Global disparity in the ecological benefits of reducing carbon emissions for coral reefs

Transcription

1 Global disparity in the ecological benefits of reducing carbon emissions for coral reefs Juan Carlos Ortiz*, Yves-Marie Bozec, Nicholas H. Wolff, Christopher Doropoulos, and Peter J. Mumby Supplementary methods: Simulation model description and parameterisation Model implementation The model is individual-based simulating the population dynamics of coral colonies dispatched across a regular square lattice of cells. The lattice grid is a toroidal structure so that every reef cell has continuous boundaries formed by 4 neighbouring cells. Each cell contains a mixture of living substrata (Tables S1 and S2) comprising multiple coral colonies and patches of algae. A number of cells are assigned to the class ungrazable substratum (e.g., sand) so that no benthic live cover can colonize those cells. The model captures rates of recruitment, growth, reproduction and mortality of corals and algae as well as their competitive interactions, calculated twice a year (every 6 months). At each time step, the toroidal lattice structure helps define probabilistic rules (within a 4-cell von Neumann neighbourhood) of competitive interactions between corals and macroalgae which reduce the growth rate of each coral taxon. Coral-algal competition is mediated by grazing randomly allocated over the grid. Grazing affects all algal classes and always results in cropped algae. The spatial arrangement of elements within an individual cell is not explicit, but coral-coral competition can occur at intra-cellular scales. Technically, the model updates a set of connected matrices (one matrix for each benthic cover) at discrete time steps according to the deterministic and probabilistic rules presented in tables S1 and S2. The model is implemented in MATLAB as a sequence of vectorized instructions (see Fig. S1) so that all the cells of the lattice grid are processed simultaneously for a given matrix. Each instruction reflects the action of a particular process occurring within a cell, in isolation or as a result of its immediate environment (4-cell von Neumann neighbourhood) defined at the previous time step. Within a time iteration, the four coral matrices are temporarily fused within a three-dimensional array ( ) for processing simultaneously all coral species. At the initial step, a number of cells are randomly designated as ungrazable cells to match the specified cover of ungrazable substratum (sand/gorgonian, etc). The remaining cells are filled with coral colonies until the total cover of each coral species reaches the desired level (as a percentage of the total reef area). Coral colony sizes are created based on a uniform distribution and each colony is randomly allocated to a cell. Each cell cannot contain more than one colony per species ( cm cells). Algal patches are created in a similar way by filling the remaining space according to their initial cover. Cover matrices are then processed and the resulting benthic covers are stored after every time iteration. The whole process (including initialisation) is repeated to obtain 100 independent reef trajectories over time. Model outputs include the cover (%) of each coral and algal species for every simulation run. NATURE CLIMATE CHANGE 1

2 Figure S1. Overview of model implementation. BC1, BC2, SC1 and SC2 represent the 4 coral types in the Caribbean model (for the Pacific model there are 6 types as explained in the next section). D and L represent macroalgal types (Dictyota and Lobophora). x and y represent the coordinates in the lattice. 2 NATURE CLIMATE CHANGE

