2.2.2 Data analysis

The coralline coverage data matrix for each reef was used in different numerical analyses. A single matrix was formed by reef, where the most common community parameters were determined in the sites, with the purpose of obtaining a robust quantitative descriptive synthesis: the dominance was determined by the index of the importance value [24]; its formula is as follows:

$$IVI = A\mathfrak{K} + F\mathfrak{K} \tag{1}$$

where A—relative abundance, F—relative frequency

and biological diversity was quantified with the Shannon-Wiener index [25] whose expression is

$$H' = -\sum\_{i=1}^{S} p\_i \log p\_i \tag{2}$$

where pi is the proportion of the abundance of the species i.

The sites were classified with the Bray-Curtis similarity index, using the flexible union criterion with a β = 0.25 [26]; the coefficient has the following equation:

$$d\_{i,k} = \frac{\sum\_{i=1}^{Z} \left| \mathbf{X}\_{i,j} - \mathbf{X}\_{i,k} \right|}{\sum\_{i=1}^{Z} \left( \mathbf{X}\_{i,j} - \mathbf{X}\_{i,k} \right)} \tag{3}$$

where j, k—objects j and k that are evaluated, i—i-ésimo descriptor, Z—number of descriptors, dj,k—affinity value determined as geometric distance, Xi, J—descriptor value i in the entity j:

A main coordinate analysis was used for spatial distribution of the species [27].
