III. Modeling Selection

1
III. Modeling Selection A. Selection for a
Dominant Allele B. Selection for an
Incompletely Dominant Allele C. Selection
that Maintains Variation
2
C. Selection that Maintains Variation 1.
Heterosis - selection for the heterozygote
p 0.4, q 0.6 AA Aa aa
Parental "zygotes" 0.16 0.48 0.36 1.00
prob. of survival (fitness) 0.4 0.8 0.2
Relative Fitness 0.5 (1-s) 1 0.25 (1-t)
Survival to Reproduction 0.08 0.48 0.09 0.65
Geno. Freq., breeders 0.12 0.74 0.14 1.00
Gene Freq's, gene pool p 0.49 q 0.51
Genotypes, F1 0.24 0.50 0.26 100
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C. Selection that Maintains Variation 1.
Heterosis - selection for the heterozygote -
Consider an 'A" allele. It's probability of
being lost from the population is a function
of
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C. Selection that Maintains Variation 1.
Heterosis - selection for the heterozygote -
Consider an 'A" allele. It's probability of
being lost from the population is a function
of 1) probability it meets another 'A'
(p)
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C. Selection that Maintains Variation 1.
Heterosis - selection for the heterozygote -
Consider an 'A" allele. It's probability of
being lost from the population is a function
of 1) probability it meets another 'A'
(p) 2) rate at which these AA are lost
(s).
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C. Selection that Maintains Variation 1.
Heterosis - selection for the heterozygote -
Consider an 'A" allele. It's probability of
being lost from the population is a function
of 1) probability it meets another 'A'
(p) 2) rate at which these AA are lost (s).
- So, prob of losing an 'A' allele ps
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C. Selection that Maintains Variation 1.
Heterosis - selection for the heterozygote -
Consider an 'A" allele. It's probability of
being lost from the population is a function
of 1) probability it meets another 'A'
(p) 2) rate at which these AA are lost (s).
- So, prob of losing an 'A' allele ps -
Likewise the probability of losing an 'a'
qt
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C. Selection that Maintains Variation 1.
Heterosis - selection for the heterozygote -
Consider an 'A" allele. It's probability of
being lost from the population is a function
of 1) probability it meets another 'A'
(p) 2) rate at which these AA are lost (s).
- So, prob of losing an 'A' allele ps -
Likewise the probability of losing an 'a' qt
- An equilibrium will occur, when the
probability of losing A an a are equal when ps
qt.
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C. Selection that Maintains Variation 1.
Heterosis - selection for the heterozygote -
An equilibrium will occur, when the probability
of losing A an a are equal when ps qt.
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C. Selection that Maintains Variation 1.
Heterosis - selection for the heterozygote -
An equilibrium will occur, when the probability
of losing A an a are equal when ps qt. -
substituting (1-p) for q, ps (1-p)t ps t
- pt ps pt t p(s t) t peq
t/(s t)
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C. Selection that Maintains Variation 1.
Heterosis - selection for the heterozygote -
An equilibrium will occur, when the probability
of losing A an a are equal when ps qt. -
substituting (1-p) for q, ps (1-p)t ps t
- pt ps pt t p(s t) t peq
t/(s t) - So, for our example, t 0.75, s
0.5 - so, peq .75/1.25 0.6
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C. Selection that Maintains Variation 1.
Heterosis - selection for the heterozygote -
so, peq .75/1.25 0.6
p 0.6, q 0.4 AA Aa aa
Parental "zygotes" 0.36 0.48 0.16 1.00
prob. of survival (fitness) 0.4 0.8 0.2
Relative Fitness 0.5 (1-s) 1 0.25 (1-t)
Survival to Reproduction 0.18 0.48 0.04 0.70
Geno. Freq., breeders 0.26 0.68 0.06 1.00
Gene Freq's, gene pool p 0.6 q 0.4 CHECK
Genotypes, F1 0.36 0.48 0.16 100
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C. Selection that Maintains Variation 1.
Heterosis - selection for the heterozygote -
so, peq .75/1.25 0.6 - so, if p gt 0.6, it
should decline to this peq
p 0.7, q 0.3 AA Aa aa
Parental "zygotes" 0.49 0.42 0.09 1.00
prob. of survival (fitness) 0.4 0.8 0.2
Relative Fitness 0.5 (1-s) 1 0.25 (1-t)
Survival to Reproduction 0.25 0.48 0.02 0.75
Geno. Freq., breeders 0.33 0.64 0.03 1.00
Gene Freq's, gene pool p 0.65 q 0.35 CHECK
Genotypes, F1 0.42 0.46 0.12 100
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C. Selection that Maintains Variation 1.
