Student: Paul Welle Collaborators: Ines Azevedo Mitchell Small Sarah Cooley Scott Doney
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Transcript of Student: Paul Welle Collaborators: Ines Azevedo Mitchell Small Sarah Cooley Scott Doney
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Student: Paul Welle
Collaborators:Ines AzevedoMitchell SmallSarah CooleyScott Doney
THE IMPACT OF CLIMATE STRESSORS
ON CORAL BLEACHING AND MORTALITY:
A CASE STUDY OF THE 2005 CARIBBEAN SUMMER
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Eakin et al. (2010) Caribbean summer 2005 Bleaching, Mortality (dependent variables) Temperature (independent variable)
BACKGROUND
Reproduced from Eakin (2010)
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TEMPERATURES 2005
Retrieved from http://coralreefwatch.noaa.gov/satellite/dhw.php
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THE DATAn=2945
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(1) Limited by the functional form of OLS
We expand to a non-linear model.
(2) Uncontrolled spatial correlation
We add in fixed effects.
(3) Limited number of explanatory variables
We extend the dataset to include photosynthetically active radiation (PAR) and pH. We also recalculate
DHW.
ANALYSIS CAN BE IMPROVED
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DHW correlates well with bleaching and mortality, although there are indications that the 12-week interval should be lengthened.
PAR Anomaly correlates well with bleaching and mortality (PAR does not), but seems to be of less importance than DHW.
In predicting mortality, it is best to use the maximum value of a stressor, while predicting bleaching the recent (observed) temperatures are more important.
Depth is very protective against PAR. For deep corals (13.5m, or 80 th percentile), PAR plays almost no part in predicting bleaching. For shallow corals (5m, or 20 th percentile), PAR is roughly as important a stressor as DHW.
WHAT WE LEARNED
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METHOD (OLS VS FRACTIONAL LOGIT)
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𝑦𝑖 = 11+ 𝑒−(𝛽0+σ 𝛽𝑗𝑥𝑖𝑗+ σ 𝛽𝑘𝑑𝑖𝑘 + 𝜖𝑖)𝑘𝑗
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METHOD (MANIPULATION OF CONTINUOUS DATA)
PAR, DHW, pH…
time
observed
maximum
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METHOD(VARIABLES)
Four stressor formulations Temperature - Degree Heating Weeks (DHW) – 12 week Photosynthetically Active Radiation – PAR 12 week average Photosynthetically Active Radiation – PAR Anomaly Simulated pH – Monthly average
Each formulation has 2 forms “Maximum” – Hypothesized to be important for mortality “Observed” – Hypothesized to be important for bleaching
Bleaching-and-
Mortality =MaxDHW, ObsDHW, MaxPAR, MaxPAR Anomaly, ObsPAR,
ObsPAR Anomaly, MaxPH, ObsPHf( )
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RESULTS
General Model:
Mortality Model
Bleaching Model
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RESULTS - MORTALITY
Robust standard errors in parentheses*** p<0.01, ** p<0.05, * p<0.1
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RESULTS - MORTALITY
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RESULTS - BLEACHING
Robust standard errors in parentheses*** p<0.01, ** p<0.05, * p<0.1
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RESULTS - BLEACHING
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RESULTS BLEACHING
Depth = 5 m
Depth = 13.5 m
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DHW correlates well with bleaching and mortality, although there are indications that the 12-week interval should be lengthened.
PAR Anomaly correlates well with bleaching and mortality (PAR does not), but seems to be of less importance than DHW.
In predicting mortality, it is best to use the maximum value of a stressor, while predicting bleaching the recent (observed) temperatures are more important.
Depth is very protective against PAR. For deep corals (13.5m, or 80 th percentile), PAR plays almost no part in predicting bleaching. For shallow corals (5m, or 20 th percentile), PAR is roughly as important a stressor as DHW.
WHAT WE LEARNED
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Eak in , C . M. , Morgan, J . a , Heron, S . F. , Smith , T. B . , L iu , G. , A lvarez-Fi l ip , L . , … Bouchon, C. (2010) . Car ibbean cora ls in c r is is : record thermal s tress , b leach ing, and morta l i ty in 2005. PloS one , 5 (11) , e13969.
