Markov set-chains as models of plant succession

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.