Kjeld Aamodt
[email protected]
Office Hours: Thursday, 1111:50 at Clics 1st floor/ patio
Sections:
A04 & B07 @ 3010A
Thursday, 1010:50 am , 1212:50 pm
Genetics  Week 7
Population Genetics:
HardyWeinberg Equilibrium conditions:
1.
__
random mating
_________
2.
___
no migration
_________
3.
___
no mutation
___________
4.
__
no selection for / against any genotype
_
5.
____
large population
_______
Equations (
on Final
)
Population Genetics Basics
f(A) = p
f(a) = q p + q = 1
f(AA) + f(Aa) + d(aa) = 1
p = f(A) = f(AA) + 1/2 f(Aa)
q = f(a) = f(aa) + 1/2 f(Aa)
If mating is random, f(AA) = p
2
f(Aa) = 2pq
f(aa) = q
2
so p
2
+ 2pq +q
2
= 1
Selection Against a Recessive Trait
W is fitness  for fittest genotype = 1; W is for lethal genotype = 0
s (selection coefficient) = 1  W
For a recessive mutation under negative selection (ie., W for AA and Aa = 1, but W for aa < 1):
After one round of selection, q
ʼ
= (q  sq
2
)/(1  sq
2
)
Mutation
Rate of conversion of A > a is
μ
(mutation rate)
q
ʼ
= q +
μ
p
Δ
q
max
=
μ
p
Mutation/Selection Balance (Equilibrium)
Recessive mutation (where W for AA and Aa = 1 but W for aa <1)
q
equilib
=
√
(
μ
/s)
(where s is the selection coefficient for aa)
Overdominance (where Aa is fittest genotype, ie., W for Aa > W for AA or aa)
P
equilib
= s
2
/ (s
1
+ s
2
) and q
equilib
= s
1
/ (s
1
+ s
2
)
(where s
1
is selection coefficient for AA and
s
2
for aa)
Migration
Let p
m
= f(A) for migrants and p
i
= f(A) for initial population before arrival of migrants
Let p = f(A) for new population made when migrants join initial population
If m is the proportion of individuals in the new population that were migrants,
p
ʼ
= mp
m
+ (1  m)p
i
Δ
p = m(p
m 
p
i
) > > m = (p
ʼ
 p
i
)/(p
m 
p
i
)
NonRandom Mating
F is the inbreeding coefficient = probability of being homozygous by descent
f(aa) = qF + q
2
(1  F)
f(Aa) = 2pg(1  F)
f(AA) = pF + p
2
(1  F)
F for a population = 1  (H/2pg) where H is the actual frequency of heterozygotes
F = (1/2)N
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 Winter '08
 Nehring
 Genetics, Population Genetics, Zygosity, Gao Gao

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