Stochastic models in the study of ecological pattern and process.

摘要

Traditional approaches to theoretical ecology have focused on the behavior of observable patterns. Presumably, the observed pattern reflects a statistical characterization of the underlying processes. I apply probability theory to model species-area curves and population dynamics. In both cases, new insights result connecting details of lower level process to higher order pattern.; Chapter 1 details the development and testing of a new theory species-area curves (SPARs). The new theory predicts z-values near 0.77 while previous theory claims z-values of about 0.26. We arrived at our prediction using two independent methods: we performed computer simulations of the scheme and we derived its analytical equation. However, although logically accurate, the new theory has an empirical problem: real SPARs tend to have z-values in the interval 0.1--0.2. To obtain these, we assumed that range size and abundance are positively correlated according to a power function.; Chapter 2 examines a real data set for the power function assumed in chapter 1. Using data from the North American Breeding Bird Survey (BBS) project, I found that both least squares regression and principal components analysis (PCA) discover a significant positive correlation between range size and abundance. From the BBS data I fit this power function to the data and estimate the value of the relationship's parameter to be c = 0.27. The resulting fit accounts for 91% of the variance in the data.; In the final chapter of the dissertation, I use stochastic processes to model both the spatial distribution and the birth and survival mechanism of individuals living in an environment of identical, but independent patches. It turns out that linear individual level density dependence easily produces non linear population level dependence. I present the first derivation of the Ricker map and show that patch number interacts with recruitment and survival to generate the carrying capacity parameter. Finally, I combine Monte Carlo simulations and Markov chain theory to study statistical properties population dynamics such as mean time to extinction.