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הרצאת סיום הדוקטורט שלי במכון למדעי החיים באוניברסיטה העברית.
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Extending Hubbell's neutral theory of biodiversity using ademographic model
Omri Allouche
Prof. Ronen Kadmon
EEB, HUJI December 2012
? Can there be one, unifying theory of species diversity?
The Big Question:
Ecological Communities show Semi-universal Patterns
Disturbance level:
Low
Medium
High
Habitat diversity
Habitat loss
ProductivityDisturbanceProductivity
Isolation
Regional diversity
Area
a b c
d e
f g hD
istu
rban
ce
Sp
ecie
s d
iver
sity
Sp
ecie
s d
iver
sity
Sp
ecie
s d
iver
sity
Saturated
Linear
Disturbance level:
Low
Medium
High
Habitat diversity
Habitat loss
ProductivityDisturbanceProductivity
Isolation
Regional diversity
Area
a b c
d e
f g hD
istu
rban
ce
Sp
ecie
s d
iver
sity
Sp
ecie
s d
iver
sity
Sp
ecie
s d
iver
sity
Saturated
Linear
Disturbance level:
Low
Medium
High
Disturbance level:
Low
Medium
High
Habitat diversity
Habitat loss
ProductivityDisturbanceProductivity
Isolation
Regional diversity
Area
a b c
d e
f g hD
istu
rban
ce
Sp
ecie
s d
iver
sity
Sp
ecie
s d
iver
sity
Sp
ecie
s d
iver
sity
Saturated
Linear
Habitat diversity
Habitat loss
ProductivityDisturbanceProductivity
Isolation
Regional diversity
Area
a b c
d e
f g hD
istu
rban
ce
Sp
ecie
s d
iver
sity
Sp
ecie
s d
iver
sity
Sp
ecie
s d
iver
sity
Habitat diversityHabitat diversity
Habitat lossHabitat loss
ProductivityProductivityDisturbanceDisturbanceProductivityProductivity
IsolationIsolation
Regional diversityRegional diversity
AreaArea
a b c
d e
f g hD
istu
rban
ce
Sp
ecie
s d
iver
sity
Sp
ecie
s d
iver
sity
Sp
ecie
s d
iver
sity
Saturated
Linear
Theories of community ecology
• Explain the distribution, abundance and interactions
of species
• Different assumptions
• Emphasize different factors as structuring ecological
communities
• Lack of a unified theory
The “godfathers” of modern community ecology
Niche theory (Hutchinson 1957)
• Communities are mainly deterministic assemblages of species, which have different niche characteristics
The theory of island biogeography (MacArthur and
Wilson 1967)
• Community structure is constantly changing. Species richness is determined by the balance between processes of extinction and colonization.
“Everything should be made as
simple as possible, but not any
simpler”
A. Einstein
Hubbell’s Neutral Theory of Biodiversity
Designing the Simplest Model of a Community
1. Individual-based
2. Individuals die and give birth
3. Functionally equivalent species
4. Single trophic level
1. No niches
2. No competitive hierarchy
3. No predation
4. No heterogeneity
5. No temporal variation
6. No dispersal limitation - Global dispersal
7. No differences among species
1. Island receiving immigrants from an
outer mainland
2. Constant community size – all sites are
occupied
3. In each time-step, one individual dies
and is immediately replaced by:
Immigrant m
Local offspring (1-m)
4. Neutral species – individuals are equal
in probability of death and
replacement, regardless of their
species identity
Hubbell’s Neutral Theory of Biodiversity
)()()(),( bababaB
j
regPm
JmP
)1(
)1(* **
1P
m
mJN
Analytic solution to Hubbell’s model
),(
),()(
**
**
JnPB
nnPnB
n
JnP
• Abundance distribution of each species
= The probability of each species to have 0,1,2,… individuals in the local community
• Species richness
J Community size
m Probability that a replacing individual is an immigrant
SR
m
J
J Community size
m Probability that a replacing individual is an immigrant
Determinants of Species Richness in Hubbell’s model
Neutral models fit empirical data
Volkov et al. 2007 Nature
Coral reef – various scales
Neutral models fit empirical data
He 2005 Func. Ecol.Volkov et al. 2005 Nature
Tropical forests
Trees
Hubbell’s model - Features
• Individual-based
• Analytically-tractable
• Fits species abundance distributions well
• Stochastic
• Emphasizes chance as structuring factor
• Non-equilibrium view of community structure
• Questions the importance of niches and differences among functionally-equivalent species
CRITICISM AGAINST THE NEUTRAL THEORY
Assumptions:
Constant community size
Confined demography
Strict neutrality
Applicability:
Limited scope
ΔN = B – D + I - E
Individual-based models and the importance of Demography
Is Hubbell’s model demographic?