3 SUPPLEMENTARY INFORMATION Table S1. Parameterisation of simulation model for the Caribbean Parameter Details Coral recruitment Corals recruit to cropped algae, A 6 and A 12, because algal turfs are not heavily sediment-laden. Recruit at size 1 cm 2. Recruitment rate of brooders and spawners (respectively): 2 and 0.2 per 0.25 m 2 of cropped algae per time interval. Recruitment rate was adjusted for rugosity (~2) and the cover of cropped algae at Glovers Reef 1. Coral growth Coral size is quantified as the cross-sectional, basal area of a hemispherical colony (cm 2 ). BC have a lateral extension rate of 0.8 cm yr -1 and SC grow slightly faster at 0.9 cm yr -1 (based on median rates for Porites astreoides, P. porites, Siderastrea siderea, Montastraea annularis, Colpophyllia natans and Agaricia agaricites) 2-6. Coral reproduction Excluded, assume constant rate of coral recruitment from outside reef (i.e. no stock-recruitment dynamics). Colonisation of Cropped algae arises (i) when macroalgae is grazed and (ii) after all coral mortality cropped algae events 7 except those due to macroalgal overgrowth (see coral-algal competition below). Colonisation of macroalgae Macroalgal growth over dead coral (cropped algae) Competition between corals Competition between corals and cropped algae Macroalgae have a 70% chance of becoming established if cropped algae are not grazed for 6 months (mostly Dictyota) and this increases to 100% probability after 12 mo of no grazing (mostly Lobophora). Rates acquired from detailed centimetre-resolution observations of algal dynamics with and without grazing, Box and Mumby unpub. data, 8. In addition to arising from cropped algae that are not grazed (above), established macroalgae also spread vegetatively over cropped algae (mostly Lobophora as Dictyota spread shows little pattern with grazing 8 ). The probability that macroalgae will encroach onto the algal turf within a cell, P A M, is given by (1) where M 4cells is the percent cover of macroalgae within the von Neumann (4-cell) neighbourhood 9. This is a key method of algal expansion and represents the opportunistic overgrowth of coral that was extirpated by disturbance. P A M = M 4cells (1) If corals fill the cell (2500 cm 2 ), the larger coral overtops smaller corals (chosen at random if more than one smaller coral share the cell). If corals have equal size, the winner is chosen at random 10. Corals always overgrow cropped algae 11. NATURE CLIMATE CHANGE 3

4 Competition between corals and macroalgae 1: effect of macroalgae on corals Competition between corals and macroalgae 2: effect of corals on macroalgae a) Growth rate of juvenile corals (area <60 cm 2 ) set to zero if M 4cells 80%, and reduced by 70% if 60% M 4cells <80%. Parameters based on both Dictyota and Lobophora 12 b) Growth rate of juvenile and adult corals (area 60cm 2 ) reduced by 50% if M 4cells 60% 11,13 c) Limited direct overgrowth of coral by macroalgae can occur 14,15. Nugues and Bak 16 found that the upper 95% CL of the mean area of overgrowth ranged from 0-18 cm 2 pa across a ~7cm length of coral edge, with an overall mean of 8 cm 2 pa. This translates to 4 cm 2 in each 6-mo time step of the model. Overgrowth (cm 2 ), O C M, was scaled to entire colonies using (2) where M 4cells is the proportion of macroalgae in the von Neumann 4-cell neighbourhood and P i is the perimeter of the coral. O C M = M 4cells P i /7 4 (2) Note that Nugues and Bak 16 did not find significant effects of Lobophora on all coral species studied. Whilst this was the correct interpretation of their data, the published results strongly suggest that an effect does exist and that a larger sample size may well have resulted in significant differences. Other studies have found negative effects of macroalgae on both massive 14 and branching corals 7. The probability with which macroalgae spread vegetatively over cropped algae, P A M (1) is reduced by 25% when at least 50% of the local neighbourhood includes coral 11,17 ( BC + SC) proportion of coral, C = 2500 (3a) P A M = 0.75 M 4cells if C 5cells 0.5 (3b) P A M = M 4cells if C 5cells < 0.5, (3c) where C 5cells is the proportion of corals in the 5 cell neighbourhood comprising the focal cell and the 4-cell von Neumann neighbourhood. 4 NATURE CLIMATE CHANGE

