5: Correlations and Associations

Task A

Author

Affiliation

A. J. Smit

University of the Western Cape

Practice Task

Work through these exercises after reading the Correlations and Associations chapter, using the Doubs River data (spe and env). Four exercises are hands-on calculations and two are short conceptual questions.

1. Using the Doubs environmental data, compute the pairwise correlation matrix and display it as a correlation plot (for example with corrplot::corrplot() or GGally::ggcorr()).

2. Identify the two strongest positive and the two strongest negative statistically significant correlations among the environmental variables. Report each coefficient and its \(p\)-value (use cor.test(), or Hmisc::rcorr() / psych::corr.test() for the full matrix of \(p\)-values).

3. Reproduce the species association matrix from the chapter: transpose the fish table so that species become the rows, then compute the among-species association (the spp_assoc1 / spp_assoc2 workflow). Visualise the result.

4. Recompute the association on the un-transposed species table. What is being correlated now, how do the dimensions of the result differ, and why is this not what we want for a species association? Demonstrate with code.

5. For the strongest environmental correlations you found in Exercise 2, give the mechanistic, ecological reason they covary along the upstream-downstream gradient of the Doubs River.

6. Explain what an association matrix, a correlation matrix, and a species dissimilarity matrix each represent and how they differ. What ecological insight does a species association matrix provide that a site-by-site dissimilarity matrix does not?

Assessment Criteria

This Task is not formally assessed. It is built around four hands-on analyses (Exercises 1–4) and two short conceptual questions (Exercises 5–6); work through all six and bring your annotated Quarto document to class for discussion.