J community size
m probability that a replacing individual is an immigrant
The demographic equation: ΔN = B – D + I - E
Includes processes of birth, death and immigration.
Demographic formulation of community dynamics
Relaxes the unrealistic assumptions of Hubbell’s model
Analytic solution
Able to qualitatively produce known patterns of species-diversity
Useful for the study of complex ecological phenomena
Develop a general demographic framework for modeling ecological
communities
The Aim:
The MCD Framework
The state of the community is described by the number of individuals of each species:
Community size: 5+3+2+7+3 = 20
Abundance of species 4: 2
Species richness: 5
Mortality
Emigrationk
Nr
Decrease by 1 in the number of individuals of species k
Possible events:
Local reproduction
Immigrationk
Ng
Increase by 1 in the number of individuals of species k
Possible transitions:from a state of
5 individuals of species 1 and
3 individuals of species 2:
The MCD Framework
k
Nr Decrease by 1 in the number of
individuals of species k
Possible events:
k
Ng Increase by 1 in the number of
individuals of species k
1
( ) M
k k
Sk k k k
k kN e N e N Nk
dP NP N e r P N e g P N g r
dt
1 if =
0 otherwisek l
k le
Abundance
Species Richness
{1,..., 1}
{1,..., 1}
1
1 0 ( 1)
( )kM
k k
k k
kNS
N m e
kk m N m e
gX N
r
Community size
Analytic Solution
1
( ) ( ) ( )MCD
N
P N X N X N
:
( ) ( )kk
MCD
N N J
p J P N
:
( ) ( )k
local
k MCD
N N n
P n P N
1
(1 (0))MS
local
k
k
SR P
1st application:
Single Species Population with
Competition for Space
• Island of area A
• Single species
• Rates of:
Birth b
Death d
Immigration i
• Individuals only establish in vacant sites
SINGLE SPECIES POPULATION WITH
COMPETITION FOR SPACE
Local reproduction:
Mortality:
Immigration from the regional
pool:
This is the stochastic formulation of the Levins’ model!
The community never occupies all available sites
Communities are never saturated
A deterministic model of reproduction and mortality* 1
eP
c
Levins’ Model of Metapopulation Dynamics (1969)
Levins’ model is a special case of the MCD framework.
2nd application:
Multispecies Community with
Competition for Space
• Island of area A
• Multiple species
• Rates of:
Birth bk
Death dk
Immigration ik
• Relative regional abundance
• Individuals only establish in vacant sites
MULTISPECIES COMMUNITY WITH COMPETITION FOR SPACE
k k
A Jb N dt
A
k kd N dt
( )reg
k ki P A J dt
Local reproduction:
Mortality:
Immigration from the regional
pool:
k
k kNr d N
k
N
reg
k k k k
g
A Jb N i P A
A
1
1( )
!
kM
k
regNS
k kNJ k
Jk k k
PA J bX N
A d N
The solution:
1
0
( )y
y
i
x x i
kk
k
iA
b
• Area A
• Geographic isolation i
• Habitat quality b, d
• Habitat adaptation bk, dk
• Life-history trade-offs bk / dk
• Local-regional relationship
• Mechanisms:
• More Individuals Hypothesis
• Rescue Effect
• Dilution effect
Multispecies Community with Competition for Space
Assumptions:
Constant community size
Confined demography
Strict neutrality
Applicability:
Limited scope
CRITICISM AGAINST THE NEUTRAL THEORY
• Individual-based
• Explicit consideration of demographic processes:
Reproduction, mortality and migration
• Demographic differences among species
• Analytically tractable
• Highly flexible
The MCD Framework
Connecting Hubbell’s Model to the
MCD Framework
SR
mb
d
A
i
J
i Immigration
b Birth
d Death
A Area
J Community size
m Probability of replacement by immigrant
Connecting Hubbell’s model to the MCD framework
positive influence
negative influence
10
100
1000
1
0.1
0.01
0.001
10
100
J
m
SR
0.1 1 10
Basic Reproductive Rate
b
Connecting Hubbell’s model to the MCD framework
• Hubbell’s model forces a constant community size
• In our model community size changes according to the demographic processes that affect species abundance
• Still, given a community size J, the abundance distribution in both models is equal
( )( | ) ( | )
( )
MCD
MCD DLM
P NP N J P N J
p J
The MCD Framework as
a General Framework for Neutral Models
General framework for Neutral Models
k
k kNr d N
k
k kNr d J
Hubbell’s zero-sum model
( )k reg
k kN
A Jg bN iP A
A
k reg
k kNg bN iP
( ) ( )k reg
k kNbg N PJ i J ( )k
kNr d J N
(Hubbell 2001)
(Volkov et al. 2003, 2005, He 2005, Etienne et al. 2007)
(Haegeman & Etienne 2008)
( 1)
iAm
iA b Awhere: b dA i dA
Independent species
Community-level density-dependence
Relaxing Hubbell’s assumption of
Strict Neutrality
Assumptions:
Constant community size
Confined demography
Strict neutrality
Applicability:
Limited scope
Median Annual Growth
An
nu
al S
urv
ival
Are species neutral? (?!)
