Glenn De'ath

CLASSIFICATION AND REGRESSION TREES: A POWERFUL YET SIMPLE TECHNIQUE FOR ECOLOGICAL DATA ANALYSIS

Classification and regression trees are ideally suited for the analysis of com- plex ecological data. For such data, we require flexible and robust analytical methods, which can deal with nonlinear relationships, high-order interactions, and missing values. Despite such difficulties, the methods should be simple to understand and give easily interpretable results. Trees explain variation of a single response variable by repeatedly splitting the data into more homogeneous groups, using combinations of explanatory var- iables that may be categorical and/or numeric. Each group is characterized by a typical value of the response variable, the number of observations in the group, and the values of the explanatory variables that define it. The tree is represented graphically, and this aids exploration and understanding. Trees can be used for interactive exploration and for description and prediction of patterns and processes. Advantages of trees include: (1) the flexibility to handle a broad range of response types, including numeric, categorical, ratings, and survival data; (2) invariance to monotonic transformations of the explanatory variables; (3) ease and ro- bustness of construction; (4) ease of interpretation; and (5) the ability to handle missing values in both response and explanatory variables. Thus, trees complement or represent an alternative to many traditional statistical techniques, including multiple regression, analysis of variance, logistic regression, log-linear models, linear discriminant analysis, and survival models. We use classification and regression trees to analyze survey data from the Australian central Great Barrier Reef, comprising abundances of soft coral taxa (Cnidaria: Octocorallia) and physical and spatial environmental information. Regression tree analyses showed that dense aggregations, typically formed by three taxa, were restricted to distinct habitat types, each of which was defined by combinations of 3-4 environmental variables. The habitat definitions were consistent with known experimental findings on the nutrition of these taxa. When used separately, physical and spatial variables were similarly strong predictors of abundances and lost little in comparison with their joint use. The spatial variables are thus effective surrogates for the physical variables in this extensive reef complex, where infor- mation on the physical environment is often not available. Finally, we compare the use of regression trees and linear models for the analysis of these data and show how linear models fail to find patterns uncovered by the trees.

MULTIVARIATE REGRESSION TREES: A NEW TECHNIQUE FOR MODELING SPECIES–ENVIRONMENT RELATIONSHIPS

Multivariate regression trees (MRT) are a new statistical technique that can be used to explore, describe, and predict relationships between multispecies data and environmental characteristics. MRT forms clusters of sites by repeated splitting of the data, with each split defined by a simple rule based on environmental values. The splits are chosen to minimize the dissimilarity of sites within clusters. The measure of species dissimilarity can be selected by the user, and hence MRT can be used to relate any aspect of species composition to environmental data. The clusters and their dependence on the environmental data are represented graphically by a tree. Each cluster also represents a species assemblage, and its environmental values define its associated habitat. MRT can be used to analyze complex ecological data that may include imbalance, missing values, nonlinear relationships between variables, and high-order interactions. They can also predict species composition at sites for which only environmental data are available. MRT is compared with redundancy analysis and canonical correspondence analysis using simulated data and a field data set.

Declining Coral Calcification on the Great Barrier Reef

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 massive Porites corals 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.

Recognition and selection of settlement substrata determine post-settlement survival in corals