5 SUPPLEMENTARY INFORMATION Grazing by fishes & impact of fishing Partial-colony mortality of corals Grazing is spatially-constrained An unfished community of parrotfishes grazes a maximum of 40% of the seabed per 6 month time interval. The dynamic basis of this grazing threshold is poorly understood seeing as most measures of grazing take place at scales of seconds and most studies of algal dynamics take place on monthly scales (hence the use of a 6 month time step). Nonetheless empirical studies 19, and experimental results scaled to the complex forereef 18, have identified a grazing limit of 30%-40% of the reef during 6 months. This value allows for a numeric positive response by parrotfish after severe coral mortality events during which colonisation space for algae increases dramatically. For example, an increase in parrotfish biomass over 5 years maintained the cover of cropped algae at Glovers Reef at 30-40% after Hurricane Mitch caused extensive coral mortality and liberated new settlement space for macroalgae 8 (i.e. grazing impact remained at around 30% 6 mo. -1 even though coral cover dropped from around 60% to 20%, suggesting that the approach is robust during phase changes). The reasons for this are not fully understood. All parrotfish species graze algal turfs and in doing so constrain the colonisation and vegetative growth of macroalgae. Direct removal of macroalgae occurs through the grazing of larger sparisomid species (up to 50% of bites in S. viride, Mumby unpub. data) and natural fluctuations in algal dynamics including annual spawning events during which their cover is decimated 21. Of course, macroalgae increase once the availability of settlement space exceeds the grazing threshold (e.g. as coral cover declines from disturbance). During a given time interval, cells are visited in a random order and all algae consumed until the total grazing impact is reached. This approach implies spatially-intensive grazing which appears to be more biologically-accurate than a spatially-extensive approach because parrotfish feed repeatedly at particular sites on time scales of days to weeks 26. All turf and macroalgae are consumed (and converted to A 6 ) until the constraint is reached. A second, species-level model of parrotfish grazing was used to estimate the effect of fishing, which alters both the density and size-distribution of parrotfishes. The detailed parrotfish grazing model includes the species, size and life phase of individual fishes and predicts instantaneous grazing intensity; the total reef surface grazed per hour 19,20. New data on the size distribution of parrotfishes from Jamaica were used to determine grazing intensity from heavilyfished sites 20. Grazing intensities were found to be around one sixth that of unfished sites in Belize. Thus, fishing can reduce the instantaneous grazing intensity of parrotfish communities by at least six-fold. It was then assumed that this shift in grazing would hold linearly over a six month period and therefore the total proportion of reef effectively grazed over 6 months (i.e. the grazing parameter in the main simulation model) was reduced from 30-40% 6 mo. -1 (unfished) to 5% 6 mo. -1 (heavily fished). Size-dependent, following empirical observations from Curaçao before major bleaching or hurricane disturbances 22. State variables reported in literature converted to dynamic variables using least squares optimization until equilibrial state in model matched observed data. Implementation uses equations 4a (probability that a partial mortality event (Ppm) occurs for a given colony size) and 4b area of tissue (Apm) lost due to partial mortality for a given colony size. Both equations are basef on a regression equation provided by Meesters et al 22.where P pm is the probability of a partial mortality event, A pm is the area of tissue lost in a single event, and χ is the size of the coral in cm 2 : P pm = 1-[( x ln(χ))/100] Ln(A pm 100) = x ln(χ) (4b) (4a) NATURE CLIMATE CHANGE 5

6 Whole-colony mortality of juvenile and adult corals Predation on coral recruits Bleaching impact on corals: whole-colony mortality Bleaching impact on corals: partialcolony mortality Bleaching frequency Incidence of mortality in juvenile corals ( cm 2 ), 2% per time interval (~4% per annum). Halved to 1% (2% pa) for mature colonies (>250 cm 2 ) 23. These levels of mortality occur in addition to macroalgal overgrowth. Algal overgrowth and predation affects juvenile corals (see above and below). Instantaneous whole-colony mortality occurs from parrotfish predation at a rate of 15% each 6 month iteration of the model 12 Predation is confined to small corals of area 5cm 2, based on Meesters et al 22 where between 60% and 95% of bite-type lesions were of this size. Whole-colony mortality is modelled to be a function of the number of degree heating weeks predicted for a given location and year (data from Eakin et al. 24 ). Corals previously exposed to elevated temperatures have a reduced risk of mortality due to bleaching data from 25. Partial-colony mortality differs for brooders and spawners (data from McField 26 ) and is a function of the number of degree heating weeks predicted for a given location and year. Rather than being on or off for a given year, bleaching occurs at a range of temperatures, but with mortality dependent on the extent and duration of thermal stress. Bleaching does not occur if a hurricane has occurred that year. Table S2. Summary of differences between Caribbean growth forms (Modified from Ortiz et al 2013, data supported by table S1) Growth form Representative Growth Thermal Competitive Reproduction taxa rate tolerance ability against macroalgae strategy Encrusting/foliose Porites astreoides, Agaricia agaricites Massive Montastraea cavernosa Plate Mycetophyllia danaana Massive Montastraea annularis Slow Low Low Brooder Fast High High Spawner Slow Low Very High Brooder Fast High Intermediate Spawner Modifications of the basic Caribbean model for the Pacific parameterization: The structure of the Pacific model is the same as that of the Caribbean model. The main difference lies in that six coral types, of varying morphology, were included in the Pacific model with taxon-specific life history parameters, whereas four coral types were used in the Caribbean and two parameters, specifically rates of natural partial- and whole-colony mortality, did not vary among taxa, although varied with size. Many of the specific parameters for the Pacific corals are expressed as a function of the values used in the Caribbean model. 6 NATURE CLIMATE CHANGE