“Life history trade-offsequalize the per capita relative fitness of species in the community, which set the stage for ecological drift”
S. Hubbell (2001)
1
1( )
!
kM
k
regNS
k kNJ k
Jk k k
PA J bX N
A d N
1
0
( )y
y
i
x x i
kk
k
iA
b
Are species neutral?
Fitness = mortality
nimmigratio,
mortality
onreproducti
• Each species has specific demographic rates
• Replacing strict neutrality with trade-offs
• Species are equal in their fitness
• Analytic solution still applies
• No effect on species abundance and species richness!
Assumptions:
Constant community size
Confined demography
Strict neutrality
Applicability:
Limited scope
CRITICISM AGAINST THE NEUTRAL THEORY
Examples of More Complex Demography
Habitat preference
Site selection
Allee effect
Density dependence
Carrying capacity
(( )
)
k
k
k
k
k
k
H Hk reg
k k k kN
H
k H
k H H
A Jg b N i
v A
v A AP
A AA k
k kNr d N
( )
( )( )k reg
k k k kN
v A J
v A J Jg b N i P A k
k kNr d N
( )k reg
k
k
k kN
kk
k
N
N
A Jg b N i P A
A
( )k reg
k k k kN
A Jg b N i P A
A ( ) k
k k
k
k
k
kN
Nd
Kr bd N
k reg
k k k kNg b N i P A
k
k kNr d
JN
K
k
k kNr d N
Sample application:
Habitat Heterogeneity
Disturbance level:
Low
Medium
High
Habitat diversity
Habitat loss
ProductivityDisturbanceProductivity
Isolation
Regional diversity
Area
a b c
d e
f g h
Dis
turb
an
ce
Sp
ecie
s d
iver
sity
Sp
ecie
s d
iver
sity
Sp
ecie
s d
iver
sity
Saturated
Linear
Disturbance level:
Low
Medium
High
Habitat diversity
Habitat loss
ProductivityDisturbanceProductivity
Isolation
Regional diversity
Area
a b c
d e
f g h
Dis
turb
an
ce
Sp
ecie
s d
iver
sity
Sp
ecie
s d
iver
sity
Sp
ecie
s d
iver
sity
Saturated
Linear
Disturbance level:
Low
Medium
High
Disturbance level:
Low
Medium
High
Habitat diversity
Habitat loss
ProductivityDisturbanceProductivity
Isolation
Regional diversity
Area
a b c
d e
f g h
Dis
turb
an
ce
Sp
ecie
s d
iver
sity
Sp
ecie
s d
iver
sity
Sp
ecie
s d
iver
sity
Saturated
Linear
Habitat diversity
Habitat loss
ProductivityDisturbanceProductivity
Isolation
Regional diversity
Area
a b c
d e
f g h
Dis
turb
an
ce
Sp
ecie
s d
iver
sity
Sp
ecie
s d
iver
sity
Sp
ecie
s d
iver
sity
Habitat diversityHabitat diversity
Habitat lossHabitat loss
ProductivityProductivityDisturbanceDisturbanceProductivityProductivity
IsolationIsolation
Regional diversityRegional diversity
AreaArea
a b c
d e
f g h
Dis
turb
an
ce
Sp
ecie
s d
iver
sity
Sp
ecie
s d
iver
sity
Sp
ecie
s d
iver
sity
Saturated
Linear
Disturbance level:
Low
Medium
High
Habitat diversity
Habitat loss
ProductivityDisturbanceProductivity
Isolation
Regional diversity
Area
a b c
d e
f g h
Dis
turb
an
ce
Sp
ecie
s d
iver
sity
Sp
ecie
s d
iver
sity
Sp
ecie
s d
iver
sity
Saturated
Linear
Disturbance level:
Low
Medium
High
Habitat diversity
Habitat loss
ProductivityDisturbanceProductivity
Isolation