Heterosis - selection for the heterozygote -
so, peq .75/1.25 0.6 - so, if p gt 0.6, it
should decline to this peq
0.6
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C. Selection that Maintains Variation 1.
Heterosis - selection for the heterozygote 2.
Multiple Niche Polymorphism -
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C. Selection that Maintains Variation 1.
Heterosis - selection for the heterozygote 2.
Multiple Niche Polymorphism - - equilibrium
can occur if AA and aa are each fit in a given
niche, within the population. The equilibrium
will depend on the relative frequencies of the
niches and the selection differentials...
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C. Selection that Maintains Variation 1.
Heterosis - selection for the heterozygote 2.
Multiple Niche Polymorphism - - equilibrium
can occur if AA and aa are each fit in a given
niche, within the population. The equilibrium
will depend on the relative frequencies of the
niches and the selection differentials... -
can you think of an example??
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C. Selection that Maintains Variation 1.
Heterosis - selection for the heterozygote 2.
Multiple Niche Polymorphism - - equilibrium
can occur if AA and aa are each fit in a given
niche, within the population. The equilibrium
will depend on the relative frequencies of the
niches and the selection differentials... -
can you think of an example?? Papilio
butterflies... females mimic different models and
an equilibrium is maintained in fact, an
equilibrium at each locus, which are also
maintained in linkage disequilibrium.
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C. Selection that Maintains Variation 1.
Heterosis - selection for the heterozygote 2.
Multiple Niche Polymorphism 3. Frequency
Dependent Selection
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C. Selection that Maintains Variation 1.
Heterosis - selection for the heterozygote 2.
Multiple Niche Polymorphism 3. Frequency
Dependent Selection - the fitness depends on
the frequency...
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C. Selection that Maintains Variation 1.
Heterosis - selection for the heterozygote 2.
Multiple Niche Polymorphism 3. Frequency
Dependent Selection - the fitness depends on
the frequency... - as a gene becomes rare, it
becomes advantageous and is maintained in the
population...
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C. Selection that Maintains Variation 1.
Heterosis - selection for the heterozygote 2.
Multiple Niche Polymorphism 3. Frequency
Dependent Selection - the fitness depends on
the frequency... - as a gene becomes rare, it
becomes advantageous and is maintained in the
population... - "Rare mate"
phenomenon...
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Elderflower orchids - dont produce nectar -
bumblebees visit most common flower color and get
discouraged, try the other color. Back and
forth. - visit equal NUMBERS of the two colors,
but that means that a plant with the rare color
is visited more often.
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(of yellow flowers)
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(No Transcript)
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- Morphs of Heliconius melpomene and H.
erato Mullerian complex between two distasteful
species... positive frequency dependence in both
populations to look like the most abundant
morph
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C. Selection that Maintains Variation 1.
Heterosis - selection for the heterozygote 2.
Multiple Niche Polymorphism 3. Frequency
Dependent Selection 4. Selection Against the
Heterozygote
p 0.4, q 0.6 AA Aa aa
Parental "zygotes" 0.16 0.48 0.36 1.00
prob. of survival (fitness) 0.8 0.4 0.6
Relative Fitness 1 0.5 0.75
Corrected Fitness 1 0.5 1.0 1 0.25
formulae 1 s 1 t
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4. Selection Against the Heterozygote
p 0.4, q 0.6 AA Aa aa
Parental "zygotes" 0.16 0.48 0.36 1.00
prob. of survival (fitness) 0.8 0.4 0.6
Relative Fitness 1 0.5 0.75
Corrected Fitness 1 0.5 1.0 1 0.25
formulae 1 s 1 t
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4. Selection Against the Heterozygote - peq
t/(s t)
p 0.4, q 0.6 AA Aa aa
Parental "zygotes" 0.16 0.48 0.36 1.00
prob. of survival (fitness) 0.8 0.4 0.6
Relative Fitness 1 0.5 0.75
Corrected Fitness 1 0.5 1.0 1 0.25
formulae 1 s 1 t
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4. Selection Against the Heterozygote - peq
t/(s t) - here .25/(.50 .25) .33
p 0.4, q 0.6 AA Aa aa
Parental "zygotes" 0.16 0.48 0.36 1.00
prob. of survival (fitness) 0.8 0.4 0.6
Relative Fitness 1 0.5 0.75
Corrected Fitness 1 0.5 1.0 1 0.25
formulae 1 s 1 t
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4. Selection Against the Heterozygote - peq
t/(s t) - here .25/(.50 .25) .33 -
if p gt 0.33, then it will keep increasing to
fixation.
