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Neutral Theory of molecular evolution
MSc in Bioinformatics Module 3. Genomics - Genome variation: I. Theory and Data
Antonio Barbadilla
MSc in Bioinformatics Module 3. Genomics - Genome variation: I. Theory and Data
Antonio Barbadilla
The Great Obsession of population genetics (Gillespie 2004) What evolutionary forces led to the observed pattern of genetic variation?
MSc in Bioinformatics Module 3. Genomics - Genome variation: I. Theory and Data
Antonio Barbadilla
H. J. Muller
Theories of variation in the 60’s
•Absence of variation
•Purifying selection
•Wild genotype is optimun
•Muller (laboratory)
•Eugenics
•Variation is ubiquitous
•Balancing selection
•No wild phenotype
•Dobzhansky (naturalist)
•¡Viva la diversidad!, non interference
Classic Theory Balancing theory
T. Dobzhansky
MSc in Bioinformatics Module 3. Genomics - Genome variation: I. Theory and Data
Antonio Barbadilla
60-70
•Electropheretic variation
The struggle for the measurement of genetic variation
MSc in Bioinformatics Module 3. Genomics - Genome variation: I. Theory and Data
Antonio Barbadilla
Neutral theory of molecular evolution (1968)
Motoo Kimura
Mutations are mainly neutral or strongly deleterious
0
DFE (Distribution fitness effect of new mutation) of Kimura’s Neutral Theory
Freq
uen
cy
MSc in Bioinformatics Module 3. Genomics - Genome variation: I. Theory and Data
Antonio Barbadilla
MSc in Bioinformatics Module 3. Genomics - Genome variation: I. Theory and Data
Antonio Barbadilla
MSc in Bioinformatics Module 3. Genomics - Genome variation: I. Theory and Data
Antonio Barbadilla
Neutral theory of molecular evolution
MSc in Bioinformatics Module 3. Genomics - Genome variation: I. Theory and Data
Antonio Barbadilla
Nature of genetic variation
Mutation
Substitution =
Divergence =
Evolutionary rate
µ K
MSc in Bioinformatics Module 3. Genomics - Genome variation: I. Theory and Data
Antonio Barbadilla
MSc in Bioinformatics Module 3. Genomics - Genome variation: I. Theory and Data
Antonio Barbadilla
Neutral theory of molecular evolution
MSc in Bioinformatics Module 3. Genomics - Genome variation: I. Theory and Data
Antonio Barbadilla
Neutral theory of molecular evolution
Substitution rate
or = mutation rate
Evolutionary rate
MSc in Bioinformatics Module 3. Genomics - Genome variation: I. Theory and Data
Antonio Barbadilla
Probability of fixation (substitution)
New mutations entering each generation in the population
MSc in Bioinformatics Module 3. Genomics - Genome variation: I. Theory and Data
Antonio Barbadilla
Probability of fixation (substitution)
New mutations entering each generation in the population
X X
MSc in Bioinformatics Module 3. Genomics - Genome variation: I. Theory and Data
Antonio Barbadilla
# substitution / generation = (#mutation /generation) ( substitution / mutation)
Question Demonstrate the K is equal for a penguin population with big N and for a bacteria population of one individual granted that µ is the same for both species
Pick a student up at random
Question Which are the most general and famous mathematical expressions of Science?
