Discussion Solution — CRAMP Data

What I intended for this part was simply inspection of pairwise scatterplots and correlation coefficients. (Three-dimensional exploration — 3-D plots, or 2-D scatterplots with panels for different ranges of a third variable — might also be useful, but was more than I expected and in any event my limited exploration of these didn’t reveal anything noteworthy.) Because many of the variables have skewed distributions, and some are extremely skewed, I chose to transform many of them to reduce the influence of the extreme observations and allow the pattern in the bulk of the data to be more evident. I chose transformations based on the severity of the skew and the presence of 0s: I did not transform coral diversity, rugosity, depth, or mean wave height; square-root transformed fish biomass, stream distance, and coral cover; log transformed watershed area and rain; and fourth-root transformed human population, macro algae, and coralline algae. Other choices of course would be reasonable and shouldn’t greatly affect the patterns seen. The most important set of relationships is shown at right. Coral cover, coral diversity, rugosity, and fish biomass all are positively associated with each other, with coral cover and rugosity mostly strongly associated and coral diversity somewhat less strongly associated than the others of these variables. The coral cover–rugosity relationship is fairly linear, but most of the others are nonlinear, with the patterns strongest at low coral cover / diversity / rugosity, and relatively flat at higher levels. These variables are not strongly associated with any of the other variables, apart from a moderate negative association of rugosity with mean wave height, as shown at right. There are fairly strong associations, in most cases negative, among some pairs of the geographic or abiotic variables (human population, stream distance, watershed area, wave height, rain), as shown at the top of the next page. Cover of macro algae and of coralline algae are somewhat associated with some of the geographic variables (stream distance, rain, human population), but in opposite directions, and so they are negatively associated with each other (graphs are on next page). There are sites at all levels of these geographic variables with no macro algae or no coralsqrtFish 200