ICTP Humanes

Transcript

1. Matrix models in coral metapopulations Presented by: adriana humanes Under

   the supervision of: maria josefina Hernandez

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...

3. ü The bathymetry Metapopulations in marine environments

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

5. ü The bathymetry ü Currents patterns ü Frequent perturbations Metapopulations

   in marine environments

6. ü The bathymetry ü Currents patterns ü Frequent perturbations ü

   Climate events Metapopulations in marine environments

7. ü The bathymetry ü Currents patterns ü Frequent perturbations ü

   Climate events ü Coastal developments Metapopulations in marine environments

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

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

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

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)

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= =

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

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)

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

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

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

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

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

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

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

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

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

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

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

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.

27. conclusions In almost closed populations of Agaricia agaricites the metapopulation

    guarantees the persistance of the populations. For open populations, storm frequency leads extinctions.

28. Thanks!