CRAMP Rapid Assessment. Univariate and Multivariate Statistical Methods
Statistics were computed with Minitab 13.0. Explanatory variables were selected from among 23 environmental predictors. To avoid multicolinearity, variables that were highly correlated (>90%) were dropped from the analysis without loss of information (Clarke and Gorley 2001).
Coral species richness data may not be suitable for use as a response variable since it is strongly dependent on sampling effort and observer variability, making it difficult to compare across sites. Richness values were determined from coral cover data. Some species of corals may be missed in data collection.
Diversity was not used as a response variable since coral diversity is low in Hawai’i and may not be an appropriate indicator of environmental conditions in this region. Hawaiian communities are often dominated by a few primary species where diversity does not decline with decreasing latitude as in other regions (Grigg 1983). Due to geographic isolation, corals in Hawai’i are depauparate relative to the Indo-West Pacific. Only 16 genera containing 42 species have been documented from the Hawaiian Islands. Difficult field identification and detection of cryptic or deep species and low digital resolution may also reduce the predictive ability of diversity.
To determine which environmental variables best explain coral cover and species richness, a general linear multiple regression model was used. Stations without coral were removed prior to analysis. Of the 152 stations at the 52 sites, 12 had no coral cover. Coral cover and species richness were regressed against the following environmental variables: rugosity, depth, sediment composition and grain-sizes, wave parameters, human population parameters, precipitation, distance from a perennial stream, watershed area, and geologic age of site. Legal protection rank and Windward/Leeward divisions were included in the model as categorical variables. A Best Subsets routine was utilized in Minitab 13.0, applying Mallows Cp and R2 as the criteria in model selection. A lack of fit test was conducted to verify the model selection. Coral diversity was not used as a response variable since coral diversity is relatively low in Hawai’i and digital quality may restrict detection of small or cryptic species.
A simple linear regression was used as an indicator to predict coral cover by Chaetodon, (butterflyfish) abundance.
To determine species tolerances, relative percent coral cover of each taxon was plotted against percent of organics and percent of silt/clay.
One-way analysis of variance (ANOVA) was conducted to determine differences in abundance of coral species between Windward and Leeward sides of the islands.
Ordination methods were used to highlight patterns in the data through spatial comparisons and habitat characterization. Ordination techniques can clarify habitat relationships and reveal trends and patterns with minimal expression of the noise typical of community data (Gauch 1982). Sample and species relationships are represented in a low-dimensional space with ordination techniques. Similar entities are placed close to each other while dissimilar species or samples are located far apart in ordination space allowing a visual representation of sample similarity.
Multivariate statistical analyses were conducted using Primer 5.0 and Multivariate Statistical Program version 3.0 (MVSP). These include the following statistical tools and techniques:
Clarke, K.R., and Gorley, R.N. 2001. PRIMER v5: user manual/Tutorial. PRIMER-E: Plymouth, United Kingdom. 91 pp.
Clarke, K.R., and Warwick, R.M. 2001. Change in marine communities: an approach to statistical analysis and interpretation. 2nd edition. PRIMER-E.: Plymouth, United Kingdom.
Gauch, H.G. Jr. 1982. Multivariate Analysis in Community Ecology. Press Syndicate of the University of Cambridge, New York, NY. 298 pp.
Grigg, R. W. 1983. Community structure, succession and development of coral reefs in Hawai‘i. Marine Ecology Progress Series 11: 1-14.
Last Update: 04/21/2008
By: Lea Hollingsworth
Hawai‘i Coral Reef Assessment & Monitoring Program
Hawai‘i Institute of Marine Biology
P.O. Box 1346
Kāne‘ohe, HI 96744