Hoegh- Guldberg, O. , Mumby, P. J . , Hooten, a J . , S teneck , R. S . , Greenfield , P. , Gomez, E . , … Hatz io los , M. E . (2007). Cora l reefs under rapid c l imate change and ocean ac id ificat ion . Sc ience (New York , N.Y. ) , 318 (5857) , 1737–42.
McWil l iams, J . , Côté, I . , & Gi l l , J . (2005). Accelerat ing impacts o f temperature-induced cora l b leach ing in the Car ibbean. Eco logy , 86 (8) , 2055–2060.
Wilk inson, C . "Cora l b leach ing and morta l i ty–The 1998 event 4 years la ter and b leach ing to 2002." Status o f cora l reefs o f the wor ld (2002) : 33-44.
Wilk inson, C l ive R. , and Dav id Souter , eds . Status o f Car ibbean cora l reefs a f ter b leach ing and hurr icanes in 2005 . G loba l Cora l Reef Monitor ing Network, 2008.
Yee, S . H. , Santavy, D. L . , & Barron , M. G. (2008). Compar ing envi ronmenta l influences on cora l b leach ing across and wi th in species us ing c lustered b inomia l regress ion . Eco log ica l Model l ing , 218 (1 -2) , 162–174.
Yee, S . H. , & Barron, M. G. (2010) . Pred ic t ing cora l b leaching in response to env ironmenta l s t ressors us ing 8 years o f g loba l -sca le data . Envi ronmenta l moni tor ing and assessment , 161 (1-4) , 423–38.
REFERENCES
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This work would not be possible without support by
SUPPORT
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DATA
>30%<30%& >0%
0%
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BLEACHING
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MORTALITY
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DESCRIPTIVE STATISTICS
Variable [units] Min Median Mean Max Dependent Variables:
Bleaching [%] 0.0 26.3 33.2 100 Mortality [%] 0.0 0.0 2.0 68.3
Candidate Explanatory Variables: Depth [m] 0.9 9.2 10.0 42.7 Maximum DHW [°C] 0.0 3.7 4.6 17.2 Observed DHW [°C] 0.0 0.5 2.8 16.6 Maximum PAR [Einsteins/m2] 35.6 47.7 47.9 53.7 Maximum PAR Anomaly [Einsteins/m2]
1.6 16.0 17.9 56.0
Observed PAR [Einsteins/m2] 26.3 39.8 40.4 52.4 Observed PAR Anomaly [Einsteins/m2]
0.0 0.75 4.67 36.5
Simulated Maximum pH [-] 8.07 8.10 8.10 8.20 Simulated Observed pH [-] 8.03 8.07 8.07 8.13 Base PAR [Einsteins /m2] 42.3 51.1 50.4 54.2
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DEGREE HEATING WEEKS
Typical Hottest Month
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DATA
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DATA
>30%<30%& >0%
0%
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CORRELATIONS
Max DHW
Obs DHW
Max PAR
Obs PAR
Max PAR Anomaly
Obs PAR Anomaly Max pH Obs pH Base
PAR Depth
Max DHW ---- 0.67*** -0.02 -0.09*** 0.19*** 0.11*** 0.00 0.41*** -0.39*** 0.15***
Obs DHW *** ---- -0.11*** -0.39*** -0.06*** -0.33*** -0.05** 0.51*** -0.26*** 0.15***
Max PAR *** ---- 0.33*** 0.21*** 0.21*** 0.15*** -0.15*** 0.59*** -0.01
Obs PAR *** *** *** ---- 0.03* 0.70*** -0.12*** -0.71*** 0.27*** 0.06*** Max PAR Anomaly *** *** *** * ---- 0.36*** 0.22*** 0.02 -0.46*** -0.10***
Obs PAR Anomaly *** *** *** *** *** ---- -0.06*** -0.51*** -0.09*** 0.00
Max pH ** *** *** *** *** ---- 0.23*** 0.11*** -0.11***
Obs pH *** *** *** *** *** *** ---- -0.18*** 0.06***
Base PAR *** *** *** *** *** *** *** *** ---- 0.05***
Depth *** *** *** *** *** *** *** ----