Pick a student up at random
MSc in Bioinformatics Module 3. Genomics - Genome variation: I. Theory and Data
Antonio Barbadilla 20 Antonio Barbadilla Lesson 6. Genome variation: I. nucleotide variation
F = ma
Schrödinger equation (general)
(Newton’s dynamics 2nd law)
(Boltzmann's entropy formula)
(Einstein’s relativity mass-energy equivalence)
MSc in Bioinformatics Module 3. Genomics - Genome variation: I. Theory and Data
Antonio Barbadilla
MSc in Bioinformatics Module 3. Genomics - Genome variation: I. Theory and Data
Antonio Barbadilla
Allelic frequency
Time
1
0
gen.4Nt fix
Dynamics of neutral substitutions
Neutral theory of molecular evolution Assumption
New mutations are mainly neutral or strongly deleterious
µ
ln2 Ntlost
•Polymorphism •Heterozygosity in the equilibrium H = = 2N x 2N µ = 4N µ
MSc in Bioinformatics Module 3. Genomics - Genome variation: I. Theory and Data
Antonio Barbadilla
Allelic frequency
Time
1
0
gen.4Nt fix
Dynamics of neutral substitutions
Neutral theory of molecular evolution Assumption
New mutations are mainly neutral or strongly deleterious
µ
•Polymorphism •Heterozygosity in the equilibrium H = = 2N x 2N µ = 4N µ
MSc in Bioinformatics Module 3. Genomics - Genome variation: I. Theory and Data
Antonio Barbadilla
Polymorphism and divergence are coupled
Species A Species B
Species B
Species A
Substitution Substitution => divergence
Time from separation
Neutral theory of molecular evolution
MSc in Bioinformatics Module 3. Genomics - Genome variation: I. Theory and Data
Antonio Barbadilla
Polymorphism and divergence are coupled
Species A
• Divergence increases over time (Molecular Clock)
D = 2Tµ
• Polymorphism reaches a dynamic equilibrium
H = = 4N µ
Neutral theory of molecular evolution
Species B
Note that Divergence increases over time
but Polymorphism reaches a dynamic equilibrium
MSc in Bioinformatics Module 3. Genomics - Genome variation: I. Theory and Data
Antonio Barbadilla
Neutral theory of molecular evolution
Motoo Kimura
•Divergence
• Substitution rate (evolution rate) of neutral mutations, k k = 2N µ 1/(2N) = µ •Expected time to fixation of a new mutation
E(t) = 4N generations •Linear relationship between divergence and time ->
Evolutionary molecular clock Divergence = Rate of evolution x 2T
•Polymorphism
•A transitory state in the process of fixation of neutral alleles •Heterozygosity in the equilibrium H = = 2N x 2N µ = 4N µ
•Divergence and polymorphism are coupled
Assumption Mutations are mainly neutral or strongly deleterious
Theorems
D = 2Tµ
MSc in Bioinformatics Module 3. Genomics - Genome variation: I. Theory and Data
Antonio Barbadilla
Poisson process (variance in time between substitutions)
Literal clock (no variance in time between substitutions)
MSc in Bioinformatics Module 3. Genomics - Genome variation: I. Theory and Data
Antonio Barbadilla
µ N
Effect of µ and N on the rate of substitution
MSc in Bioinformatics Module 3. Genomics - Genome variation: I. Theory and Data
Antonio Barbadilla
Allelic frequency
Time
1
0
The intellectual elegance of Neutral theory: Play the role of null hypothesis
The Myth of Sisyphus and molecular evolution
MSc in Bioinformatics Module 3. Genomics - Genome variation: I. Theory and Data
Antonio Barbadilla
Neutral theory of molecular evolution (1968)
Motoo Kimura
Mutations are mainly neutral or strongly deleterious
Tomoko Ohta
0 0
DFE (Distribution fitness effect of new mutation)
Freq
ue
ncy
Clarifying question Does Neutralism mean that positive selection is not acting in the genome?
Pick a student up at random
MSc in Bioinformatics Module 3. Genomics - Genome variation: I. Theory and Data
Antonio Barbadilla
II: Mutaciones selectivamente ventajosas
gen. )2ln(2
Ns
t
1
0
1
μ4Ns
Population dynamics of selectively advantage mutations
Allelic frequency
Time
MSc in Bioinformatics Module 3. Genomics - Genome variation: I. Theory and Data
Antonio Barbadilla
Freq
uen
cy
0
1. DFE (Distribution fitness effect of new mutation)
+
-
Fitness (s)
Two main functions describing molecular polymorphism and divergence
Allele frequency
1
0
Time
2. Fixation probability a new mutation =
Two main functions describing molecular polymorphism and divergence
Population Dynamics of new mutations accoding their fitness effect
Population Dynamics of new mutations according their fitness effect
u(N,s) = Fixation probability of a new mutation fitness in a population with size N
MSc in Bioinformatics Module 3. Genomics - Genome variation: I. Theory and Data
Antonio Barbadilla
1
0 Time
K =
X
DFE Fixation probability new mutation Time fixation = 1/Fixation probability
Molecular evolutionary rate = Substitution rate = K
Fitness (s)
Two main functions describing molecular polymorphism and divergence
Probability of fixation of a mutation fitness s
Density of new mutations with fitness s
From the general expression of substitution rate derive the value of K assuming that all new mutations are neutral
Pick a student up at random
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