Extending Hubbells neutraltheory of biodiversity using ademographic model                      Omri Allouche              ...
?    The Big Question:    Can there be    one, unifying theory of    species diversity?
Ecological Communities show Semi-                                                      universal Patterns                 ...
Theories of community ecology• Explain the distribution, abundance and interactions  of species• Different assumptions• Em...
The “godfathers” of modern    community ecologyNiche theory (Hutchinson 1957)   • Communities are mainly deterministic ass...
Hubbell’s Neutral Theory     of Biodiversity“Everything should be made as simple as possible, but not any simpler”        ...
Designing the Simplest Model of                      a Community1.   Individual-based2.   Individuals die and give birth3....
Hubbell’s Neutral Theory of                                   Biodiversity1. Island receiving immigrants from an   outer m...
Analytic solution to Hubbell’s model                                                   J   B( n      P * , n*    n)J     C...
Determinants of Species Richness          in Hubbell’s modelJ   Community size                         mm   Probability th...
Neutral models fit empirical data         Coral reef – various scales                                       Volkov et al. ...
Trees                            Neutral models fit                             empirical data                            ...
Hubbell’s model - Features•   Individual-based•   Analytically-tractable•   Fits species abundance distributions well•   S...
CRITICISM AGAINST THE NEUTRAL THEORY Assumptions:      Constant community size      Confined demography      Strict neutra...
Individual-based models and the   importance of Demography        ΔN = B – D + I - E
Is Hubbell’s model demographic?Includes processes ofbirth, death andimmigration.J   community sizem   probability that a r...
The Aim:             Develop a general demographic          framework for modeling ecological                             ...
The MCD FrameworkThe state of the community is described by the numberof individuals of each species:                     ...
Possible events:  Increase by 1 in the number of                                           Local reproduction  individuals...
The MCD FrameworkPossible transitions:from a state of   5 individuals of species 1 and   3 individuals of species 2:
dP( N )   SM           k                                        k               k           k                P N   ...
Analytic Solution                                                                           k                           ...
1st application:          Single Species         Population with       Competition for Space
SINGLE SPECIES POPULATION WITH                  COMPETITION FOR SPACE• Island of area A• Single species• Rates of:        ...
Mortality:  Local reproduction:  Immigration from the regional  pool:This is the stochastic formulation of                ...
Levins’ Model of Metapopulation Dynamics                   (1969)A deterministic model of reproduction and mortality      ...
2nd application:           Multispecies         Community with       Competition for Space
MULTISPECIES COMMUNITY WITH             COMPETITION FOR SPACE• Island of area A• Multiple species• Rates of:         Birth...
Mortality:                                                k                                               rN              ...
Multispecies Community with Competition for Space•   Area                                A•   Geographic isolation        ...
CRITICISM AGAINST THE NEUTRAL THEORY Assumptions:      Constant community size      Confined demography      Strict neutra...
The MCD Framework• Individual-based• Explicit consideration of demographic processes:       Reproduction, mortality and mi...
Connecting Hubbell’s   Model to the  MCD Framework
Connecting Hubbell’s modelto the MCD frameworki   Immigrationb   Birth                        id   Death                  ...
1000J    100      10       1      0.1m     0.01    0.001      100                                             bSR       10...
Connecting Hubbell’s model to             the MCD framework• Hubbell’s model forces a constant community size• In our mode...
The MCD Framework asa General Framework for Neutral Models
General framework for Neutral ModelsHubbell’s zero-sum model(Hubbell 2001)             k                         reg      ...
Relaxing Hubbell’s                   assumption of                  Strict NeutralityAssumptions:         Constant communi...
Are species                         “Life history trade-offs       neutral? (?!)                     equalize the per capi...
Are species neutral?                                                                   ik                                 ...
CRITICISM AGAINST THE NEUTRAL THEORY Assumptions:      Constant community size      Confined demography      Strict neutra...
Examples of More Complex Demography                           k                     reg                                   ...
Sample application:        Habitat Heterogeneity    b                                       c                             ...
Habitat Heterogeneity1. An island consisting of A   sites, divided among H   habitats2. Each species is able to   establis...
k                    reg                                    AH k       J Hkg       N        (bk N k    ik P k      A)    ...
The Area-Heterogeneity Tradeoff (AHTO)“Unless niche width of all species isunlimited, any increase inenvironmental heterog...
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...
Increasing Niche Width shifts the inflection pointto Higher Heterogeneity values
AHTO – Meta-analysis• 54 datasets with data on  area, elevation range and species  richness• 43 show positive relationship...