p 0.4, q 0.6 AA Aa aa
Parental "zygotes" 0.16 0.48 0.36 1.00
prob. of survival (fitness) 0.8 0.4 0.6
Relative Fitness 1 0.5 0.75
Corrected Fitness 1 0.5 1.0 1 0.25
formulae 1 s 1 t
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4. Selection Against the Heterozygote - peq
t/(s t) - here .25/(.50 .25) .33 -
if p gt 0.33, then it will keep increasing to
fixation. - However, if p lt 0.33, then p will
decline to zero... AND THERE WILL BE FIXATION FOR
A SUBOPTIMAL ALLELE....'a'... !! UNSTABLE
EQUILIBRIUM!!!!
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Population Genetics I. Basic Principles II.
X-linked Genes III. Modeling Selection IV. OTHER
DEVIATIONS FROM HWE
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Deviations from HWE I. Mutation A.
Basics
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Deviations from HWE I. Mutation A. Basics 1.
Consider a population with f(A) p .6
f(a) q .4
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Deviations from HWE I. Mutation A. Basics 1.
Consider a population with f(A) p .6
f(a) q .4 2. Suppose 'a' mutates to 'A'
at a realistic rate of µ 1 x 10-5
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Deviations from HWE I. Mutation A. Basics 1.
Consider a population with f(A) p .6
f(a) q .4 2. Suppose 'a' mutates to 'A'
at a realistic rate of µ 1 x 10-5 3.
Well, what fraction of alleles will change? 'a'
will decline by qm .4 x 0.00001
0.000004 'A' will increase by the same
amount.
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Deviations from HWE I. Mutation A. Basics 1.
Consider a population with f(A) p .6
f(a) q .4 2. Suppose 'a' mutates to 'A'
at a realistic rate of µ 1 x 10-5 3.
Well, what fraction of alleles will change? 'a'
will decline by qm .4 x 0.00001
0.000004 'A' will increase by the same
amount. 4. So, the new gene frequencies will
be p1 p µq .600004 q1 q - µq
q(1-µ) .399996
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Deviations from HWE I. Mutation A. Basics 4.
So, the new gene frequencies will be p1 p
µq 1 - q µq 1- q(1-µ) .600004 q1 q -
µq q(1-µ) .399996 5. How about with both
FORWARD and backward mutation? ?q ?p - µq

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Deviations from HWE I. Mutation A. Basics 4.
So, the new gene frequencies will be p1 p
µq 1 - q µq 1- q(1-µ) .600004 q1 q -
µq q(1-µ) .399996 5. How about with both
FORWARD and backward mutation? ?q ?p - µq -
so, if A -gt a v 0.00008 and a-gtA µ
0.00001, and p 0.6 and q 0.4, then
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Deviations from HWE I. Mutation A. Basics 4.
So, the new gene frequencies will be p1 p
µq 1 - q µq 1- q(1-µ) .600004 q1 q -
µq q(1-µ) .399996 5. How about with both
FORWARD and backward mutation? ?q ?p - µq -
so, if A -gt a v 0.00008 and a-gtA µ
0.00001, and p 0.6 and q 0.4, then
?q ?p - µq 0.000048 - 0.000004
0.000044 q1 .4 0.000044 0.400044
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Deviations from HWE I. Mutation A. Basics 5.
How about with both FORWARD and backward
mutation? - ?q ?p - µq - and qeq v/ v
µ
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Deviations from HWE I. Mutation A. Basics 5.
How about with both FORWARD and backward
mutation? - ?q ?p - µq - and qeq v/ v
µ - and qeq v/ v µ 0.00008/0.00009
0.89
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Deviations from HWE I. Mutation A. Basics 5.
How about with both FORWARD and backward
mutation? - ?q ?p - µq - and qeq v/ v
µ - and qeq v/ v µ 0.00008/0.00009
0.89 - so, if ?q ?p µq, then ?q
(.11)(0.00008) - (.89)(0.00001) 0.0.....
check.
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Deviations from HWE I. Mutation A. Basics
B. Other Considerations
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Deviations from HWE I. Mutation A. Basics
B. Other Considerations - Selection
Selection can BALANCE mutation... so a
deleterious allele might not accumulate as
rapidly as mutation would predict, because it it
eliminated from the population by selection each
generation. We'll model these effects
later.
