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From Two to Many: Multivariate Statistics

Ecological data are multivariate. Your statistics should be too.

We often start by asking how two variables are related. But ecological datasets rarely stop there. A community contains many species, an environment contains many variables, and biological responses are shaped by multiple factors at once.

We work with communities, environmental gradients, multiple traits, and interacting predictors. Multivariate methods give us a way to analyse these complex datasets by considering multiple variables together rather than reducing them to a pile of separate, disconnected tests.

What you will learn

  • 01  Understand

    Why multivariate methods are needed, how unsupervised and supervised approaches differ, and the key assumptions and limitations of common methods.

  • 02  Explore

    Find structure in complex datasets, and understand what ordination axes and distances actually represent.

  • 03  Explain

    Choose an appropriate method for a biological question, and test whether groups, predictors, or environmental variables explain the structure you found.

  • 04  Apply

    Perform common multivariate analyses in R, interpret the results and visualisations, and recognise common pitfalls such as pseudoreplication, multicollinearity, and inappropriate distance measures.

The course

The two days follow a simple logic: first find structure in your data, then explain it.

Day 1 · Explore Day 2 · Explain
Clustering Linear Discriminant Analysis
Principal Component Analysis Logistic Regression
NMDS / PCoA PERMANOVA
Constrained Ordination

Day 1 – Explore: find structure in your data without specifying a response.

Day 2 – Explain: test whether known groups, predictors, or environmental variables explain that structure.

Course Details

  • Course number: 78085-01
  • Credit points: 1 ECTS
  • Dates: Tuesday 23 March 2027 + Wednesday 24 March 2027
  • Time: 09:15-16:00 each day
  • Format: In-person, hands-on computer lab
  • Locations: TBA
  • Programme: TBA
  • Prerequisites: Basic R knowledge (data frames, subsetting, plotting)
  • Preparation: See R Setup & Basics
Handouts

Getting started

Why Multivariate Statistics?

Ecological systems are complex, and a single response variable is rarely enough to describe them. Rather than tracking the abundance of one species, ecologists typically work with entire communities: dozens or hundreds of species measured simultaneously across many sites or treatments.

Add to that the multiple environmental drivers you might want to account for (temperature, soil chemistry, land use, disturbance history) and it quickly becomes clear why running separate univariate tests for each variable is both impractical and statistically problematic. Running many separate tests increases the risk of false positives and makes it harder to interpret the overall structure of the data.

Multivariate methods address this directly. They allow us to analyse several variables together, account for their relationships, and reveal patterns and gradients that may be difficult to detect when variables are examined separately. The result is a richer, more honest picture of your system.

Textbooks

These are the key references for the course, ranging from accessible introductions to authoritative ecological treatments:

  • Borcard, D., Gillet, F., & Legendre, P. (2018). Numerical Ecology with R (2nd ed.). Springer: most directly relevant to this course
  • Legendre, P. & Legendre, L. (2012). Numerical Ecology (3rd ed.). Elsevier: the comprehensive ecological reference
  • James, G., Witten, D., Hastie, T., & Tibshirani, R. (2021). An Introduction to Statistical Learning (2nd ed.). Free PDF: accessible introduction
  • Hastie, T., Tibshirani, R., & Friedman, J. (2009). The Elements of Statistical Learning (2nd ed.). Free PDF: the advanced reference

Online Resources

Instructor

Jean-Claude Walser · GDC, ETH Zurich ✉ jean-claude.walser[🙈]usys.ethz.ch