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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)

100100

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)