ICTP Humanes

Transcript

1. Matrix models in coral
   metapopulations
   Presented by: adriana humanes
   Under the supervision of: maria josefina Hernandez
   

   View Slide

2. Metapopulations in marine environments
   Is it possible to study marine populations under a metapopulation
   view?
   X ...in the sea there are no evident physical barriers that limit the
   dispersal and migration of individuals
   Waples 1989, Caley et al. 1996, Grimm et al. 2003, Smedbol et al. 2004
   Various authors consider that...
   

   View Slide

3. ü The bathymetry
   Metapopulations in marine environments
   

   View Slide

4. ü The bathymetry
   ü Currents patterns
   Metapopulations in marine environments
   

   View Slide

5. ü The bathymetry
   ü Currents patterns
   ü Frequent perturbations
   Metapopulations in marine environments
   

   View Slide

6. ü The bathymetry
   ü Currents patterns
   ü Frequent perturbations
   ü Climate events
   Metapopulations in marine environments
   

   View Slide

7. ü The bathymetry
   ü Currents patterns
   ü Frequent perturbations
   ü Climate events
   ü Coastal developments
   Metapopulations in marine environments
   

   View Slide

8. ¿Is it possible to study marine populations under a
   metapopulation view?
   X ...in the sea there are no evident physical barriers that can
   limit the dispersal and migration of individuals
   ü ...can act as barriers breaking temporal and spatial connections
   between local populations.
   Waples 1989, Caley et al. 1996, Ruzzante et al. 1998, Grimm et al. 2003, Smedbol et al. 2004
   Metapopulation approach in marine species
   ü...local populations can have dynamics that are not dependent on
   the input of external individuals, although eventual interchanges
   may exist
   Metapopulations in marine environments
   

   View Slide

9. Local populations that inhabit patches with discrete geographic
   limits, where dispersion between patches is not so low to limit
   the connectivity with demographic importance, but no so high for
   considering everything as one population Sale et al 2006.
   Metapopulations in marine environments
   

   View Slide

10. Mumby 1999, 2006
    * Hard to delimit populations (larval stage)
    * Relationship between physical and biotic factors is unknown at
    temporal and spatial scales
    CORALS:
    * Difficulty in the estimation of life history traits:
    Indeterminate growth, colonials, partial mortality, fission, vital rates vs size,
    sexual reproduction : “brooders” and “spawners”
    Solutions: molecular biology, technology, autoecology
    Metapopulations in marine environments
    

    View Slide

11. Matrix models in populations
    Corals:
    Size: area of the colony that
    is alive and determines F, P,
    S, G.
    Matrix models
    Colonial organisms:
    Model with size structure
    (vital rates related to the size
    of the colony)
    

    View Slide

12. Hughes 1984, Hughes y Connell 1987, Done 1987, 1988, Babcok
    1991, Ruessink 1997, Hughes y Tanner 2000, Fong y Glynn 2000,
    Lirman y Miller 2003, Smith et al. 2005, Edmunds y Elahi 2007
    Dynamic equation:
    Density-independent
    constant environment
    (constant matrix)
    Matrix models in coral populations
    Predictions:
    * Dominant Eigenvalue (λ) = growth
    rate
    * Grows (λ>1) or decreases (λ <1)
    exponentially.
    * Stable size distribution
    Ã= =
    

    View Slide

13. Metapopulation model proposal for Caribbean corals
    R J A
    0 0 f*r
    g l s
    0 g l
    R J A
    0 0 f*r
    g l s
    0 g l
    Ā =
    0 0 f(1-r)
    0 0 0
    0 0 0
    0 0 f(1-r)
    0 0 0
    0 0 0
    Time interval: 1 year
    Larvae migration
    r: proportion of larvae that stay
    Inclusion of:
    Fecundity
    Recruits: survival and growth
    

    View Slide

14. Metapopulation matrix for agaricia agaricites
    Van Moorsel 1983, Hughes 1984, Hughes & Tanner 2000, Brazeau et al. 2005, Ramula & Lehtilä 2005
    Brooders release larvae for several months
    (5 months in Belice and 9 in Curaçao)
    Brooders larvae: able to settle 4 hours
    after release up to 3 months
    Majority recruits near parental colonies
    but migration may also occur
    The matrix:
    Hughes 1984, Hughes & Tanner 2000
    RB: 2 matrices (calm and storm)
    

