Data-driven models for regional coral-reef dynamics.

Coral reefs have been affected by natural and anthropogenic disturbances. Coral cover has declined on many reefs, and macroalgae have increased on some. The existence of alternative stable states with high or low coral cover has been widely debated, but not clearly established. We evaluate the evidence for alternative stable states in benthic coral-reef dynamics in the Caribbean, Kenya and Great Barrier Reef (GBR), using stochastic semi-parametric models based on large numbers of time series of cover of hard corals, macroalgae and other components. Only the GBR showed a consistent short-term regional decline in coral cover. There was no evidence for regional increases in macroalgae. The equilibrium distributions of our models were close to recently observed distributions, and differed among regions. In all three regions, the equilibrium distributions were unimodal rather than bimodal, and thus did not suggest the existence of alternative stable states on a regional scale, under current conditions.

Among-site variability in the stochastic dynamics of East African coral reefs.

Coral reefs are dynamic systems whose composition is highly influenced by unpredictable biotic and abiotic factors. Understanding the spatial scale at which long-term predictions of reef composition can be made will be crucial for guiding conservation efforts. Using a 22-year time series of benthic composition data from 20 reefs on the Kenyan and Tanzanian coast, we developed Bayesian vector autoregressive state-space models for reef dynamics, incorporating among-site variability, and quantified their long-term behaviour. We estimated that if there were no among-site variability, the total long-term variability would be approximately one-third of its current value. Thus, our results showed that among-site variability contributes more to long-term variability in reef composition than does temporal variability. Individual sites were more predictable than previously thought, and predictions based on current snapshots are informative about long-term properties. Our approach allowed us to identify a subset of possible climate refugia sites with high conservation value, where the long-term probability of coral cover ≤0.1 (as a proportion of benthic cover of hard substrate) was very low. Analytical results show that this probability is most strongly influenced by among-site variability and by interactions among benthic components within sites. These findings suggest that conservation initiatives might be successful at the site scale as well as the regional scale.

Modeling the beta diversity of coral reefs.

Quantifying the beta diversity (species replacement along spatiotemporal gradients) of ecosystems is important for understanding and conserving patterns of biodiversity. However, virtually all studies of beta diversity focus on one-dimensional transects orientated along a specific environmental gradient that is defined a priori. By ignoring a second spatial dimension and the associated changes in species composition and environmental gradients, this approach may provide limited insight into the full pattern of beta diversity. Here, we use remotely sensed imagery to quantify beta diversity continuously, in two dimensions, and at multiple scales across an entire tropical marine seascape. We then show that beta diversity can be modeled (0.852 > or = r2 > or = 0.590) at spatial scales between 0.5 and 5.0 km2, using the environmental variables of mean and variance of depth and wave exposure. Beta diversity, quantified within a "window" of a given size, is positively correlated to the range of environmental conditions within that window. For example, beta diversity increases with increasing variance of depth. By analyzing such relationships across seascapes, this study provides a framework for a range of disparate coral reef literature including studies of zonation, diversity, and disturbance. Using supporting evidence from soft-bottom communities, we hypothesize that depth will be an important variable for modeling beta diversity in a range of marine systems. We discuss the implications of our results for the design of marine reserves.

Model-free estimation of the psychometric function.

A subject's response to the strength of a stimulus is described by the psychometric function, from which summary measures, such as a threshold or a slope, may be derived. Traditionally, this function is estimated by fitting a parametric model to the experimental data, usually the proportion of successful trials at each stimulus level. Common models include the Gaussian and Weibull cumulative distribution functions. This approach works well if the model is correct, but it can mislead if not. In practice, the correct model is rarely known. Here, a nonparametric approach based on local linear fitting is advocated. No assumption is made about the true model underlying the data, except that the function is smooth. The critical role of the bandwidth is identified, and its optimum value is estimated by a cross-validation procedure. As a demonstration, seven vision and hearing data sets were fitted by the local linear method and by several parametric models. The local linear method frequently performed better and never worse than the parametric ones. Supplemental materials for this article can be downloaded from app.psychonomic-journals.org/content/supplemental.