Regional diversity
Area
a b c
d e
f g h
Dis
turb
an
ce
Sp
ecie
s d
iver
sity
Sp
ecie
s d
iver
sity
Sp
ecie
s d
iver
sity
Saturated
Linear
Disturbance level:
Low
Medium
High
Disturbance level:
Low
Medium
High
Habitat diversity
Habitat loss
ProductivityDisturbanceProductivity
Isolation
Regional diversity
Area
a b c
d e
f g h
Dis
turb
an
ce
Sp
ecie
s d
iver
sity
Sp
ecie
s d
iver
sity
Sp
ecie
s d
iver
sity
Saturated
Linear
Habitat diversity
Habitat loss
ProductivityDisturbanceProductivity
Isolation
Regional diversity
Area
a b c
d e
f g h
Dis
turb
an
ce
Sp
ecie
s d
iver
sity
Sp
ecie
s d
iver
sity
Sp
ecie
s d
iver
sity
Habitat diversityHabitat diversity
Habitat lossHabitat loss
ProductivityProductivityDisturbanceDisturbanceProductivityProductivity
IsolationIsolation
Regional diversityRegional diversity
AreaArea
a b c
d e
f g h
Dis
turb
an
ce
Sp
ecie
s d
iver
sity
Sp
ecie
s d
iver
sity
Sp
ecie
s d
iver
sity
Saturated
Linear
1. An island consisting of A sites, divided among H habitats
2. Each species is able to establish and persist in only one habitat
3. Individuals disperse and immigrate to random sites
Habitat Heterogeneity
( ) k kk reg
k k k k
H H
N
Ag b N
Ji
AP A
k
k kNr d N
1 1
1( ) 1
!
kM
k
h
regNSH k k
Nkh hJ J
h k k k
PbX N A J
A d N
The Area-Heterogeneity Tradeoff (AHTO)
“Unless niche width of all species is
unlimited, any increase in
environmental heterogeneity within
a fixed space must lead to a
reduction in the average amount of
effective area available for individual
species”
Empirical Test of the AHTO
Predictions
Study System
• Breeding bird distributions in Catalonia (NE Spain)
• 372 UTM cells of 10x10 km
• Measure Elevation Range in a radius around each cell
• Two distinct surveys
– 1975-1982 with most data collected in 1980-82
– 1999-2002
• Interval between the two surveys (two decades) was larger than the typical lifespan of most bird species
• 10x10km is small enough to detect extinction events but large enough to show within-cell heterogeneity in conditions
• Data include estimates of species abundance
Increasing Niche Width shifts the inflection point to Higher Heterogeneity values
AHTO – Meta-analysis
• 54 datasets with data on
area, elevation range and species
richness
• 43 show positive relationship
• After correcting for the effect of area:
• 6 positive
• 14 unimodal
• 30 non-significant
• Similar results for habitat diversity
Sample application:
Habitat Loss
HABITAT LOSS
• Classically studied using Species-Area curves
• No mechanistic view
• Mostly deterministicmodels
0 20 40 60 80 1000
20
40
60
80
100
Habitat loss (%)
Specie
s r
ichness
1.5
3
5
10
Reproduction
AD = The number of destroyed sites
Habitat Loss“The greatest existing threat to biodiversity “
( )k reg
k k kD
kN
A Jg b N i P A
A
A
k
k kNr d N
k
k
k
iA
b1
1( ) ,
!