    View Slide

15. Size average fecundity:
    F
    i
    = P * mi
    P: survival of larvae until recruitment per unit time t
    mi
    : average number of larvae produced by colony of size i (maternity)
    Soong & Lang 1992
    Discovery Bay
    y = 0,0061x + 4,9388
    0
    1
    2
    3
    4
    5
    6
    7
    8
    9
    0 200 400 600 800 1000
    Talla (cm2)
    Maternidad (plánulas*cm2*año-1)
    Río Bueno
    y = 0,003x + 4,9697
    0
    1
    2
    3
    4
    5
    6
    7
    8
    9
    0 200 400 600 800 1000
    Van Moorsel (1983): larvae*cm2*day, puberty size
    Juveniles: 2-10cm2 non reproductive
    Adults 1: 10-50cm2, < maternity
    Adults 2: 50-500 cm2 (DB), 50-1000 cm2 (RB), > maternity
    Metapopulation matrix for agaricia agaricites
    

    View Slide

16. Average maternity of the sizes:
    Size frequency distribution
    of each class: unknown
    Minor and medium size
    Average
    maternity
    min. and max.
    Effect of extreme
    maternity values in
    the model
    Metapopulation matrix for agaricia agaricites
    Size (cm2)
    # colonies
    

    View Slide

17. 0.05
    0.1
    Migration
    0.5
    1
    Same reef
    Storm
    Calm
    Survival (%)
    Larvae survival until recruitment
    Higher in parental reef
    Lower during storm periods
    I assigned a hypothetical value to
    test the model
    Average maternity of the sizes:
    Size frequency distribution
    of each class: unknown
    Minor and medium size
    Average
    maternity
    min. and max.
    Effect of extreme
    maternity values in
    the model
    Metapopulation matrix for agaricia agaricites
    Size (cm2)
    # colonies
    

    View Slide

18. Recruits survival:
    Hughes & Jackson (1985): recruits tagged in each reef and followed
    for 3 years
    Larvae migration:
    Migration from RB to DB
    Almost closed population:
    10% of migration
    Open population:
    90% of migration
    Metapopulation matrix for agaricia agaricites
    

    View Slide

19. Ā =
    0 0 f*r f*r
    g l s s
    0 g l s
    0 g g l
    0 0 0 0
    0 0 0 0
    0 0 0 0
    0 0 0 0
    0 0 f(1-r) f(1-r)
    0 0 0 0
    0 0 0 0
    0 0 0 0
    0 0 f f
    g l s s
    0 g l s
    0 g g l
    R J A A
    R J A A
    Río Bueno
    Discovery Bay
    8 matrices
    Larvae migration (low and high)
    Fecundity (low and high)
    Environmental conditions (calm and storm)
    Growth rates
    each population
    each metapopulation
    Metapopulation matrix for agaricia agaricites
    

    View Slide

20. λ
    Without
    migration
    RB DB
    Āc Low fecundity 1.211 0.971
    Āt Low fecundity 1.070 0.864
    Āc High fecundity 1.669 1.325
    Āt High fecundity 1.522 1.129
    Hughes 1984 Āc 0.982
    Hughes 1984 Āt 0.889
    Hughes & Tanner 2000 0.673
    Inclusion F and Grecruits
    Predicts a higher growth rate
    RB: λ < 1 to > 1
    DB: λ < 1 t > 1 only with high fecundity
    Metapopulation matrix for agaricia agaricites
    

    View Slide

21. λ
    Without
    migration
    Low migration
    RB DB RB DB M
    Āc Low fecundity 1.211 0.971 1.198 0.971 1.198
    Āt Low fecundity 1.070 0.864 1.060 0.864 1.060
    Āc High fecundity 1.669 1.325 1.642 1.325 1.642
    Āt High fecundity 1.522 1.129 1.496 1.129 1.496
    Hughes 1984 Āc 0.982
    Hughes 1984 Āt 0.889
    Hughes & Tanner 2000 0.673
    Larvae migration:
    decreases λ RB
    Stay = λ DB
    Connecting the two populations by migration
    λ RB = M
    RB leads the
    dynamics of the
    Metapopulation
    Effect of
    migration
    RB
    source
    DB sink
    Metapopulation matrix for agaricia agaricites
    

