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![Page 1: Neutral Theory: From molecular evolution to community ecology Fangliang He Department of Renewable Resources University of Alberta.](https://reader035.fdocuments.in/reader035/viewer/2022062718/56649e6a5503460f94b68879/html5/thumbnails/1.jpg)
Neutral Theory:
From molecular evolution to community ecology
Fangliang He
Department of Renewable Resources
University of Alberta
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“Nothing in biology makes sense except
in the light of evolution.”
Dobzhansky (1973)
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A Brief History of (Molecular) Evolution
• In 1859, Charles Darwin proposed that:
(1) all organisms on earth evolved from a single proto-organism by
descend with modification,
(2) the primary force of evolution is natural selection.
• Natural selection is not the only force of evolution, may not even be a
dominant force. The alternative mechanisms: transmutation theory,
Lamarckism, geographical isolation, and nonadaptive evolution.
• Mutationism: represented by the post-Mandelian geneticist Morgan in 1920’s.
A strong critic of natural selection, argued for the importance of
advantageous mutations. Natural selection merely serves as a sieve to filter
deleterious mutations. (Also proposed that some part of morphological
evolution is caused by neutral mutation.)
Nei, M. 2005. Selectionism and neutralism in molecular evolution. Mol. Biol. Evol. 22:2318-2342.
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• Neo-Darwinism: Represented by Fisher, Wright, Haldane, Dobzhansky in the
30-50’s. Natural selection is claimed to play much more role than mutation.
Two main reasons:
(1) the amount of genetic variation contained in natural populations
are so large that any genetic change can occur by natural selection
with no need of new mutations,
(2) math showed that the gene frequency change by selection the
change by mutation.
• Neutralism in 60’s: The foundation of Neo-Darwinism started to shake as
molecular data on evolution accumulated in the 60’s. Evidence:
(1) Amino acid sequences show that most amino acid substitutions in
a protein do not change the protein function (hemoglobins 血红蛋白 ,
cytochrome c 细胞色素 , fibrinopetides 纤维蛋白钛 ),
(2) Genetic variation within populations is much higher than
previously thought.
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Neutral Theory of Molecular Evolution
Neutral theory: Most molecular polymorphism and substitutions are due to neutral
mutations and genetic drift. Genetic drift is the main force changing allele
frequencies.
Hemoglobins are evolving at a steady rate of 1.410-7 amino acid substitutions/yr ~
one nucleotide pair/2 yr (too high based on the cost of natural selection).
Kimura (1968) argued that many of the substituted alleles must be neutral.
King and Jukes independently proposed that most amino acid substitutions are
neutral. The inverse relationship between the importance of a protein or site
within a protein and its rate of evolution (Principle of Molecular Evolution).
Kimura, M. 1968. Evolutionary rate at the molecular level. Nature 217:624-626.King, J. L. and Jukes, T. H. 1969. Non-Darwinian evolution. Science 164:788-798.
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Items Population genetics Macroecology
Operational units Population MetacommunitySubdivision Subpopulations Local communitiesFocal unit Gene SpeciesObserved data Allele frequency Species abundance
Neutral definition Alleles are selectively neutral, Individuals have equal vital ratesselection coefficient 0, or < 1/2Ne
Driving forces Genetic drift (1/2Ne) Ecological drift (1/JM or 1/JL)
Mutation SpeciationGene flow among subpopulations Dispersal among local communities
Spatial structure Population genetic structure Species distribution and abundancevariation among local communities
Model Island model Island biogeographyStepping stone modelIsolation by distance Dispersal limitationMainland-island Metacommunity-local communityCline pattern (speciation phases)
Measurement Fis diversity
Fst diversity
Spatial autocorrelation Species-area power law
Parameters = 4Ne = 4JM or = 4JL
Average number of migrants (Nem) Average number of migrants (JLm)
Effective population size (Ne) Effective community size (JM or JL)
Distribution of allele frequency Distribution of species abundance Fixed (extinct) probability of an allele Fixed (extinct) probability of a species
Assembly rules Genetic drift/mutation Ecological drift/speciationGenetic drift/migration Ecological drift/dispersalGenetic drift/migration/mutation Ecological drift/dispersal/ speciation
Mathematical tools Statistical methods Statistical methodsDiffusion model Diffusion modelCoalescent theory Phylogeny
Hu et al. 2006. Oikos 113:548-556.
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Infinite-allele Model
1
2 11
1)1( tt F
NNF
Ft: the probability that two randomly sampled alleles at generation t are identical.
: mutation rate.
