Glenn De'ATh

The world’s coral reefs are being degraded, and the need to reduce local pressures to offset the effects of increasing global pressures is now widely recognized. This study investigates the spatial and temporal dynamics of coral cover, identifies the main drivers of coral mortality, and quantifies the rates of potential recovery of the Great Barrier Reef. Based on the world’s most extensive time series data on reef condition (2,258 surveys of 214 reefs over 1985–2012), we show a major decline in coral cover from 28.0% to 13.8% (0.53% y ⁻¹ ), a loss of 50.7% of initial coral cover. Tropical cyclones, coral predation by crown-of-thorns starfish (COTS), and coral bleaching accounted for 48%, 42%, and 10% of the respective estimated losses, amounting to 3.38% y ⁻¹ mortality rate. Importantly, the relatively pristine northern region showed no overall decline. The estimated rate of increase in coral cover in the absence of cyclones, COTS, and bleaching was 2.85% y ⁻¹ , demonstrating substantial capacity for recovery of reefs. In the absence of COTS, coral cover would increase at 0.89% y ⁻¹ , despite ongoing losses due to cyclones and bleaching. Thus, reducing COTS populations, by improving water quality and developing alternative control measures, could prevent further coral decline and improve the outlook for the Great Barrier Reef. Such strategies can, however, only be successful if climatic conditions are stabilized, as losses due to bleaching and cyclones will otherwise increase.

The multinomial diversity model, MDM, is a new method for relating Shannon diversity to complex environmental, spatial, and temporal predictors. It is based on a parameterized formulation of Shannon entropy and diversity, and a novel link between entropy and the log‐likelihood of the multinomial model. The MDM relates diversity to the predictors by minimizing the entropy of the estimated species values. Model effects can be expressed as changes in entropy. Entropy can be partitioned within and between sites, species, and models, and changes in entropy can be attributed to model predictors. All entropies translate into diversity for meaningful ecological interpretation. This greatly enhances our capacity to model complex data sets, and yet also provide simple interpretations. By formulating diversity as a statistical model and working in terms of entropy, diversity is simplified both conceptually and analytically, and diversity analyses are extended beyond traditional simple hierarchies of α, β, γ, and measures of turnover. The MDM inherits the properties of generalized linear models, and thus proven methods can be used for model selection and graphical and numerical interpretation. A weighted version of the Shannon diversity model is proposed in order to extend the MDM to non‐Shannon diversities. Two example analyses, based on simulated and field data, illustrate the theoretical concepts and the analytical methods.

Degradation of inshore coral reefs due to poor water quality is a major issue, yet it has proved difficult to demonstrate this linkage at other than local scales. This study modeled the relationships between large‐scale data on water clarity and chlorophyll and four measures of reef status along the whole Great Barrier Reef, Australia (GBR; 12–24° S). Four biotic groups with different trophic requirements, namely, the cover of macroalgae and the taxonomic richness of hard corals and phototrophic and heterotrophic octocorals, were predicted from water quality and spatial location. Water clarity and chlorophyll showed strong spatial patterns, with water clarity increasing more than threefold from inshore to offshore waters and chlorophyll decreasing approximately twofold from inshore to offshore and approximately twofold from south to north. Richness of hard corals and phototrophic octocorals declined with increasing turbidity and chlorophyll, whereas macroalgae and the richness of heterotrophic octocorals increased. Macroalgal cover experienced the largest water quality effects, increasing fivefold with decreasing water clarity and 1.4‐fold with increasing chlorophyll. For each of the four biota, ∼45% of variation was predictable, with water quality effects accounting for 18–46% of that variation and spatial effects accounting for the remainder. Effects were consistent with the trophic requirements of the biota, suggesting that both macroalgal cover and coral biodiversity are partially controlled by energy supply limitation. Throughout the GBR, mean annual values of >10 m Secchi disk depth (a measure of water clarity) and <0.45 g/L chlorophyll were associated with low macroalgal cover and high coral richness, indicating these values to be potentially useful water quality guidelines. The models predict that on the 22.8% of GBR reefs where guideline values are currently exceeded, water quality improvement, e.g., by minimizing agricultural runoff, should reduce macroalgal cover on average by 39% and increase the richness of hard corals and phototrophic octocorals on average by 16% and 33%, respectively (all else being equal). Such guidelines may help focus efforts to implement effective pollution reduction and integrated coastal management policies for the GBR and other Indo‐Pacific coral reefs.

Reef-building corals are under increasing physiological stress from a changing climate and ocean absorption of increasing atmospheric carbon dioxide. We investigated 328 colonies of massivePoritescorals from 69 reefs of the Great Barrier Reef (GBR) in Australia. Their skeletal records show that throughout the GBR, calcification has declined by 14.2% since 1990, predominantly because extension (linear growth) has declined by 13.3%. The data suggest that such a severe and sudden decline in calcification is unprecedented in at least the past 400 years. Calcification increases linearly with increasing large-scale sea surface temperature but responds nonlinearly to annual temperature anomalies. The causes of the decline remain unknown; however, this study suggests that increasing temperature stress and a declining saturation state of seawater aragonite may be diminishing the ability of GBR corals to deposit calcium carbonate.

Accurate prediction and explanation are fundamental objectives of statistical analysis, yet they seldom coincide. Boosted trees are a statistical learning method that attains both of these objectives for regression and classification analyses. They can deal with many types of response variables (numeric, categorical, and censored), loss functions (Gaussian, binomial, Poisson, and robust), and predictors (numeric, categorical). Interactions between predictors can also be quantified and visualized. The theory underpinning boosted trees is presented, together with interpretive techniques. A new form of boosted trees, namely, “aggregated boosted trees” (ABT), is proposed and, in a simulation study, is shown to reduce prediction error relative to boosted trees. A regression data set is analyzed using ABT to illustrate the technique and to compare it with other methods, including boosted trees, bagged trees, random forests, and generalized additive models. A software package for ABT analysis using the R software environment is included in the Appendices together with worked examples.