)?
  • 46. Mini Revision Session First things first; we need to draw a pedigree of the offspring of full sib parents. One thing that was confusing people is that the question did not specify the genotypes of either the parents or the offspring. Remember that we are trying to work out the probability of identity by descent – in other words, the probability that the two genes in the offspring are descended from the same gene copy in an earlier generation. We do not need to know any genotypes to work this out! To make this point clear, I have drawn genes in the grandparents as dots, rather than letters.
  • 47. Mini Revision Session 1.  We know that one gene copy in the offspring came from the father, and one from the mother. The question is; where did each of these come from in the grandparental generation?
  • 48. Mini Revision Session 1.  We know that one gene copy in the offspring came from the father, and one from the mother. The question is; where did each of these come from in the grandparental generation? 2.  Looking just at the paternal side, there is an equal chance that this gene came from any of the 4 gene copies in the grandparents. Thus, we can say that the probability of each of these events is ¼.
  • 49. Mini Revision Session 1.  We know that one gene copy in the offspring came from the father, and one from the mother. The question is; where did each of these come from in the grandparental generation? 2.  Looking just at the paternal side, there is an equal chance that this gene came from any of the 4 gene copies in the grandparents. Thus, we can say that the probability of each of these events is ¼. 3.  The same is true of the maternal side. The probability of this gene descending from each of the genes in the grandparents is ¼.
  • 50. Mini Revision Session 4.  Combining this knowledge, we can work out the probability that both offspring genes are descended from the same copy. Looking at the first grandparental gene (ie. the first black dot), we know that the probability of both the maternal and paternal genes coming from here is ¼ × ¼ = 1/16.
  • 51. Mini Revision Session 4.  Combining this knowledge, we can work out the probability that both offspring genes are descended from the same copy. Looking at the first grandparental gene (ie. the first black dot), we know that the probability of both the maternal and paternal genes coming from here is ¼ × ¼ = 1/16. 5.  The same is true of the second grandparental gene (second black dot). In fact, this is true of any of the 4 grandparental genes.
  • 52. Mini Revision Session 6.  In summary; there are 4 ways that the offspring genes could be descended from the same gene copy. Each of these has probability 1/16. Thus, the overall probability of identity by descent is… 1/16 + 1/16 + 1/16 + 1/16 = 4/16 Or f = 1/4
  • 53. Mini Revision Session In a random mating population, there is a disease that is encoded by a dominant allele. About 50 out of 1000 individuals have this disease. Calculate the genotype frequencies for AA, Aa, and aa. p2 2pq q2 p2 2p(1-p) (1-p)2
  • 54. Mini Revision Session + gAA + gAa = 50/1000 = 0.05 gaa = (1 - 0.05) = 0.95 p2 = 0.95 p ≈ 0.974679 gAa = 2p(1-p) ≈ 0.04936 0.05 gAA = (1-p)2 ≈ 0.00064