Generalized contact processes in ecology

This thesis applies principles of statistical physics and non-equilibrium dynamics to problems of scale, randomness, and growth in plant communities. It includes three projects related by their methodology and distinct in the nature of their applications. In the first project, we analyze the relationship between resource availability and species richness in community and regional level models of plant/tree communities. At local scales, vegetative communities tend to follow a unimodal relationship between resources and species richness. However, as per the results of species-energy theory, they tend to obey a monotonically increasing relationship at large scales. We use a multi-species neutral contact process coupled to a heterogeneous resource landscape to explain the scale-dependent transition. We find that the unimodal curve at the community scale may be understood as a tradeoff between colonization of and competition for limited resources. We then construct statistical aggregates of community level ecosystems and find two necessary conditions for a scale-dependent transition: (i) the spatial distribution of resources is highly correlated and (ii) the extent of species pools increases in regions with higher overall resources. The second project integrates the analysis of size-structured populations into the study of the contact process. We introduce the contact process with ontogeny to describe the growth and spread of organisms with size-structured juvenile and adult stages. We derive a mean field theory of the contact process with ontogeny, which we solve yielding an additional oscillatory phase. The mean field phase diagram is found in terms of A, the dimensionless reproductive rate, and 0, the dimensionless growth rate.

Department dc:contributor.department

Massachusetts Institute of Technology. Dept. of Physics.

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2003

Author dc:creator

• Weitz, Joshua Stephen, 1975-

Advisor dc:contributor.advisor

• Daniel H. Rothman and John Joannopoulos.

• Physics.

Statement dc:rights

• M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/17586

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/17586