Sample application:              Habitat Loss
HABITAT LOSS• Classically studied using  Species-Area curves• No mechanistic view• Mostly deterministic  models
Habitat Loss                                                                          “The greatest existing              ...
The MCD Framework• General framework for modeling ecological communities   • Individual-based   • Stochastic   • Basic dem...
The MCD Framework• Provides a stochastic, multispecies version of Levins’       model• A general framework for neutral mod...
Semi-universal patterns                                                                                          The model...
Limitations of The MCD Framework• Solution applies only in some cases• Single trophic level• No competitive takeover• Impl...
CRITICISM AGAINST THE NEUTRAL THEORY Assumptions:      Constant community size      Confined demography      Strict neutra...
“… neutral theory in ecology is a first approximation to  reality. Ideal gases do not exist, neither do neutral        com...
Special thanks to Ronen Kadmon, our lab members – past andpresent, Uzi Motro, Lewi Stone, Guy Sella, Gur Yaari, NadavShner...
הרצאת דוקטורט
הרצאת דוקטורט
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הרצאת דוקטורט

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הרצאת סיום הדוקטורט שלי במכון למדעי החיים באוניברסיטה העברית.

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  • All of these patterns remained statisticallysignificant after controlling for the effects of area, spatialautocorrelation, absolute elevation, mean annual temperature,mean annual rainfall, population density, and broad-scale spatialeffects (SI Appendix, SI Methods and Tables S1–S3). The unimodaleffect of heterogeneity on species richness was still significantafter the removal of four possible outliers (the two right-mostand two lowest points in Fig. 2D). Sampling effort had a statisticallysignificant effect on species richness for both survey periodsbut did not affect the results of the analyses (SI Appendix, SIMethods, Figs. S1 and S2, and Tables S4–S6).
  • Ronen Ron, Michael Kalyuzhni, Eyal Ben Hur, Rachel Shukrun, Hila Sagre and NivDeMalach
  • הרצאת דוקטורט

    1. 1. Extending Hubbells neutraltheory of biodiversity using ademographic model Omri Allouche Prof. Ronen KadmonEEB, HUJI December 2012
    2. 2. ? The Big Question: Can there be one, unifying theory of species diversity?
    3. 3. Ecological Communities show Semi- universal Patterns a b cSpecies diversity Area Isolation Habitat diversitySpecies diversity d e ar ne Li Saturated Disturbance level: Low Habitat loss Regional diversity Medium High f g hSpecies diversity Disturbance Productivity Disturbance Productivity
    4. 4. 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
    5. 5. The “godfathers” of modern community ecologyNiche theory (Hutchinson 1957) • Communities are mainly deterministic assemblages of species, which have different niche characteristicsThe 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.
    6. 6. Hubbell’s Neutral Theory of Biodiversity“Everything should be made as simple as possible, but not any simpler” A. Einstein
    7. 7. Designing the Simplest Model of a Community1. Individual-based2. Individuals die and give birth3. Functionally equivalent species4. 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
    8. 8. Hubbell’s Neutral Theory of Biodiversity1. Island receiving immigrants from an outer mainland2. Constant community size – all sites are occupied3. 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
    9. 9. Analytic solution to Hubbell’s model J B( n P * , n* n)J Community size P(n) n B( P* , n* J)m Probability that a B(a, b) (a) (b) (a b) replacing individual is m( J 1) j J m P* Preg N* P* an immigrant (1 m) 1 m • Abundance distribution of each species = The probability of each species to have 0,1,2,… individuals in the local community • Species richness
    10. 10. Determinants of Species Richness in Hubbell’s modelJ Community size mm Probability that a replacing individual is an SR immigrant J
    11. 11. Neutral models fit empirical data Coral reef – various scales Volkov et al. 2007 Nature
    12. 12. Trees Neutral models fit empirical data Tropical forests He 2005 Func. Ecol.Volkov et al. 2005 Nature
    13. 13. 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
    14. 14. CRITICISM AGAINST THE NEUTRAL THEORY Assumptions: Constant community size Confined demography Strict neutrality Applicability: Limited scope
    15. 15. Individual-based models and the importance of Demography ΔN = B – D + I - E