7 SUPPLEMENTARY INFORMATION Table S3. Modifications of the basic Caribbean model for the Pacific parameterization (parameters not included in this table were the same as for Caribbean parameterization). * represents Ortiz umpublished data from permanet transect on Heron Island (Great Barrier Reef) Coral colony growth rate (cm yr -1 ) Coral recruitment (Proportion of the maximum number of recruits m -2 ) Whole coral colony natural mortality (% of colonies yr -1 ) juveniles; adults Partial coral colony mortality area (Multiplying coefficient from Caribbean size mortality relationship) Coral sensitivity to bleaching (Multiplying coefficient from Caribbean DHW mortality relationship) Partial mortality due to bleaching (Multiplying coefficient from Caribbean DHW mortality relationship) Productivity of macroalgae (proportion of productivity of windward Caribbean reefs) Branching Tabular Corymbose Corymbose Small Large Thickets acroporids others massive massive ; ; 10 19; ; 12 4; 2 4; % Source 27-54, * 55-58, 45,59-62 * 45,59-62, * REFERENCES 1 Mumby, P. J. Bleaching and hurricane disturbances to populations of coral recruits in Belize. Marine Ecology-Progress Series 190, (1999). 2 Highsmith, R. C., Lueptow, R. L. & Schonberg, S. C. Growth and Bioerosion of three Massive Corals on the Belize Barrier Reef. Marine Ecology-Progress Series 13, (1983). 3 Huston, M. Variation in coral growth rates with depth at Discovery Bay, Jamaica. Coral Reefs 4, (1985). NATURE CLIMATE CHANGE 7

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10 49 Supriharyono, S. Growth rates of the massive coral Porites lutea (Edward and Haime), on the coast of Bontang, East Kalimantan, Indonesia. Journal of Coastal Development 7, (2004). 50 Suzuki, A., Hibino, K., Iwase, A. & Kawahata, H. Intercolony variability of skeletal oxygen and carbon isotope signatures of cultured Porites corals: Temperature-controlled experiments. Geochimica et cosmochimica acta 69, (2005). 51 Tanzil, J. T. I., Brown, B. E., Tudhope, A. W. & Dunne, R. P. Decline in skeletal growth of the coral Porites lutea from the Andaman Sea, South Thailand between 1984 and Coral Reefs 28, , doi: /s (2009). 52 Ward, S. The effect of damage on the growth, reproduction and storage of lipids in the scleractinian coral Pocillopora damicornis (Linnaeus). J. Exp. Mar. Biol. Ecol. 187, (1995). 53 Weil, S. M., Buddemeier, R. W., Smith, S. V. & Kroopnick, P. M. The stable isotopic composition of coral skeletons: control by environmental variables. Geochimica et cosmochimica acta 45, (1981). 54 Wellington, G. M. An experimental analysis of the effects of light and zooplankton on coral zonation. Oecologia 52, (1982). 55 Doropoulos, C. Disturbance effects to coral recruitment dynamics on the Great Barrier Reef PhD thesis, The University of Queensland, (2012). 56 Dunstan, P. K. & Johnson, C. R. Spatio-temporal variation in cores recruitment at different scales on Heron Reef, southern Great Barrier Reef. Coral Reefs 17, 71-81, doi: /s (1998). 57 Harriott, V. J. & Fisk, D. A. Recruitment patterns of scleractinian corals. A study of 3 reefs. Australian Journal of Marine and Freshwater Research 39, (1988). 58 Wallace, C. C. Seasonal peaks and annual fluctuations in recruitment of Juvenile scleractinian corals. Marine Ecology Progress Series 21, , doi: /meps (1985). 59 Harriott, V. J. Mortality rates of scleractinian corals before and during a mass bleaching event. Marine Ecology Progress Series 21, 81-88, doi: /meps (1985). 60 Pratchett, M., Pisapia, C. & Sheppard, C. Background mortality rates for recovering populations of Acropora cytherea in the Chagos Archipelago, central Indian Ocean. Marine environmental research 86, (2013). 61 Wesseling, I., Uychiaoco, A. J., Alino, P. M. & Vermaat, J. E. Partial mortality in Porites corals: Variation among Philippine reefs. International Review of Hydrobiology 86, 77-85, doi: / (200101)86:1<77::aid-iroh77>3.3.co;2-z (2001). 62 Yap, H. T., Alino, P. M. & Gomez, E. D. Trends in growth and mortality of 3 coral species (Anthozoa, Scleractinia), including effects of transplantation. Marine Ecology Progress Series 83, , doi: /meps (1992). 63 Baird, A. H. & Marshall, P. A. Mortality, growth and reproduction in scleractinian corals following bleaching on the Great Barrier Reef. Marine Ecology-Progress Series 237, (2002). 64 Edwards, H. J. et al. How much time can herbivore protection buy for coral reefs under realistic regimes of hurricanes and coral bleaching? Global Change Biology 17, , doi: /j x. 65 Marshall, P. A. & Baird, A. H. Bleaching of corals on the Great Barrier Reef: differential susceptibilities among taxa. Coral Reefs 19, (2000). 66 Roff, G. & Mumby, P. J. Global disparity in the resilience of coral reefs. Trends in Ecology & Evolution 27, , doi: /j.tree (2012). 10 NATURE CLIMATE CHANGE

