Doctoral Dissertations

Date of Award

5-2001

Degree Type

Dissertation

Degree Name

Doctor of Philosophy

Major

Ecology and Evolutionary Biology

Major Professor

Mark Kot, Thomas G. Hallam

Committee Members

Mitch Cruzan, James A. Drake, Robert V. O'Neill, Daniel Simberloff, Jake Weltzin

Abstract

In this dissertation I examine Markov set-chains as a new approach for modeling plant succession. Set-chains are an extension of Markov chains, due to Hartfiel (1991, 1998), that makes it possible to model succession when transition probabilities are uncertain or fluctuating. In Markov set-chains each transition probability is expressed as an interval containing the range of all possible values for that parameter. In turn, a set-chain predicts community composition as a range of possible frequencies for each species. First, I give an introduction to Markov set-chains and methods for iterating and finding their asymptotic behavior. I demonstrate the formulation and computation of a set-chain with an example from a grassland restoration experiment. Next, I use set-chains to investigate the dynamics of experimental grassland plots planted with different species diversities. The set-chain predicts that plots with more planted species will vary less in composition than those with fewer species. I analyze a restricted, two-state set-chain and show that these differences in variability reflect variability thresholds that identify four distinct regions of parameter-space. These regions delineate which transition probability intervals lead to widening, or narrowing, distribution intervals as the system develops. Finally, I use simulations to investigate several questions about how uncertainty propagates from data to parameter estimates and predictions in Markov set-chains. Markov set-chains are an important contribution to our understanding of what controls variability in ecological systems; they may be useful tools for getting more predictable outcomes from ecological restoration and construction.

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