    16. 16. Is Hubbell’s model demographic?Includes processes ofbirth, death andimmigration.J community sizem probability that a replacing individual is an immigrantThe demographic equation: ΔN = B – D + I - E
    17. 17. The Aim: Develop a general demographic framework for modeling ecological communitiesDemographic formulation of community dynamicsRelaxes the unrealistic assumptions of Hubbell’s modelAnalytic solutionAble to qualitatively produce known patterns of species-diversityUseful for the study of complex ecological phenomena
    18. 18. The MCD FrameworkThe state of the community is described by the numberof individuals of each species: Community size: 5+3+2+7+3 = 20 Abundance of species 4: 2 Species richness: 5
    19. 19. Possible events: Increase by 1 in the number of Local reproduction individuals of species k Immigration k g  N Decrease by 1 in the number of individuals of species k Mortality k rN  Emigration
    20. 20. The MCD FrameworkPossible transitions:from a state of 5 individuals of species 1 and 3 individuals of species 2:
    21. 21. dP( N ) SM    k   k  k k P N ek rN  ek P N ek g N   ek P N gN  rN  dt k 1  1 if k = l ek l 0 otherwisePossible events: Increase by 1 in the number of k individuals of species k gN  Decrease by 1 in the number of k individuals of species k r  N
    22. 22. Analytic Solution k   1   SM N k 1 g N{1,...,k 1}   m ek PMCD ( N ) X (N ) X (N ) X (N ) k  N k 1 m 0 rN{1,...,k 1}   ( m 1) ek Community size p( J )  PMCD ( N ) N: Nk J k local Abundance Pk ( n)  PMCD ( N ) N : Nk n SMSpecies Richness SR (1 Pklocal (0)) k 1
    23. 23. 1st application: Single Species Population with Competition for Space
    24. 24. 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
    25. 25. Mortality: Local reproduction: Immigration from the regional pool:This is the stochastic formulation of the Levins’ model!
    26. 26. Levins’ Model of Metapopulation Dynamics (1969)A deterministic model of reproduction and mortality * e P 1 cLevins’ model is a special case of the MCD framework. Communities are never saturated The community never occupies all available sites
    27. 27. 2nd application: Multispecies Community with Competition for Space
    28. 28. 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
    29. 29. Mortality: k rN  dk Nk dk Nk dt Local reproduction: A J bk N k dt k gN  A A J reg Immigration from the regional bk Nk iP A k k pool: A ik Pkreg ( A J )dtThe solution: ik A  A J 1 SM bk Nk k Pkreg k bk J Nk X (N ) J y 1 A k 1 dk Nk ! ( x) y x i i 0
    30. 30. Multispecies Community with Competition for Space• Area A• Geographic isolation i• Habitat quality b, d• Habitat adaptation bk, dk• Life-history trade-offs bk / d k• Local-regional relationship• Mechanisms: • More Individuals Hypothesis • Rescue Effect • Dilution effect
    31. 31. CRITICISM AGAINST THE NEUTRAL THEORY Assumptions: Constant community size Confined demography Strict neutrality Applicability: Limited scope
    32. 32. The MCD Framework• Individual-based• Explicit consideration of demographic processes: Reproduction, mortality and migration• Demographic differences among species• Analytically tractable• Highly flexible
    33. 33. Connecting Hubbell’s Model to the MCD Framework
    34. 34. Connecting Hubbell’s modelto the MCD frameworki Immigrationb Birth id Death m bA Area SR dJ Community size Jm Probability of replacement A by immigrant positive influence negative influence
    35. 35. 1000J 100 10 1 0.1m 0.01 0.001 100 bSR 10 0.1 1 10 Basic Reproductive Rate
    36. 36. 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   PMCD ( N )  PMCD ( N | J ) PDLM ( N | J ) p( J )
    37. 37. The MCD Framework asa General Framework for Neutral Models
    38. 38. General framework for Neutral ModelsHubbell’s zero-sum model(Hubbell 2001) k reg A J k g  N (bNk iP k A) rN  dk J k A iA where: b dA i dA m iA b( A 1)Independent species(Volkov et al. 2003, 2005, He 2005, Etienne et al. 2007) k gN  bN k iPkreg k rN  dk NkCommunity-level density-dependence(Haegeman & Etienne 2008) k g k  b( J ) Nk i( J ) P k reg r  N d ( J ) Nk N
    39. 39. Relaxing Hubbell’s assumption of Strict NeutralityAssumptions: Constant community size Confined demography Strict neutralityApplicability: Limited scope
    40. 40. Are species “Life history trade-offs neutral? (?!) equalize the per capita relative fitness of species in the community, which set the stage for ecological drift”Annual Survival S. Hubbell (2001) Median Annual Growth
    41. 41. Are species neutral? ik A  A J 1 SM bk Nk k Pkreg k bk J NkX (N ) J y 1 A k 1 dk Nk ! ( x) y x i i 0 reproducti on immigratio n Fitness = mortality , mortality• 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!