1
1
12
1
NF N2where
121
2
N
ND Heterozygosity expected from
mutation vs random drift.
Kimura, M. & Crow, J.F. 1964. The number of alleles that can be maintained in a finite population. Genetics 49:725-738.
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Frequency of Spectrum
Ewens, W.J. 1972. The sampling theory of selectively neutral alleles. Theor. Popul. Biol. 3:87-112.
11)1()( xxx 10 x
N2where
)( within alleles ofnumber )( dxx, xdxx
1
0
1)(
n
in i
SE
n
SE n 1ln)(
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Age of Species
)ln(1
2)( pp
pNpt
p
Tim
e
Kimura, M. 1983. The neutral allele theory of molecular evolution. Cambridge Univ. Press.
Overestimate the age of tree species in orders!
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CommunityPatterns
Speciescomposition
Spatialstructure
Temporalstructure
Agestructure
Sizestructure
Atmospheric inputs
Edaphic conditionsGeographical processes
Disturb:
WindsFires
LoggingPollution
.....
Geneticstructure
Community Assembly Rules
BirthDeath
GrowthCompetition
Predation.....
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Hubbell’s Neutral Theory
• Random walk
• Dispersal limitation
• Speciation
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Metacommunity Neutral Model
112
2
N
ND
Expected diversity (Simpson index):
Hubbell, S.P. 2001. The unified neutral theory of biodiversity and biogeography. Princeton Univ. Press.
Expected # of species:
Species-abundance model:
n
xnf
n)(
n
SE n 1ln)(
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Random Walk
j-1 j+1j0 N
Extinction FixationInitial state
1...0000
..................
0...0
0...0
0...0001
222
111
prq
prq
0
2
1
N
…
0 1 2 3 … N
1,1,,
1,
1,
1
1
1
jjjjjjj
jjj
jjj
pppr
N
jN
N
jpq
N
j
N
jNpp
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Coexistence of Neutral Species
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Probability of Extinction
Competitive exclusion in the two species system
occurs if the red species starting from j is finally
absorbed into either state N (the red species wins)
or 0 (the blue species wins).
The probability to extinction is defined as chance
for the focal species traveling from j to 0.
j-1 j+1j0 N
Extinction FixationInitial state
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Time to Extinction
The time to extinction is defined as the average #
of steps for the focal species traveling from j to N
or 0.
j-1 j+1j0 N
Extinction FixationInitial state
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j
tj
N = 20
j
pj
N = 20
Extinction probability Extinction time
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Differential Birth Rates
Zhang and Lin (1997) consider the case of differential birth rates
1,1,,
1,
1,
1
)1(
1
jjjjjj
jj
jj
ppp
jjuN
jN
N
jp
jujN
uj
N
jNp
t
u
N = 100j = 50
u 1, higher birth rate in focal species
Zhang, D. Y. & Lin, K. 1997. The effects of competitive asymmetry on the rate of competitive displacement: how robust is Hubbell’s community drift model? J Theor Biol 188:361-367.
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Differential Death Rates
Yu et al (1998) consider
the case of differential
death rates by simulation.
Yu, D. W., Terborgh, J. W. & Potts, M. D. 1998. Can high tree species richness be explained by Hubbell’s null model? Ecol Lett 1:193-199.
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Differential Birth & Death Rates
Metacommunity model
1,1,,
1,
1,
1
)1(
1
jjjjjj
jj
jj
ppp
jjuN
jN
jvjN
vjp
jujN
uj
jvjN
jNp
)(
)(
jNQPj
jNQ
jvjN
jN
P is the prob of sampling an individual from the
focal species (abundance = j) and Q is the prob
of sampling an individual from the other species
(abundance = N-j). P+Q =1. If we randomly
sample one individual from the community (to
kill), the prob that the sampled individual belongs
to the other species (not the focal species) is:
This leads to , where Q
Pv
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Effects of Birth and Death Rates on Coexistence Prob.