47
Deviations from HWE I. Mutation A. Basics
B. Other Considerations - Selection
Selection can BALANCE mutation... so a
deleterious allele might not accumulate as
rapidly as mutation would predict, because it it
eliminated from the population by selection each
generation. We'll model these effects later. -
Drift The probability that a new allele
(produced by mutation) becomes fixed (q 1.0) in
a population 1/2N (basically, it's frequency
in that population of diploids). In a small
population, this chance becomes measureable and
likely. So, NEUTRAL mutations have a reasonable
change of becoming fixed in small populations...
and then replaced by new mutation
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Deviations from HWE I. Mutation II. Migration
A. Basics - Consider two populations
p2 0.7 q2 0.3
p1 0.2 q1 0.8
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Deviations from HWE I. Mutation II. Migration
A. Basics - Consider two populations
p2 0.7 q2 0.3
p1 0.2 q1 0.8
suppose migrants immigrate at a rate such that
the new immigrants represent 10 of the new
population
50
Deviations from HWE I. Mutation II. Migration
A. Basics - Consider two populations
p2 0.7 q2 0.3
p1 0.2 q1 0.8
suppose migrants immigrate at a rate such that
the new immigrants represent 10 of the new
population
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Deviations from HWE I. Mutation II. Migration
A. Basics - Consider two populations
p2 0.7 q2 0.3
p1 0.2 q1 0.8
suppose migrants immigrate at a rate such that
the new immigrants represent 10 of the new
population
p(new) p1(1-m) p2(m)
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Deviations from HWE I. Mutation II. Migration
A. Basics - Consider two populations
p2 0.7 q2 0.3
p1 0.2 q1 0.8
suppose migrants immigrate at a rate such that
the new immigrants represent 10 of the new
population
p(new) p1(1-m) p2(m) p(new) 0.2(0.9)
0.7(0.1) 0.25
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Deviations from HWE I. Mutation II. Migration
A. Basics B. Advanced - Consider three
populations
p1 0.7 q1 0.3
p2 0.2 q2 0.8
p3 0.6 q3 0.4
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Deviations from HWE I. Mutation II. Migration
A. Basics B. Advanced - Consider three
populations - How different are they,
genetically? (this can give us a handle on how
much migration there may be between them...)
p1 0.7 q1 0.3
p2 0.2 q2 0.8
p3 0.6 q3 0.4
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Deviations from HWE I. Mutation II. Migration
A. Basics B. Advanced - Consider three
populations - How different are they,
genetically? (this can give us a handle on how
much migration there may be between them...) -
Compute Nei's Genetic Distance D -ln
?pi1pi2/ v ?pi12 ? pi22
p1 0.7 q1 0.3
p2 0.2 q2 0.8
p3 0.6 q3 0.4
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Deviations from HWE I. Mutation II. Migration
A. Basics B. Advanced - Consider three
populations - How different are they,
genetically? (this can give us a handle on how
much migration there may be between them...) -
Compute Nei's Genetic distance D -ln
?pi1pi2/ v ?pi12 ? pi22 - So, for Population 1
and 2 - ?pi1pi2 (0.70.2) (0.30.8)
0.38 - denominator v (.49.09) (.04.64)
0.628 D12 -ln (0.38/0.62) 0.50
p1 0.7 q1 0.3
p2 0.2 q2 0.8
p3 0.6 q3 0.4
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- Compute Nei's Genetic distance D -ln
?pi1pi2/ v ?pi12 ? pi22 - So, for Population 1
and 2 - ?pi1pi2 (0.70.2) (0.30.8)
0.38 - denominator v (.49.09) (.04.64)
0.628 D12 -ln (0.38/0.628) 0.50 - For
Population 1 and 3 - ?pi1pi2 (0.70.6)
(0.30.4) 0.54 - denominator v (.49.09)
(.36.16) 0.55 D13 -ln (0.54/0.55)
0.02 - For Population 2 and 3 - ?pi1pi2
(0.20.6) (0.80.4) 0.44 - denominator v
(.04.64) (.36.16) 0.61 D23 -ln
(0.44/0.61) 0.33
p1 0.7 q1 0.3
p2 0.2 q2 0.8
p3 0.6 q3 0.4
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Deviations from HWE I. Mutation II.
Migration III. Non-Random Mating A. Positive
Assortative Mating "like phenotype mates with
like phenotype"
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Deviations from HWE I. Mutation II.
Migration III. Non-Random Mating A. Positive
Assortative Mating "like phenotype mates with
like phenotype" 1. Pattern
AA Aa aa
.2 .6 .2
offspring ALL AA 1/4AA1/2Aa1/4aa ALL aa
.2 .15 .3 .15 .2
F1 .35 .3 .35
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1. Pattern
AA Aa aa
.2 .6 .2
offspring ALL AA 1/4AA1/2Aa1/4aa ALL aa
.2 .15 .3 .15 .2
F1 .35 .3 .35
2. Effect - reduction in heterozygosity at this
locus increase in homozygosity.
