Diversity in evolving systems : scaling and dynamics of genealogical trees

Diversity is a fundamental property of all evolving systems. This thesis examines spatial and temporal patterns of diversity. The systems I will study consist of a population of individuals, each with a potentially unique state, together with a dynamics consisting of copying or reproduction of individual states with small modifications to them (innovations). I show that properties of diversity can be understood by modelling the evolving genealogical tree of the population. This formulation is general enough that it captures interesting features of a range of natural and artificial systems, though I will pay particular attention to genetic diversity in biological populations, and discuss the implications of the results to conservation. I show that diversity is unevenly distributed in populations, and a disproportionate fraction is found in small sub-populations. The evolution of diversity is a dynamic process, and I show that large fluctuations in diversity can result purely from the internal dynamics of the population, and not necessarily from external causes. I also show how diversity is affected by the structure of the population (spatial or well-mixed), and determine the scaling of diversity with habitat area in spatial systems. Predictions from the model agree with existing experimental genetic data on global populations of bacteria. I then apply the method of modelling the genealogical tree of a population to further questions in evolution.

Department dc:contributor.department

Massachusetts Institute of Technology. Dept. of Electrical Engineering and Computer Science.

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2004

Author dc:creator

• Rauch, Erik, 1974-

Advisor dc:contributor.advisor

• Gerald Ray Sussman.

• Electrical Engineering and Computer Science.

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/1721.1/30091

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/30091