Methods used to measure complexity in Caribbean reefs To determine which methods are commonly used by researchers to measure habitat complexity on coral reefs, we conducted a preliminary literature search using the ISI web of Knowledge in July 2007 for papers containing any of the following words in the title, abstract or keywords: “rugosity”, “spatial heterogeneity”, “spatial index”, “habitat structure”, “habitat complexity”, “structural complexity”, “substratum complexity”, “reef relief”, “coral complexity”, and “complexity index”. Additionally, the same words were searched in the entire text of the 1368 papers published in Volumes 1 (June 1982) to 26 (September 2007) of the journal Coral Reefs. We retained all papers that reported work carried out in the Caribbean and in which the methodology used to measure architectural complexity was clearly explained. A total of 49 papers met these two criteria. The description and frequency of use of the various methodologies used to describe habitat complexity in Caribbean coral reefs are presented in table S1. Table S1. Description and percentage of use (% of studies) of methodologies used to measure reef structural complexity in the Caribbean. Method % Rugosity index. A fine-link chain is laid over the contours of the substratum, and the 59.2 ratio between the total length of the chain (a) to the planar distance between the ends of the chain (b) is calculated. The greater the ratio, the more complex the substratum. Some papers use a modified rugosity index: 1- (b / a). Visual assessment. Semi-quantitative estimates of reef structural complexity on an 14.3 arbitrary scale, e.g. scores 0–5 where 0 corresponds to a totally flat surface and 5 represents maximum reef complexity. Maximum relief. The difference (usually in cm) between the lowest and highest 10.2 points of the substratum along a transect or within a quadrat. Larger differences indicate greater complexity. Remote sensing. Optical analyses of data obtained from aerial photographs or 10.2 scanners (e.g., light detection and ranging altimeter). Layers. An imaginary vertical line is placed through a transect or quadrat and the 4.1 number of times it passes from coral to water to coral again represents structural complexity. A structural complexity value of 0 indicates a flat surface, while greater values represent a substratum with more layers and hence more complexity. Number of holes. The number of holes of different sizes within an area or transect is counted, and complexity increases with increasing number of holes. 2.0