1. Mutation
source of all new alleles and genes
no mutation is a condition of HWE
importance for changing allele frequencies
importance relative to selection in shaping
population genetic variation

2. single locus, neutral alleles
A A* once: pr(loss) = 1; pr(loss) = 1 – 2s
recurrent: A A* (typically, m = 10-4 – 10-8)
if f(A*) = q, pt = (1 – m)tp0 where p0 is initial f(A)
how long until pt = p0 ??
if m = 10-5, t = 70,000 generations m 1 2

3. single locus, neutral alleles recurrent, reversible: A A*
if f(A*) = q, q = and p = m n
m + n v

4. recurrent, deleterious mutations AA AA* A*A* A A* and wij 1 1 1-s
f(A*) will via mutation and via selection m
-sq2(1-q)
1-sq2
Dqmut= m(1-q) Dqsel=
sq2
1-sq2
m =
m /(1+ m)  m v m s
q =

5. recurrent mutation can change allele
recurrent mutation can change allele frequencies in a population, but only very slowly
mutation is a weak force relative to selection, gene flow or genetic drift
simultaneous forward and backward mutation
produces equilibrium allele frequencies
recurrent mutation can maintain a deleterious
allele at low frequency

6. Measuring Selection in Natural Populations
Methods based on assumption of equilibrium
Deviations from expected genotype frequencies
Changes in allele frequencies
Within generation fitness comparisons
Responses of populations to perturbations
Functional studies

7. Mutation – Selection Equilibriumv m s
q =
Suppose we know allele frequency and mutation rate
and can assume equilibrium. Then we can estimate
selection.
e.g. q = 0.01, m = 10-5
s = m /q2
s = 0.1

8. Equilibrium frequency and heterozygote advantage
We make the observation that the frequency of the
sickle-cell anemia in Yemen is 1.4%.
Sickling allele confers some resistance to malaria, but
we will assume that homozygotes die.
What can we say about the cost of malaria in this region?
AA SA SS
1-t s
Susceptible to malaria Resistant to Malaria Anaemic v q
= t/(t+s) = t/(t+1)
q2 = .014, q = 0.12
t = 0.14

9. Deviations from H-W equilibrium Sickle-cell in Yemen again
Genotype
Observed
Expected
Ratio (O/E)
Relative Fitness SS 29
187.4
.155
0.155/1.12 = 0.14 = 1-s SA
2993
2672.4
1.12
1.0 AA
9365
9527.2
.983
0.88= 1-t
total
12,387

10. Using changes in allele frequencies to estimate
selection.
Remember what happens when there is selection against
a recessive deleterious trait. p’ = p/(1-sq2).
p’- p’sq2 = p, or p’ - p = p’sq2 .
This will simplify to: s = Dp/p’q2
We look at the increase in frequency of the dominant allele

11. Estimating the strength of
selection from allele frequency
changes in the Peppered Moth,
Biston betularia

12. Intro bio version: melanic moths increased because
industrial air pollution caused the typical form to
be more conspicuous to bird predators --
improvements in air quality have caused the melanic
form to decline
but: this species does not rest on tree trunks, so most
experiments were artificial -- the melanic form has
higher survival in conditions where predators are
absent -- melanism affects features other than
crypsis
phenotypic evolution has occurred in the Peppered Moth,
but the causes of that evolution are uncertain

13. Consistent change in allele frequencies 10-5 0.8
allele frequency
year “C” c
Consistent change in allele frequencies
in ~50 generations {p’ = p/(1-sq2)}
s if change due solely to selection

14. Warfarin resistance in Rattus novegicus
1953 first use in U.K.
1958 first resistance
but, resistance did not
fix in populations
what maintains the
polymorphism??

15. disrupts vitamin K dependent clotting factors,
how warfarin works:
anticoagulant
disrupts vitamin K dependent clotting factors,
leading to hemorrhage and death
resistance
alteration of vitamin K oxide reductase
less sensitive to blockage by warfarin
less effective in normal activities (Vit.K req.)
Phenotype Rw1Rw1 Rw1Rw2 Rw2Rw2
resistance susceptible resistant resistant
Vitamin K
(mg/100g/day)

16. Warfarin disrupts activation +/or production of one or
more of the vitamin K dependent clotting factors

17. disrupts vitamin K dependent clotting factors,
how warfarin works:
anticoagulant
disrupts vitamin K dependent clotting factors,
leading to hemorrhage and death
resistance
alteration of vitamin K oxide reductase
less sensitive to blockage by warfarin
less effective in normal activities (Vit.K req.)
Phenotype Rw1Rw1 Rw1Rw2 Rw2Rw2
resistance susceptible resistant resistant
Vitamin K (Wales)
(mg/100g/day) (Germany)

18. warfarin
hedgerow

19. s = .2/(.23X.95) ~ .91 Fitness of Rw1Rw1 =.09
warfarin
hedgerow
Proportion resistant before application
about 0.05.
Within short time phenotypic resistance
rises to about 40%
What is p?
~0.025 is freq of Rw2
What is p’?
If 40% are resistant,
Rw1Rw2 or Rw2Rw2 ,
or, p2 + 2pq = 0.4
p’ ~ .23
What is Dp?
~0.2
What is q2
~0.95
s = .2/(.23X.95) ~ Fitness of Rw1Rw1 =.09

20. on survival? (the resistance allele)
What is the effect of Rw2
on survival? (the resistance
allele)
Rw1Rw2 x Rw1Rw Rw1Rw2 x Rw1Rw1
Litter Size:
1:2: :1
Rw2Rw2 pups are more likely to die before weaning

21. wij Rw1Rw1 Rw1Rw2 Rw2Rw2
warfarin ~
no warfarin
(two populations)

22. Within generation comparisons of fitness:
tail length and mating success in widowbirds
Euplectes progne
nests in savannah, multiple females on one male’s
territory
males have a 50 cm long tail, used in displays to
females
does tail length affect mating success??

23. two treatments:
experimentally lengthened
experimentally shortened
two controls:
cut and re-attach
capture but not cut
new nests
each male is his own control
males have significantly
more new nests

24. Selection in widowbirds, con’t
shortened control lengthened
initial # nests
wij
# new nests
wij
adj. wij

25. disturbed popns
sexual
selection
viability
undisturbed popns

26. Kingsolver et al. 2001
Am. Nat. 157:245
Median = 0.16

27. measuring selection in natural populations
calculations based on equilibrium expectations
deviations from expected genotype frequencies
temporal patterns
allele frequency change in B. betularia, warfarin
resistance
within generation fitness comparisons
tail manipulations in widowbirds
responses of populations to perturbations
AZT resistance, G. fortis, warfarin resistance
functional studies
enzyme kinetics of PGI in Colias