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Deviations from HWE I. Mutation II.
Migration III. Non-Random Mating A. Positive
Assortative Mating B. Inbreeding 1.
Overview
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Deviations from HWE I. Mutation II.
Migration III. Non-Random Mating A. Positive
Assortative Mating B. Inbreeding 1.
Overview Inbreeding is like mating with like,
but across the entire genome.
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B. Inbreeding 1. Overview - Autozygous -
inherited alleles common by descent - F
inbreeding coefficient prob. of autozygosity
- so, (1-F) prob. of allozygosity
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B. Inbreeding 1. Overview - Autozygous -
inherited alleles common by descent - F
inbreeding coefficient prob. of autozygosity
- so, (1-F) prob. of allozygosity -
SO f(AA) p2(1-F) p2(F) D f(Aa)
2pq(1-F) H (observed) f(aa) q2(1-F)
q2(F) R
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B. Inbreeding 1. Overview - Autozygous -
inherited alleles common by descent - F
inbreeding coefficient prob. of autozygosity
- so, (1-F) prob. of allozygosity -
SO f(AA) p2(1-F) p2(F) D f(Aa)
2pq(1-F) H (observed) f(aa) q2(1-F)
q2(F) R - SO!! the net effect is a
decrease in heterozygosity at a factor of (1-F)
each generation. - So, the fractional demise of
heterozygosity compared to HWE expectations is
also a direct measure of inbreeding! F (2pq
- H)/2pq (Hexp - Hobs)/ Hexp When this is done
on multiple loci, the values should all be
similar (as inbreeding affects the whole
genotype).
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B. Inbreeding 1. Overview - Example F
(2pq - H)/2pq (Hexp - Hobs)/ Hexp p .5, q
.5, expected HWE heterozygosity 2pq
0.5 OBSERVED in F1 0.3... so F (.5 - .3)/.5
0.4
AA Aa aa
.2 .6 .2
offspring ALL AA 1/4AA1/2Aa1/4aa ALL aa
.2 .15 .3 .15 .2
F1 .35 .3 .35
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Deviations from HWE I. Mutation II.
Migration III. Non-Random Mating A. Positive
Assortative Mating B. Inbreeding 1.
Overview 2. Effects
68
Deviations from HWE I. Mutation II.
Migration III. Non-Random Mating A. Positive
Assortative Mating B. Inbreeding 1.
Overview 2. Effects - reduce
heterozygosity across entire genome
69
Deviations from HWE I. Mutation II.
Migration III. Non-Random Mating A. Positive
Assortative Mating B. Inbreeding 1.
Overview 2. Effects - reduce
heterozygosity across entire genome - rate
dependent upon degree of relatedness
70
Deviations from HWE I. Mutation II.
Migration III. Non-Random Mating A. Positive
Assortative Mating B. Inbreeding 1.
Overview 2. Effects - reduce
heterozygosity across entire genome - rate
dependent upon degree of relatedness - change
in genotypic frequencies but no change in gene
frequencies as a result of non-random mating
ALONE....
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Deviations from HWE I. Mutation II.
Migration III. Non-Random Mating A. Positive
Assortative Mating B. Inbreeding 1.
Overview 2. Effects - reduce
heterozygosity across entire genome - rate
dependent upon degree of relatedness - change
in genotypic frequencies but no change in gene
frequencies as a result of non-random mating
ALONE.... - BUT... increasing homozygosity
may reveal deleterious recessives.
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Deviations from HWE I. Mutation II.
Migration III. Non-Random Mating A. Positive
Assortative Mating B. Inbreeding 1.
Overview 2. Effects - reduce
heterozygosity across entire genome - rate
dependent upon degree of relatedness - change
in genotypic frequencies but no change in gene
frequencies as a result of non-random mating
ALONE.... - BUT... increasing homozygosity
may reveal deleterious recessives. - these
will be quickly selected against....?
73
Deviations from HWE I. Mutation II.
Migration III. Non-Random Mating A. Positive
Assortative Mating B. Inbreeding 1.
Overview 2. Effects - reduce
heterozygosity across entire genome - rate
dependent upon degree of relatedness - change
in genotypic frequencies but no change in gene
frequencies as a result of non-random mating
ALONE.... - BUT... increasing homozygosity
may reveal deleterious recessives. - these
will be quickly selected against, but that
reduces fecundity (inbreeding depression) and
reduces genetic variation.