Models of Selection Goal: to build models that can predict a population’s response to natural selection What are the key factors? Today’s model: haploid, one locus Outline: triclosan in biosolids fitness haploid life cycle selection coefficients long term predictions
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Models of Selection Goal: to build models that can predict a population’s response to natural selection What are the key factors? Today’s model: haploid,
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Models of Selection
Goal: to build models that can predict a population’s response to natural selection
What are the key factors?
Today’s model: haploid, one locus
Outline: triclosan in biosolids fitness haploid life cycle selection coefficients long term predictions
When does selection act?
Triclosan and
biosolids
Triclosan:
Biosolids:
Triclosan in biosolids??
Fitness: The sum total effect of selection within a generation
Absolute Fitness =
Relative Fitness =
Key questions for model
One-locus haploid modelFor what organisms is this model appropriate?
Initial frequencies, fitnessf(A) = p(t)
f(a) = q(t)
WA = relative fitness of A
Wa = relative fitness of a
One-locus haploid model
p[t]q[t]
WA
Wa
f'(A) = __WAp(t)___ WAp(t) + Waq(t)
f'(a) = __Waq(t)___ WAp(t) + Waq(t)
Example:p(t) = 0.5; q(t) = 0.5WA = 1; Wa = 0.8
One-locus haploid model
p(t)WA
p(t)WA + q(t)Wa
Relative, not absolute, fitness determines changes in allele
frequencies
a
Aa
A
A
A A
Aa
a
a
a
a
Aa
A
A
A A
Aa
a
a
a
a
A
A
A
A A
Aa
a
a
a
a
A
A A
a
6 A, 6 a 6 A, 6 a
Survival of A = 1, of a = 2/3
Survival of A = 1/2, of a = 1/3
f’(A) = 0.6 f’(A) = 0.6
Haploid selection: rest of life cycle
Adults mate at random
Undergo meiosis
One-locus haploid model
One-locus haploid model
p(t+1) = p(t)WA
p(t)WA + q(t)Wa
p = p(t+1) – p(t) = (WA – Wa)p(t)q(t)
W(t)
W(t) = p(t)WA + q(t)Wa
One-locus haploid model
p = p(t+1) – p(t) = (WA – Wa)p(t)q(t)
W(t)
What does this tell us about selection?
A note about variance
• We can use a simple trick to answer this question. If we divide p[t+1] by q[t+1]:
What will happen over periods of time longer than one generation?
The ratio of p[t] to q[t] changes by W
A/W
a every generation.
p(t+1) p(t)WA
q(t+1) q(t)Wa
=
Predicting allele frequencies
q(t) = 1- p(t), so
p(0)WAt
p(0)WAt + q(0)Wa
t
p(t) =
Now, for any generation t:
p(t) p(0)WAt
q(t) q(0)Wat=
hint: keep right side together, divide by fraction
Using the model I
What would the frequency of allele A be after 100 generations of selection if A is 10% more fit than allele a and if one in
every hundred alleles is initially A?
p(0)WAt
p(0)WAt + q(0)Wa
t
p(t) =
Using the model IIIf A changes in frequency from
0.001 to 0.01 in 10 generations, by how much must it be favored?
p(t) p(0)WAt
q(t) q(0)Wat=
Selection coefficients
Selection coefficient exampleHow long would it take for 95% of the
alleles to be A if A is initially present in 5% of the population and if the selection
coefficient favoring allele A is...s = 0.1?
The time needed for an allele to go from low frequency to high is the inverse of the selection coefficient s = 0.1 -> tens of generations
Some general principles
Does the mean fitness of a population always increase over
ReferencesHeidler, J. et al. 2006. Partitioning, Persistence, and Accumulation in Digested Sludge of the Topical Antiseptic Triclocarban during Wastewater Treatment. Environ. Sci. Technol.; 40(11); 3634-3639
More questionsWould a dominant or recessive allele change frequency faster in a haploid organism? why?
Calculate the relative fitnesses for these two genotypes:genotype: A a starting count (before selection) 100 100 ending count (after selection) 90 30What is the selection co-efficient?Assume that the mixture starts out with f(A) = 0.5. What will the frequency be after 20 generations?