kM
k
regNS
k kND J k
Jk k k
PA A J bX N
A d N
The MCD Framework
• General framework for modeling ecological communities
• Individual-based
• Stochastic
• Basic demographic processes
• Demographic differences among species
• Analytically tractable
• Relaxes the unrealistic assumptions of Hubbell’s model
The MCD Framework
• Provides a stochastic, multispecies version of Levins’
model
• A general framework for neutral models
• Highly flexible
• Useful for the study of complex ecological phenomena
• Provides novel predications
Disturbance level:
Low
Medium
High
Habitat diversity
Habitat loss
ProductivityDisturbanceProductivity
Isolation
Regional diversity
Area
a b c
d e
f g h
Dis
turb
an
ce
Sp
ecie
s d
iver
sity
Sp
ecie
s d
iver
sity
Sp
ecie
s d
iver
sity
Saturated
Linear
Disturbance level:
Low
Medium
High
Habitat diversity
Habitat loss
ProductivityDisturbanceProductivity
Isolation
Regional diversity
Area
a b c
d e
f g h
Dis
turb
an
ce
Sp
ecie
s d
iver
sity
Sp
ecie
s d
iver
sity
Sp
ecie
s d
iver
sity
Saturated
Linear
Disturbance level:
Low
Medium
High
Disturbance level:
Low
Medium
High
Habitat diversity
Habitat loss
ProductivityDisturbanceProductivity
Isolation
Regional diversity
Area
a b c
d e
f g h
Dis
turb
an
ce
Sp
ecie
s d
iver
sity
Sp
ecie
s d
iver
sity
Sp
ecie
s d
iver
sity
Saturated
Linear
Habitat diversity
Habitat loss
ProductivityDisturbanceProductivity
Isolation
Regional diversity
Area
a b c
d e
f g h
Dis
turb
an
ce
Sp
ecie
s d
iver
sity
Sp
ecie
s d
iver
sity
Sp
ecie
s d
iver
sity
Habitat diversityHabitat diversity
Habitat lossHabitat loss
ProductivityProductivityDisturbanceDisturbanceProductivityProductivity
IsolationIsolation
Regional diversityRegional diversity
AreaArea
a b c
d e
f g h
Dis
turb
an
ce
Sp
ecie
s d
iver
sity
Sp
ecie
s d
iver
sity
Sp
ecie
s d
iver
sity
Saturated
Linear
Disturbance level:
Low
Medium
High
Habitat diversity
Habitat loss
ProductivityDisturbanceProductivity
Isolation
Regional diversity
Area
a b c
d e
f g h
Dis
turb
an
ce
Sp
ecie
s d
iver
sity
Sp
ecie
s d
iver
sity
Sp
ecie
s d
iver
sity
Saturated
Linear
Disturbance level:
Low
Medium
High
Habitat diversity
Habitat loss
ProductivityDisturbanceProductivity
Isolation
Regional diversity
Area
a b c
d e
f g h
Dis
turb
an
ce
Sp
ecie
s d
iver
sity
Sp
ecie
s d
iver
sity
Sp
ecie
s d
iver
sity
Saturated
Linear
Disturbance level:
Low
Medium
High
Disturbance level:
Low
Medium
High
Habitat diversity
Habitat loss
ProductivityDisturbanceProductivity
Isolation
Regional diversity
Area
a b c
d e
f g h
Dis
turb
an
ce
Sp
ecie
s d
iver
sity
Sp
ecie
s d
iver
sity
Sp
ecie
s d
iver
sity
Saturated
Linear
Habitat diversity
Habitat loss
ProductivityDisturbanceProductivity
Isolation
Regional diversity
Area
a b c
d e
f g h
Dis
turb
an
ce
Sp
ecie
s d
iver
sity
Sp
ecie
s d
iver
sity
Sp
ecie
s d
iver
sity
Habitat diversityHabitat diversity
Habitat lossHabitat loss
ProductivityProductivityDisturbanceDisturbanceProductivityProductivity
IsolationIsolation
Regional diversityRegional diversity
AreaArea
a b c
d e
f g h
Dis
turb
an
ce
Sp
ecie
s d
iver
sity
Sp
ecie
s d
iver
sity
Sp
ecie
s d
iver
sity
Saturated
Linear
2 4 6 8 100
40
80
120
Heterogeneity
1.5
3
5
10
0 200 400 600 800 10000
100
200
300
400
Regional Diversity
0 200 400 600 800 100020
40
60
80
100
Isolation
0 2 4 6 8 10100
300
500
Productivity
Low
Medium
High
RealityThe model
0 2 4 6 8 10
x 104
0
100
200
300
400
500
Area
Sp
ecie
s D
ivers
ity
0 20 40 60 80 1000
20
40
60
80
100
Habitat loss (%)
1.5
3
5
10
Sp
ecie
s D
ivers
ity
0.2 0.4 0.6 0.8 1
40
60
80
100
Productivity
b=1.55
1020
Sp
ecie
s D
ivers
ity
0
50
100
0 1 2
Disturbance
Semi-universal patterns
Limitations of The MCD Framework
• Solution applies only in some cases
• Single trophic level
• No competitive takeover
• Implicit space
• No sex
• No evolutionary processes
CRITICISM AGAINST THE NEUTRAL THEORY
Assumptions:
Constant community size
Confined demography
Strict neutrality
Applicability:
Limited scope
“… neutral theory in ecology is a first approximation to reality. Ideal gases do not exist, neither do neutral
communities. Similar to the kinetic theory of ideal gases in physics,
neutral theory is a basic theory that provides the essential ingredients to further explore
theories that involve more complexassumptions”
Special thanks to Ronen Kadmon, our lab members – past and present, Uzi Motro, Lewi Stone, Guy Sella, Gur Yaari, NadavShnerb, Sarit Levy, Jonathan Rubin, Liat Segal and many manyothers
AND TO YOU FOR LISTENING :)