Exploring coral reef communities in Puerto Rico using Bayesian networks

Abstract

Most coral reef studies focus on scleractinian (stony) corals to indicate reef condition, but there are other prominent assemblages that play a role in ecosystem structure and function. In Puerto Rico these include fish, gorgonians, and sponges. The U.S. Environmental Protection Agency conducted unique surveys of coral reef communities across the southern coast of Puerto Rico that included simultaneous measurement of all four assemblages. Evaluating the results from a community perspective demands endpoints for all four assemblages, so patterns of community structure were explored by probabilistic clustering of measured variables with Bayesian networks. Most variables were found to have stronger associations within than between taxa, but unsupervised structure learning identified three cross-taxa relationships with potential ecological significance. Clusters for each assemblage were constructed using an expectation-maximization algorithm that created a factor node jointly characterizing the density, size, and diversity of individuals in each taxon. The clusters were characterized by the measured variables, and relationships to variables for other taxa were examined, such as stony coral clusters with fish variables. Each of the factor nodes were then used to create a set of meta-factor clusters that further summarized the aggregate monitoring variables for the four taxa. Once identified, taxon-specific and meta-clusters represent patterns of community structure that can be examined on a regional or site-specific basis to better understand risk assessment, risk management and delivery of ecosystem services.

Keywords: Bayesian networks; Cluster analysis; Community ecology; Coral reefs.

Fig. 1.

Distance mapping of the coral reef monitoring variables using (a) Pearson correlation and (b) mutual information. Node C-SA is behind C-Fp in 1a and 1b. Coral reef nodes are blue, fish nodes are green, sponge nodes are red and gorgonian nodes are yellow. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Fig. 2.

Maximum weight spanning tree structure with (a) structural coefficient of 1.0 and (b) structural coefficient of 0.80 to fully connect all nodes of the network. Coral reef nodes are blue, fish nodes are green, sponge nodes are red and gorgonian nodes are yellow. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Fig. 3.

Final Bayesian network structure with node force (node size) and Kullback-Leibler divergence (arc size and numerical values) showing the strength of relationships among measured variables. Coral reef nodes are blue, fish nodes are green, sponge nodes are red and gorgonian nodes are yellow. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Fig. 4.

Cluster networks for each community component. Target nodes are latent factors containing cluster states. Percentage numbers are percentage strengths of contributions between the target node and manifest variables. SF = sponge factor; FF = fish factor; GF = gorgonian factor; CF = coral factor.

Fig. 5.

Network structure for supervised learning of the fish factor (FF) with all measured variables as predictors. The latent FF comprised the manifest variables from corals, sponges and gorgonians.

Fig. 6.

Hierarchical cluster model structure. The meta-factor (MF) root node clusters the factor nodes for each community component. The leaf (terminal) nodes are the manifest nodes representing probability distributions from measured reef components. Intermediate nodes (between the root and leaf nodes) are the factor nodes for each of the community components. The names of these factor nodes reflect the manifest node with the highest contribution and the number of nodes in the cluster states in parentheses.

Fig. 7.

Photographs of representative stations for meta-clusters: MC1 (top left), MC2 (top right), MC3 (bottom left) and MC4 (bottom right).