Habitat recognition and selective settlement by dispersive propagules greatly increases the post-settlement survival chances of sessile organisms. To better understand the key role some species can play in the structure of highly complex coral reef ecosystems, we compare the role of two independent, but sequential, processes: settlement choice and post-settlement survival. This study describes the chemical and physical recognition and ranking of specific settlement substrata by coral larvae. Several species of crustose coralline algae (CCA) are known to induce coral settlement; however they also employ physical and biological anti-settlement defense strategies that vary greatly in effectiveness. We examine the interactions between settling larvae of two common reef building coral species (Acropora tenuis and A. millepora) and five species of CCA (Neogoniolithon fosliei, Porolithon onkodes, Hydrolithon reinboldii, Titanoderma prototypum, and Lithoporella melobesioides) that co-occur on reef crests and slopes of the Great Barrier Reef, Australia. Distinct settlement patterns were observed when coral larvae were provided with a choice of settlement substrata. Settlement on the most preferred substratum, the CCA species T. prototypum, was 15 times higher than on N. fosliei, the least preferred substratum. The rates of post-settlement survival of the corals also varied between CCA species in response to their anti-settlement strategies (shedding of surface cell layers, overgrowth, and potential chemical deterrents). Rates of larval settlement, post-settlement survival, and the sensitivity of larvae to chemical extracts of CCA were all positively correlated across the five species of CCA. Nonliving settlement substrata on coral reefs is sparse; consequently the fact that only a few CCA species (notably T. prototypum) facilitate coral recruitment, has important implications for structuring the reef ecosystem.

Water quality as a regional driver of coral biodiversity and macroalgae on the Great Barrier Reef

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 degrees 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.

IDENTIFYING ECOLOGICAL CHANGE AND ITS CAUSES: A CASE STUDY ON CORAL REEFS

The successful management of ecosystems depends on early detection of change and identification of factors causing such change. Determination of change and causality in ecosystems is difficult, both philosophically and practically, and these difficulties increase with the scale and complexity of ecosystems. Management also depends on the communication of scientific results to the broader public, and this can fail if the evidence of change and causality is not synthesized in a transparent manner. We developed a framework to address these problems when assessing the effects of agricultural runoff on coral reefs of the Australian Great Barrier Reef (GBR). The framework is based on improved methods of statistical estimation (rejecting the use of statistical tests to detect change), and the use of epidemiological causal criteria that are both scientifically rigorous and understood by nonspecialists. Many inshore reefs of the GBR are exposed to terrestrial runoff from agriculture. However, detecting change and ...

Spatial and temporal patterns of near-surface chlorophyll a in the Great Barrier Reef lagoon

Surface chlorophyll a concentrations in the Great Barrier Reef (GBR) lagoon were monitored at individual stations for periods of 6 to 12 years. The monitoring program was established to detect spatial and temporal changes in water quality resulting from increased loads of nutrients exported from the catchments adjoining the GBR. Sampling occurred monthly at up to 86 sites that were located in transects across the width of the continental shelf. In the central and southern GBR (16–21°S), there was a persistent cross-shelf chlorophyll a gradient, with higher concentrations near the coast. No cross-shelf gradient was observed in the far northern GBR (12–15°S). Mean chlorophyll a concentrations in the far northern GBR (0.23 µg L–1) were less than half those in the south and central GBR (0.54 µg L–1). Chlorophyll a varied seasonally within regions, with mean summer-wet season (December–April) concentrations ~50% greater than those in the winter-dry season (May–November). Sub-annual, inter-annual and event-related variations in chlorophyll a concentrations were observed in several zones. Multi-year patterns in concentrations suggest that relatively short (5–8 years) time series may give spurious estimates of secular trends. Higher chlorophyll a concentrations in inshore waters south of 16°S were most likely related to the levels of river nutrient delivery associated with agricultural development on adjacent catchments.

Ecological effects of ocean acidification and habitat complexity on reef-associated macroinvertebrate communities

The ecological effects of ocean acidification (OA) from rising atmospheric carbon dioxide (CO2) on benthic marine communities are largely unknown. We investigated in situ the consequences of long-term exposure to high CO2 on coral-reef-associated macroinvertebrate communities around three shallow volcanic CO2 seeps in Papua New Guinea. The densities of many groups and the number of taxa (classes and phyla) of macroinvertebrates were significantly reduced at elevated CO2 (425–1100 µatm) compared with control sites. However, sensitivities of some groups, including decapod crustaceans, ascidians and several echinoderms, contrasted with predictions of their physiological CO2 tolerances derived from laboratory experiments. High CO2 reduced the availability of structurally complex corals that are essential refugia for many reef-associated macroinvertebrates. This loss of habitat complexity was also associated with losses in many macroinvertebrate groups, especially predation-prone mobile taxa, including crustaceans and crinoids. The transition from living to dead coral as substratum and habitat further altered macroinvertebrate communities, with far more taxa losing than gaining in numbers. Our study shows that indirect ecological effects of OA (reduced habitat complexity) will complement its direct physiological effects and together with the loss of coral cover through climate change will severely affect macroinvertebrate communities in coral reefs.

