coral_bleach.txt



Coral Bleaching, temperature stress

http://coralreefwatch.noaa.gov/satellite/education/tutorial/crw22_bleachingthreshold.php



Cheryl A. Logan, John P Dunne, C. Mark Eakin, Simon D. Donner

A framework for comparing coral bleaching thresholds

Proceedings of the 12th International Coral Reef Symposium, Cairns, Australia, 9-13 July 2012

10A Modelling reef futures

http://www.icrs2012.com/proceedings/manuscripts/ICRS2012_10A_3.pdf



Fitt WK, et al. 2001. Coral Reefs 20:51-65

Coral bleaching: interpretation of thermal tolerance limits and thermal

thresholds in tropicla corals.

http://link.springer.com/article/10.1007/s003380100146#page-2



~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~



Fit logistic regression model for coral bleaching as function of temperature.

   Simplified version (many stressors contribute to bleaching risk).



> # Coral bleaching, w/ temp threshold = 30.5C



> t.cool <- runif(100, 25, 30.7)    # generate temps with no bleaching

> t.bleach <- runif(20, 30.5, 33)   # generate temps with bleaching

> t.all <- c(t.cool, t.bleach)      # combine temps as 1 explanatory variable

> status.coral <- c(rep(1, 100), rep(0, 20))  # generate binary response var

                                              # 1 = not bleached, 0 = bleached



> plot(t.all, status.coral, xlab="Water temperature (C)", ylab="Coral status")



> mod.coral <- glm(status.coral ~ t.all, family=binomial)

> summary(mod.coral)



Call:

glm(formula = status.coral ~ t.all, family = binomial)



Deviance Residuals: 

   Min      1Q  Median      3Q     Max  

-1.656   0.000   0.000   0.000   1.508  



Coefficients:

            Estimate Std. Error z value Pr(>|z|)  

(Intercept)  477.600    268.750   1.777   0.0755 .

t.all        -15.586      8.771  -1.777   0.0756 .

---

Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1



(Dispersion parameter for binomial family taken to be 1)



    Null deviance: 108.1347  on 119  degrees of freedom

Residual deviance:   7.5044  on 118  degrees of freedom

AIC: 11.504



Number of Fisher Scoring iterations: 12

> mod.coral$coefficients[1]

(Intercept) 

   477.5996 

> mod.coral$coefficients[2]

    t.all 

-15.58606 



> # Plot model as solid line

> t.seq <- seq(from=25, to=33, length=200)

> pred.coral <- exp(mod.coral$coefficients[1] + mod.coral$coefficients[2]*t.seq) /

+    (1 + exp(mod.coral$coefficients[1] + mod.coral$coefficients[2]*t.seq))

> lines(t.seq, pred.coral)



> # Calculate log-likelihood R^2:

> logR2 <- 1 - 7.504 / 108.1

> logR2

[1] 0.9305828



> # Predict probability(bleaching) at temp =30.56C

> p.306 <- exp(mod.coral$coefficients[1] + mod.coral$coefficients[2]*30.6) /

+    (1 + exp(mod.coral$coefficients[1] + mod.coral$coefficients[2]*30.6))

> p.306



> # Predict probability(bleaching) at temp =29.0C

> p.29 <- exp(mod.coral$coefficients[1] + mod.coral$coefficients[2]*29) /

+    (1 + exp(mod.coral$coefficients[1] + mod.coral$coefficients[2]*29))

> p.29

(Intercept) 

          1 

> # Predict probability(bleaching) at temp =31.0C

> p.31 <- exp(mod.coral$coefficients[1] + mod.coral$coefficients[2]*31) /

+    (1 + exp(mod.coral$coefficients[1] + mod.coral$coefficients[2]*31))

> p.31

(Intercept) 

0.003802225 







# ********************************************************************



# Coral bleaching, w/ temp threshold = 30.5C



t.cool <- runif(100, 25, 30.7)    # generate temps with no bleaching

t.bleach <- runif(20, 30.5, 33)   # generate temps with bleaching

t.all <- c(t.cool, t.bleach)      # combine temps as 1 explanatory variable

status.coral <- c(rep(1, 100), rep(0, 20))  # generate binary response var

                                            # 1 = not bleached, 0 = bleached



plot(t.all, status.coral, xlab="Water temperature (C)", ylab="Coral status")

mod.coral <- glm(status.coral ~ t.all, family=binomial)

summary(mod.coral)

# AIC value not relevant if only one model

mod.coral$coefficients[1]

mod.coral$coefficients[2]



# Plot model as solid line

t.seq <- seq(from=25, to=33, length=200)

pred.coral <- exp(mod.coral$coefficients[1] + mod.coral$coefficients[2]*t.seq) /

   (1 + exp(mod.coral$coefficients[1] + mod.coral$coefficients[2]*t.seq))

lines(t.seq, pred.coral)



# Calculate log-likelihood R^2:

logR2 <- 1 - 7.504 / 108.1

logR2



# Predict probability(bleaching) at temp =30.6C

p.306 <- exp(mod.coral$coefficients[1] + mod.coral$coefficients[2]*30.6) /

   (1 + exp(mod.coral$coefficients[1] + mod.coral$coefficients[2]*30.6))

p.306



# Predict probability(bleaching) at temp =29.0C

p.29 <- exp(mod.coral$coefficients[1] + mod.coral$coefficients[2]*29) /

   (1 + exp(mod.coral$coefficients[1] + mod.coral$coefficients[2]*29))

p.29



# Predict probability(bleaching) at temp =31.0C

p.31 <- exp(mod.coral$coefficients[1] + mod.coral$coefficients[2]*31) /

   (1 + exp(mod.coral$coefficients[1] + mod.coral$coefficients[2]*31))

p.31