    42. 42. CRITICISM AGAINST THE NEUTRAL THEORY Assumptions: Constant community size Confined demography Strict neutrality Applicability: Limited scope
    43. 43. Examples of More Complex Demography k reg AHk J Hk vk AHk Habitat preference g  N (bk Nk i P A) k k k rN  dk Nk AHk vk AHk ( A AHk ) Site selection k v( A J ) gN  (bk N k ik Pkreg A) k rN  dk Nk v( A J ) J Allee effect k Nk A J k gN  (bk N k ik Pkreg A) rN  dk Nk Nk k A A J k NkDensity dependence g k  (bk Nk reg i P A) rN  dk (bk dk ) Nk N k k A Kk k k J Carrying capacity gN  bk Nk ik Pkreg A rN  dk Nk K
    44. 44. Sample application: Habitat Heterogeneity b c a b c Species diversity Isolation Area Habitat diversity Isolation Habitat ecies diversity e d e ar ar ine Line L D
    45. 45. Habitat Heterogeneity1. An island consisting of A sites, divided among H habitats2. Each species is able to establish and persist in only one habitat3. Individuals disperse and immigrate to random sites
    46. 46. k reg AH k J Hkg  N (bk N k ik P k A) A krN  dk Nk  1 H SM bk Nk k Pkreg NkX (N ) Ah Jh 1 AJ h 1 Jh k 1 dk Nk !
    47. 47. The Area-Heterogeneity Tradeoff (AHTO)“Unless niche width of all species isunlimited, any increase inenvironmental heterogeneity withina fixed space must lead to areduction in the average amount ofeffective area available for individualspecies”
    48. 48. Empirical Test of the AHTO Predictions
    49. 49. 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
    50. 50. Increasing Niche Width shifts the inflection pointto Higher Heterogeneity values
    51. 51. 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
    52. 52. Sample application: Habitat Loss
    53. 53. HABITAT LOSS• Classically studied using Species-Area curves• No mechanistic view• Mostly deterministic models
    54. 54. Habitat Loss “The greatest existing threat to biodiversity “ 100 Reproduction 1.5 80 3 Species richness 5 k A AD J 60 10gN  (bk Nk ik Pkreg A) A k 40rN  dk Nk 20AD = The number of 0 destroyed sites 0 20 40 60 80 100 Habitat loss (%)  A AD J 1 SM bk Nk k Pkreg ik J NkX (N ) , k A AJ k 1 dk Nk ! bk
    55. 55. 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
    56. 56. 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
    57. 57. Semi-universal patterns The model Reality a b c a b c Species diversity 500 Species diversity 100Species Diversity 120 400 80 300 80 60 200 40 1.5 100 40 3 5 0 10 20 0 0 2 4 6 8 10 0 200 400 600 800 1000 2 4 6 8 10 Area Area x 10 4 Isolation Isolation Habitat diversity Area Isolation Habitat diversity Heterogeneity 400 Species diversity Species diversity 100Species Diversity d 1.5 e d e 80 3 300 5 60 10 200 ar ar ne ne 40 Li Li 100 20 Disturbance level: Disturbance level: Saturated Saturated 0 Low Low 0 20 40 60 80 100 00 200 400 600 800 1000 Habitat loss Regional diversity Medium Habitat loss Regional diversity Medium Habitat loss (%) Regional Diversity High High f g h f g h Species diversity Species diversity 100 100 500Species Diversity Low Medium High Disturbance Disturbance 80 50 300 60 b=1.5 5 40 10 20 0 100 0.2 0.4 0.6 0.8 1 0 1 2 0 2 4 6 8 10 Productivity Disturbance Disturbance Productivity Productivity Productivity Disturbance Productivity Productivity
    58. 58. Limitations of The MCD Framework• Solution applies only in some cases• Single trophic level• No competitive takeover• Implicit space• No sex• No evolutionary processes
    59. 59. CRITICISM AGAINST THE NEUTRAL THEORY Assumptions: Constant community size Confined demography Strict neutrality Applicability: Limited scope
    60. 60. “… 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 complex assumptions”
    61. 61. Special thanks to Ronen Kadmon, our lab members – past andpresent, Uzi Motro, Lewi Stone, Guy Sella, Gur Yaari, NadavShnerb, Sarit Levy, Jonathan Rubin, Liat Segal and many manyothersAND TO YOU FOR LISTENING :)

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