    View Slide

22. λ
    Without
    migration
    Low migration High migration
    RB DB RB DB M RB DB M
    Āc Low fecundity 1.211 0.971 1.198 0.971 1.198 1.032 0.971 1.032
    Āt Low fecundity 1.070 0.864 1.060 0.864 1.060 0.942 0.864 0.942
    Āc High fecundity 1.669 1.325 1.642 1.325 1.642 1.230 1.325 1.325
    Āt High fecundity 1.522 1.129 1.496 1.129 1.496 1.122 1.129 1.129
    Hughes 1984 Āc 0.982
    Hughes 1984 Āt 0.889
    Hughes & Tanner 2000 0.673
    Many larvae migrate to the sink
    Extinction of the source
    Extinction of the metapopulation
    Metapopulation matrix for agaricia agaricites
    

    View Slide

23. STORMS EFFECT
    Decreases # reproductive colonies
    and fecundity
    limits the growth
    of populations
    Temporal projections
    Different storm frequency: alternating
    the storm and calm matrix
    Metapopulation matrix for agaricia agaricites
    

    View Slide

24. 1
    10
    100
    1000
    10000
    100000
    1000000
    10000000
    0 10 20 30 40 50
    1
    10
    100
    1000
    10000
    100000
    1000000
    10000000
    1975 1980 1985 1990 1995 2000 2005 2010
    Río Bueno Río Bueno* Discovery Bay
    Discovery Bay * Metapoblación
    Without storms
    1
    10
    100
    1000
    10000
    100000
    1000000
    10000000
    1975 1980 1985 1990 1995 2000 2005 2010
    Río Bueno Río Bueno* Discovery Bay
    Discovery Bay * Metapoblación
    Real frequency
    1
    10
    100
    1000
    10000
    100000
    1000000
    10000000
    0 10 20 30 40 50
    Every two years
    1
    10
    100
    1000
    10000
    100000
    1000000
    10000000
    0 10 20 30 40 50
    Rescue effect
    Metapopulation
    = RB
    Every year
    Low larvae migration, low fecundity
    Metapopulation matrix for agaricia agaricites
    * With migration
    

    View Slide

25. High larvae migration, low fecundity
    1
    10
    100
    1000
    10000
    100000
    1000000
    10000000
    0 10 20 30 40 50
    Every two years
    1
    10
    100
    1000
    10000
    100000
    1000000
    10000000
    0 10 20 30 40 50
    Every year
    1
    10
    100
    1000
    10000
    100000
    1000000
    10000000
    1970 1980 1990 2000 2010
    Río Bueno Río Bueno*
    Discovery Bay Discovery Bay *
    Metapoblación
    Real frequency
    1
    10
    100
    1000
    10000
    100000
    1000000
    10000000
    1975 1980 1985 1990 1995 2000 2005 2010
    Río Bueno Río Bueno* Discovery Bay
    Discovery Bay * Metapoblación
    1
    10
    100
    1000
    10000
    100000
    1000000
    10000000
    0 10 20 30 40 50
    Without storms
    Extinction
    Metapopulation matrix for agaricia agaricites
    * With migration
    

    View Slide

26. conclusions
    ü It is possible to construct
    metapopulation models for corals,
    however additional information of
    recruits transitions probability and
    fecundity are needed.
    üThe assumptions of this model are
    restrictive for doing long term
    projections (constant environment
    and density-independent population
    growth).
    ü The model can also be used to
    analize other migration scenarios.
    

    View Slide

27. conclusions
    In almost closed populations of Agaricia agaricites the
    metapopulation guarantees the persistance of the populations. For
    open populations, storm frequency leads extinctions.
    

    View Slide

28. Thanks!
    

    View Slide