Indirect gradient analysis by Markov-chain Monte Carlo

Classical gradient analysis continues to be used to explore and test theories and models in community ecology. Yet the foundations of classical gradient analysis were developed at a time when computational power was limited, relative to current computational power. I argue that this history has left a lasting legacy on the field. Consequently, many gradient analyses do not to take advantage of current computer technology. Here I show how to use computationally intensive Markov-chain Monte Carlo methods to improve gradient analyses of presence–absence community data. The methods that I use were developed by quantitative social scientists in the early 1990s, and therefore tested and efficient software already exists for practical data analysis. As an example, I analyze the classic dune meadow vegetation data. A main advantage of the Bayesian approach to indirect gradient analysis is that, unlike essentially all classical indirect methods, it is able to make empirically testable probabilistic predictions of observed species occurrence patterns. The Bayesian approach also poses challenges for statistical ecology. In particular, the development of Markov-chain Monte Carlo methods for a wider class of Bayesian indirect gradient analysis models would permit more flexible approaches to generating probabilistic predictions.