Appendix A

Water quality sampling methods and analytical techniques.

Water quality data were collected at various times using the same water sampling and analytical methods. All data were obtained from the AIMS Water Quality database. Areasonable number of individual measurements were available for Low Isles and Fitzroy Is., spanning several years. For Havannah Is. only very limited data were available. For describing the mean water quality at this study reef, the Havannah Is. data were pooled with data from two other sites very close to Havannah Is. (10-25 km away), after testing that there was no significant difference between the sites (General Linear model with location as a fixed factor; NCSS 2007, version 07.1.10, Kaysville, Utah).

Discrete water samples were collected from two to three depths through the water column with Niskin bottles at all three study locations. Sub-samples for total dissolved nitrogen and phosphorus (TDN, TDP)were immediately filtered through a 0.45µm filter cartridge (Sartorius MiniSart N) into acid-washed screw-cap plastic test tubes and stored at -18ºC until analysis). TDN and TDP were analyzed after persulphate digestion by standard wet chemical methods for inorganic nutrients implemented on a segmented flow analyzer. Sub-samples for particulate nutrients and chlorophyll a were collected on pre-combusted glass fibre filters (Whatman GF/F) and stored at -18ºC until analyses. Particulate nitrogen (PN) was determined by high-temperature combustion using an ANTEK 707/720 Nitrogen Analyzer. Particulate phosphorus (PP) was determined spectrophotometrically as inorganic P (PO4) after digestion in 5% potassium persulphate. Chlorophyll aconcentrations were measured fluorometrically using a Turner Designs 10AU fluorometer after grinding the filters in 90% acetone. Sub-samples for suspended solids (SS) were collected on pre-weighed 0.4µm polycarbonate filters (47mm diameter, GE Water & Process Technologies) and SS concentrations were determined gravimetrically from the difference in weight between loaded and unloaded filters after drying overnight at 60oC. Depth-weighted means were calculated from results for discrete depths.

Appendix B

Analytical methods to assess relationships between corals, macroalgae and fishes

To quantify the location-dependent, space-limited relationship between coral and macroalgae with fish in each of the three critical phases we used a multinomial model of habitat proportions (Gelman et al. 2004). This approach was particularly appropriate to our data as the habitat information collected for each transect (i) consisted of 200 (n) randomly-selected points assigned to one of 3 potential habitat classes (k) ofcoral, macroalgae, or other. The number of points per habitat class could then be described by a multinomial response:

(1)

with pik, the probability of observing y of 200 points from habitat category k on transect i. We parameterized the multinomial generalized linear model in terms of the log-ratio for the probability of observing algae or other habitat categories relative to that of coral, our baseline category:

(3).

The parameter vector  indicates the relative change in the probability of observing habitat k, relative to coral, as the result of a unit increase in the associated covariate of vector X. Put differently; we estimated the odds of observing macroalgae to coral using a linear function of the covariates contained in X. This structure was necessary because coral and algae directly compete for space (i.e., they cannot occupy the same unit of habitat at the same time) and are therefore not independent response variables.

To differentiate the role of herbivore groups among phases we estimated an independent parameter for each group in each phase (Phase 1 – Phase 3) using indicator variables within the linear part of the model. In our analysis the relative abundance of macroalgae versus coral (i.e., their log-odds) was of primary interest, therefore we report parameter estimates only for the macroalgal portion of the model. Model parameters were estimated in a Bayesian framework, using a Markov chain Monte Carlo (MCMC) algorithm implemented in the PyMC module (Patil et al. 2010) for the Python programming language ( All parameters were assigned uniformative prior distributions; logit-linear coefficients were given mean-zero normal priors with low precision (variance = 10000). The model was run for 100,000 iterations with the first 50,000 discarded as a burn-in period. Based on inspection of traces, convergence diagnostics, and goodness-of-fit measures provided by PyMC there was no evidence of lack of convergence or lack of fit.

Reference

Gelman A, Carlin JB, Stern HS, Rubin DB (2004) Bayesian data analysis. Chapman and Hall/CRC Press, Boca Raton, FL

Patil, A, Huard D, Fonnesbeck CJ (2010) PyMC: Bayesian Stochastic Modelling in Python. Journal of Statistical Software, 35(4):1-81.