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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 DATA

n=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 eff ects.

(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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� �� ܦܪ� ൌ��� �ఈభή�ௗ�௧ ήܦܪ�� ݔܯ� ͳൌ�� �ఈభή�ௗ�௧ ή� �� ݏܦܪ�� �� ܣ� ൌ��� �ఈమή�ௗ�௧ ή� ܣ� ݔݔݔݔݔݔݔݔݔݔݔݔݔܯ� ݔ ݕ�� � ܣ ͳൌ�� �ఈమήݐ�� � ή� �� ܣ� ݏ ݕ�� � ܣ

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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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Eakin, 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 cr is is : record thermal s t ress , b leaching, and morta l i ty in 2005. PloS one , 5 (11) , e13969.

Hoegh- Guldberg, O. , Mumby, P. J . , Hooten, a J . , Steneck, R. S . , Greenfi eld, P. , Gomez, E . , … Hatz io los , M. E . (2007). Cora l reefs under rapid c l imate change and ocean ac id ifi cat ion. Science (New York, N.Y. ) , 318 (5857), 1737–42.

McWil l iams, J . , Côté, I . , & Gi l l , J . (2005). Accelerat ing impacts of temperature-induced cora l b leaching in the Car ibbean. Ecology , 86 (8) , 2055–2060.

Wilkinson, C. "Cora l b leaching and morta l i ty–The 1998 event 4 years later and b leaching to 2002."  Status of cora l reefs of the wor ld   (2002): 33-44.

Wilkinson, C l ive R. , and David Souter , eds.   Status of Car ibbean cora l reefs af ter b leaching and hurr icanes in 2005 . Global Cora l Reef Monitor ing Network, 2008.

Yee, S. H. , Santavy, D. L . , & Barron, M. G. (2008). Compar ing environmental infl uences on cora l b leaching across and with in spec ies us ing c lustered b inomial regress ion. Ecologica l Model l ing , 218 (1-2) , 162–174.

Yee, S. H. , & Barron, M. G. (2010). Predict ing cora l b leaching in response to environmental s t ressors us ing 8 years of g lobal -scale data. Environmental monitor 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 fi ts best- maximum, observed, or

weighted average?Bleaching – Weighted AverageMortality – Maximum

Does PAR or PAR anomaly fi t the data better?Bleaching – PAR AnomalyMortality – PAR Anomaly

Does measuring independent maximums of temperature and radiation suffi ce, or must one account for simultaneously high peaks?

Bleaching – IndependentMortality – Independent

Is 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 Eff ects 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-Likelihood

AIC

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)