Factors affecting the behaviour of crown-of-thorns starfish (Acanthaster planci L.) on the Great Barrier Reef: : 2: Feeding preferences

The feeding behaviour of the crown-of-thorns starfish, Acanthaster planci (L.), was studied on fifteen reefs of the Great Barrier Reef between June 1986 and December 1987. Feeding preferences of A. planci for the ten most common genera and six most common forms of scleractinian corals were defined by pairwise comparisons of the corals being preyed upon and its nearest neighbouring coral. The preferences were quantified using a novel approach, the Bradley–Terry model, and shown to form a well-ordered hierarchy. Acropora was the most preferred genus, being favoured 14:1 over Porites, the least preferred. When feeding on Acropora, A. planci showed a preference for tabular corals over other forms. Taken over all genera, tabular forms were preferred 35:1 over massives, the least preferred form, and branching, submassive and foliaceous forms were equally preferable, being favoured about 7:1 over massives. Genera and form preference were shown to be strongly dependent with tabular and branching forms of Acropora preferred over similar forms of Montipora, but for foliaceous and encrusting forms, this pattern was reversed. A. planci were shown to spend longer on larger corals, with feeding times proportional to the colony diameter raised to the power of 0.72. Feeding preferences adjusted for colony size were estimated, and the preference for Acropora was generally reduced, in the case of Porites to 8:1. The preference of A. planci for Acroporidae over other corals decreased moderately with deceasing relative abundance of Acroporidae. Overall, these findings were relatively consistent across all reefs surveyed, suggesting that the starfishs preference for particular types and forms of corals were not greatly influenced by factors such as starfish density or size, time of day, or depth.

Principal curves : A new technique for indirect and direct gradient analysis

Principal curves are smooth one-dimensional curves in a high dimensional space that are ideally suited for indirect gradient analysis of multispecies abundance data. A principal curves ordination will simultaneously estimate the species response curves and locate sites on a single ecological gradient. By means of theoretical argument and simulations, they are shown to be superior to both correspondence analysis and multidimensional scaling, outperforming them in 77% and 72% of simulations, respectively. The species response curves used in the simulations varied from simple Gaussian form with equal maxima and tolerances to complex multimodal curves with varying maxima and tolerances. Simulations were conducted both with and without noise. When species response curves are smooth, and a reasonable initial configuration is provided, principal curve gradient analysis can succeed even when the curves are complex and beta diversity is high. Principal curves can also be adapted for direct gradient analysis in order to relate species composition to environmental variables. Although ordination techniques are used both to uncover ecological gradients and to represent species composition, it is argued that these two aims are distinct. Hence, a single ordination technique cannot generally achieve both objectives simultaneously. However, by superimposing a principal curve on a principal components biplot, joint representation of an ecological gradient and species composition can be achieved. Information from either an indirect or direct principal curve gradient analysis can be added to the biplot, thereby relating environmental variables to species composition and locations of sites on the gradient. Two ecological data sets, comprising abundances of hunting spiders and species of grasses, are analyzed using principal curve gradient analysis. The results are contrasted with previous analyses, using canonical-correspondence analysis and canonical-correlation analysis, and indicate that principal curve gradient analysis can find one-dimensional gradients that explain species composition as well as, or better than, higher dimensional solutions from other techniques. This, in turn, can lead to a more succinct representation and better understanding of ecological systems.