Ecological problems often require multivariate analyses. Ever since Bray and Curtis (1957) drew an analogy between Euclidean distance and community dissimilarity, most multivariate ecological inference has been based on geometric ideas. For example, ecologists routinely use distance-based ordination methods (e.g. multidimensional scaling) to enhance the interpretability of multivariate data. More recently, distance-based diversity indices that account for functional differences between species are now routinely used. But in most other areas of science, inference is based on Fisher's (1922) likelihood concept; statisticians view likelihood as an advance over purely geometric approaches. Nevertheless, likelihood-based reasoning is rare in multivariate statistical ecology. Using ordination and functional diversity as case studies, my thesis addresses the questions: Why is likelihood rare in multivariate statistical ecology? Can likelihood be of practical use in multivariate analyses of real ecological data? Should the likelihood concept replace multidimensional geometry as the foundation for multivariate statistical ecology? I trace the history of quantitative plant ecology to argue that the geometric focus of contemporary multivariate statistical ecology is a legacy of an early 20th century debate on the nature of plant communities. Using the Rao-Blackwell and Lehmann-Scheffé theorems, which both depend on the likelihood concept, I show how to reduce bias and sampling variability in estimators of functional diversity. I also show how to use likelihood-based information criteria to select among ordination methods. Using computationally intensive Markov-chain Monte Carlo methods, I demonstrate how to expand the range of likelihood-based ordination procedures that are computationally feasible. Finally, using philosophical ideas from formal measurement theory, I argue that a likelihood-based multivariate statistical ecology outperforms the geometry-based alternative by providing a stronger connection between analysis and the real world. Likelihood should be used more often in multivariate ecology.
| Identifer | oai:union.ndltd.org:TORONTO/oai:tspace.library.utoronto.ca:1807/26336 |
| Date | 23 February 2011 |
| Creators | Walker, Steven C. |
| Contributors | Jackson, Donald Andrew |
| Source Sets | University of Toronto |
| Language | en_ca |
| Detected Language | English |
| Type | Thesis |
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