11 SUPPLEMENTARY INFORMATION Supplementary Analysis: Pacific model sensitivity analysis The sensitivity, of the original Caribbean model used in this article, to small changes in the values used for the different parameters of the model was previously explored 1-3. The model is particularly sensitive to changes in the grazing intensity and the growth rate of corals, while the variability in the other parameters showed little change in model outputs explored 1-3. To explore if the new parameterization of the previous model for Pacific reefs is particularly sensitive to small changes in the values used in each of the parameters included in the model, 10 sets of 50 simulations of the model were run increasing or decreasing each of the 5 parameters modified from the Caribbean model by 10 and 20%. The yearly population coral recovery rate was calculated for the first ten years of recovery with an initial cover of 30% for each set of simulations and then the percentage change between this rate and the one obtained with the original parameter was calculated. The results are summarized in figure S2. The model appears to be robust to small changes in the main parameters. The highest change in the yearly rate of coral recovery was 11% when a 20% reduction in grazing intensity was implemented, while an average of 2.0 and 2.1% across parameters was observed when an increase or reduction of 10 % was considered respectively. The low sensitivity to changes in the parameters considered increase the confidence of the Pacific parameterization. The lower sensitivity to changes in grazing intensity and coral growth rate in comparison to the Caribbean model may be a consequence of the combination of the higher growth rate of corals in the Pacific, and the lower productivity potential of macroalgae. These results suggest that Pacific reefs may not be subject to thresholds of grazing intensity, and may not be likely to show alternative stable states under these levels of macroalgal productivity potential 4. Figure S2. Pacific model sensitivity analysis. Change in the model output (annual growth rate) when the value of each parameter (x axis) is increase or decrease by 10% in comparison to the values used in the parameterization (black bar), or 20% (grey bar) NATURE CLIMATE CHANGE 11

12 1 Mumby, P. J., Hastings, A. & Edwards, H. J. Thresholds and the resilience of Caribbean coral reefs. Nature 450, (2007). 2 Mumby, P. J. The impact of exploiting grazers (Scaridae) on the dynamics of Caribbean coral reefs. Ecological Applications 16, (2006). 3 Ortiz, J., González-Rivero, M. & Mumby, P. An Ecosystem-Level Perspective on the Host and Symbiont Traits Needed to Mitigate Climate Change Impacts on Caribbean Coral Reefs. Ecosystems, 1-13, doi: /s z (2013). 4 Roff, G. & Mumby, P. J. Global disparity in the resilience of coral reefs. Trends in Ecology & Evolution 27, , doi: /j.tree (2012). 12 NATURE CLIMATE CHANGE