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Questions:Which stressor form fits best- maximum, observed, or weighted average?Bleaching – Weighted AverageMortality – MaximumDoes PAR or PAR anomaly fit the data better?Bleaching – PAR AnomalyMortality – PAR AnomalyDoes measuring independent maximums of temperature and radiation suffice, or must one account for simultaneously high peaks?Bleaching – IndependentMortality – IndependentIs there evidence for a depth-stressor interaction?Bleaching – YesMortality - No
SUMMARY
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MORTALITY MODELS
Model 4
Model 5
General Model:
Model 1
Model 2
Model 3
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MORTALITY MODELS
(1) (2) (3) (4) (5) VARIABLES Model Model Model Model Model
Maximum DHW 0.164*** 0.166*** 0.188*** 0.176*** 0.187***
(0.0279) (0.0295) (0.0286) (0.0628) (0.0289) Maximum PAR 0.0452 0.156***
(0.0352) (0.0576) Depth -0.0535*** -0.0501*** -0.0479*** -0.173*** -0.0477***
(0.0112) (0.0121) (0.0118) (0.0670) (0.0117) Base PAR -0.167***
(0.0641) Maximum PAR 0.0283*** -0.0276* 0.0261***
Anomaly (0.00851) (0.0149) (0.00939)
Depth x 0.000333 Maximum DHW (0.00486)
Depth x 0.00551**
*
Maximum PAR (0.00125)
Maximum DHW 0.00109 x Maximum PAR Anomaly Follow
(0.00215)
Maximum PAR
Anomaly x Max DHW Follow
-0.00449 (0.00595)
Constant -6.648*** -3.823** -5.496*** -4.068*** -5.515***
(1.547) (1.845) (0.430) (0.784) (0.468)
Log-Likelihood -62.4294 -62.0861 -62.0672 -61.4354 -62.0358
AIC 0.163501 0.164758 0.162808 0.165427 0.166576
Observations 1,045 1,045 1,045 1,045 1,045
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BLEACHING MODELS
Model 5
Model 6
General Model:
Model 1
Model 2
Model 3
Model 4
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BLEACHING MODELS (1) (2) (3) (4) (5) (6)
VARIABLES Model Model Model Model Model Model
Observed DHW 0.145*** 0.148*** 0.138*** 0.170*** 0.204*** (0.00982) (0.00974) (0.00982) (0.00924) (0.0155)
Observed PAR -0.0273*** -0.0245*** (0.00601) (0.00601)
Depth 0.00962** 0.0103** 0.00863* 0.0106** 0.0731*** 0.0739*** (0.00464) (0.00461) (0.00463) (0.00463) (0.0113) (0.0115)
Base PAR -0.0364** (0.0179)
Observed PAR Anomaly
-0.0213*** (0.00377)
Maximum PAR
Anomaly 0.00909**
(0.00359) 0.0340*** (0.00593)
Depth x Observed
DHW -0.00333***
(0.000999)
Depth x Observed
PAR -0.00269***
(0.000492)
Weighted Average DHW (α=0.0282)
0.213*** (0.0152)
Weighted Average PAR (α=0.0034)
0.0416*** (0.00662)
Depth x Weighted
Average DHW -0.00322***
(0.000967)
Depth x Weighted Average PAR
-0.00301*** (0.000559)
Constant -0.332 1.329 -1.264*** -1.680*** -2.258*** -2.452***
(0.266) (0.894) (0.107) (0.144) (0.175) (0.173)
Log-Likelihood -1267.13 -1266.48 -1265.58 -1268.99 -1263.85 -1260.05 AIC 0.87683 0.877067 0.875777 0.878091 0.875961 0.87472
Observations 2,945 2,945 2,945 2,945 2,945 2,945
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Fixed Effects Fractional Logit Model Logit – Used for binary dependent variables Fractional Logit – Repurposed for bounded dependent
variable Fixed Effects – Used to control for homogeneity within
groupsMaximize quasi-likelihood function:
Returns sigmoid in range (0,1)
MODEL
𝑦𝑖 = 11+ 𝑒−(𝛽0+σ 𝛽𝑗𝑥𝑖𝑗+ σ 𝛽𝑘𝑑𝑖𝑘 + 𝜖𝑖)𝑘𝑗
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VARIABLES
Maximum DHW
Maximum PAR Anomaly
Depth
Constant
Log-LikelihoodAIC
Observations
Coefficients
0.188***(0.0286)
0.0283***(0.0085)
-0.0479***(0.0118)-5.50***(0.430)-62.070.16281,045
Marginal Effects(at means)
0.00152***(0.000197)
0.000229***(0.0000587)-0.000139***(0.0000342)