1.01.2
1.41.6
1.82.01.0
1.2
1.4
1.6
1.8
2.0
0.00.20.40.60.81.0
v
u
ej
u
v
1.0 1.2 1.4 1.6 1.8 2.01
.01
.21
.41
.61
.82
.0
c
extinction
fixation
d
N = 50j = 25
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1.01.2
1.41.6
1.82.01.0
1.2
1.4
1.6
1.8
2.0
0.00.20.40.60.81.0
u
v
ej
1.0 1.2 1.4 1.6 1.8 2.01
.01
.21
.41
.61
.82
.0
ef
extinction
fixation
N = 50j = 45
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Effects of Birth and Death Rates on Coexistence Time
N = 50j = 25
1.01.2
1.41.6
1.82.01.0
1.2
1.4
1.6
1.8
2.0
5001000
1500
v
u
tj
1.0 1.2 1.4 1.6 1.8 2.01
.01
.21
.41
.61
.82
.0
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N = 50j = 25
1.0 1.2 1.4 1.6 1.8 2.0
1.0
1.2
1.4
1.6
1.8
2.0
v
1.01.2
1.41.6
1.82.01.0
1.2
1.4
1.6
1.8
2.0
200400600800
10001200
v
u
tj
e f
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t-u profiles for different death rates v’s.
N = 50j = 25
vu
t1.0 1.2 1.4 1.6 1.8 2.0
50
01
50
0
1.0 1.2 1.4 1.6 1.8 2.0
50
01
50
01.0 1.2 1.4 1.6 1.8 2.0
50
01
50
0
1.0 1.2 1.4 1.6 1.8 2.05
00
15
00
1.0 1.2 1.4 1.6 1.8 2.0
50
01
50
0
v = 1 v = 1.1tj
v = 1.5 v = 1.8 v = 2
u u u
tj
1.0 1.2 1.4 1.6 1.8 2.0
50
01
50
0
v = 1.2
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Local Community Model
1,1,,
1,
1,
1
)1()1(
)1(
1)1(
jjjjjj
jj
jj
ppp
mjjuN
jNm
jvjN
vjp
mjujN
ujm
jvjN
jNp
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Effects of Birth and Death Rates on Extinction
1.01.2
1.41.6
1.82.00.0
0.2
0.4
0.6
0.8
1.0
0.00.20.40.60.81.0
u
ej
m1.0
1.21.4
1.61.8
2.00.0
0.2
0.4
0.6
0.8
1.0
0.00.20.40.60.81.0
u
N = 50j = 5
N = 50j = 25
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1.01.2
1.41.6
1.82.00.00
0.05
0.10
0.15
0.20
2e+054e+056e+058e+05
1.01.2
1.41.6
1.82.00.0
0.2
0.4
0.6
0.81.0
0e+002e+144e+146e+148e+141e+15
v=1
1.01.2
1.41.6
1.82.00.0
0.2
0.4
0.6
0.81.0
0e+00
1e+13
2e+13
3e+13
1.01.2
1.41.6
1.82.00.00
0.05
0.10
0.15
0.20
2e+054e+056e+058e+051e+06
v=1.2
tj
tj
u
m
u
m
Effects of Birth, Death & Immigration Rates on Coexistence
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Summary
1. The nearly neutral model which generalizes Hubbell’s neutral theory.
2. Birth and death have compensatory effects on coexistence but their
effects are not symmetric. Birth rates must be slightly higher than death
rates to maintain maximum coexistence.
3. The nearly neutral models provide a potential theory for reconciling
neutral and niche paradigms (?)
4. Immigration cannot prevent eventual extinction of a species but will
always increase the time of coexistence.
5. Nearly neutral systems have substantially shorter time of coexistence
than that of neutral systems. This reduced time provides a promising
solution to the “problem of time”.
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Metacommunity model
1,1,,
1,
1,
1
)1()1(
)1(
1)1(
jjjjjj
jj
jj
ppp
mjjuN
jNm
jvjN
vjp
mjujN
ujm
jvjN
jNp
1,1,,
1,
1,
1
)1(
1
jjjjjj
jj
jj
ppp
jjuN
jN
jvjN
vjp
jujN
uj
jvjN
jNp
1,1,,
1,
1,
1
1
1
jjjjjj
jj
jj
ppp
N
jN
N
jp
N
j
N
jNp
1,1,,
1,
1,
1
)1(1
)1(
1)1(
jjjjjj
jj
jj
ppp
mN
jNm
N
jp
mN
jm
N
jNp
Local community model
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The variation in birth and death rates
(subject to niche differentiation) determines
the fitness landscape. The focal species j
has a higher fitness (higher u, lower v) than
the other species. In this case, there is a
strong competitive exclusion, thus a short
coexistence time.
v
u
t
The effects of birth rate (u) and death
rate (v) on species coexistence are not
symmetric. A slightly higher birth rate
than the death rate is needed to
maintain a maximum coexistence.
x
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The Problem of Time
v
u
t
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Future Work
1. Derive macroecological patterns (species-abundance
distribution, species-area curves etc) as functions of u,
v and m.
2. Investigate trade-off in u and v.
3. Develop methods for testing the nearly neutral theory.