Wade Leitner

Stochastic models of ecological pattern and process

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.

Species-area curves, describing the accumulation of species diversity with area sampled, have been studied longer than any other pattern in ecology. Theoretical explanations of this pattern have maintained that the pattern was largely a statistical artifact that results from the nature of the log-normal distribution of species’ abundance. My thesis advisor, Mike Rosenzweig, and I developed a new theory of species-area curves (SPARs) after we found serious flaws with previous theory. We arrived at our theory using two independent methods: we performed computer simulations of the scheme and applied conditional expectation techniques to analyze the sampling process. To obtain realistic curves, we discovered that we needed to incorporate a biological process assumption. Thus, the statistical artifact explanation was insufficient to explain species-area relationships. We conjectured a power function relationship between range size and abundance. Such a power function can be seen in the range size and average densities of North American birds.

At a finer scale, I study the generation of population dynamics from individual biology. I use stochastic processes to model both the spatial distribution and the birth and survival mechanism of individuals living in an environment of habitat patches. It turns out that linear individual level density dependence easily produces non linear population level dependence. The stochastic process formulation leads to the use of Monte Carlo simulations and Markov chain theory in the study of statistical properties population dynamics such as mean time to extinction. My work in this area now focuses on deriving scaling laws for extinction rates, life history process descriptions, environmental heterogeneity and inclusion of multispecies interactions.

Biographical Data

Originally trained as a biochemist, I worked for several years as an electrical engineer. Working briefly on biomedical projects, I learned the value of mathematics applied to biological problems. Having had a lifelong interest in birds and bird biology, I decided to pursue a Ph. D. in ecology, bringing with me the engineer’s appreciation for applied mathematics. The Flinn/IGERT program in biomathematics helped me to make the transition back to graduate school because it draws the biomathematical community together. Students participating in Flinn/IGERT gain access to these biologists, physicists, mathematicians and other scientists, both on campus and from other universities. The interactions I had in this regard helped me to better understand model design and resulted in a collaboration with another recent Flinn/IGERT graduate, Kevin Anderson. Like many other students, I benefited from Flinn/IGERT faculty serving on my graduate committee. Beyond the formal duties entailed in committee work, I’ve found the close interactions with these faculty to have been extremely productive. Due to the breadth of the Flinn/IGERT program, I expect many students would realize a similar graduate experience.

Leitner, W.A. and M.L. Rosenzweig. 1997. Nested species-area curves and stochastic sampling: a new theory. Oikos 79:503-512.

Leitner, W.A. 1998. Generating population dynamics from stochastic process models of individual biology. Manuscript submitted.

Leitner, W.A. 1998. A power function relating range size and density in North American birds. Manuscript submitted.

Anderson, K. and W.A. Leitner. A test of estimation methods for mean time to extinction. Manuscript in preparation.