School Seminars and Colloquia

Relative Abundance

AMSI Seminar

by Thomas Vincent


Institution: Emeritus Professor in Aerospace and Engineering, University of Arizona.
Date: Mon 17th October 2005
Time: 1:00 PM
Location: AMSI Seminar Room, ICT Building, 111 Barry Street Carlton

Abstract: A modified version of a well known model for coexistence is used to examine the conditions that determine the relative abundance of species that are in an evolutionarily stable state.Â



Relative abundance is a term used to refer to the ranking of the number of individuals present within tropically similar species in an ecosystem. We use the G-function method to understand and explain why relative abundance relationships take up the form so often found in field data. We assume that the ecosystem is at or near an evolutionary equilibrium and seek evolutionarily stable strategies (ESS) to identify a coalition individual species.Â



A given G-function can have an ESS coalition of one or more. In these terms, relative abundance refers to ranking, by number of individuals, for each species belonging to the coalition. In order to have a coalition greater than one the model must be frequency dependent, implying that the fitness of any given individual depends on the strategies used by all individuals in the population.Â



This is an essential element of the evolutionary game. Otherwise evolution would drive the population to a single strategy (i.e. a coalition of one) corresponding to an optimal or group fitness strategy. We start with a classical version of the Lotka-Volterra equation that is not frequency dependent and make it frequency dependent in three different ways, thus allowing for the modeling of relative abundance. The first two methods involve a single resource niche and rely on modifications of the competitive effects to provide for a coalition of two or more. These models yield relative abundance distribution curves that are generally convex and are not typical of the majority of field data. The third method creates several resource niches and the simulated results are able to create concave curves (e.g. log normal) that are much closer to field data obtained for natural systems. The models also allows us to make observations and predictions based on the removal of species, changes in competitive effects, and niche availability.Â




About the speaker



Thomas Vincent is an Emeritus Professor in Aerospace and Engineering at the University of Arizona. He graduated as a mechanical engineer and has worked for most of his career at the University of Arizona, Boeing and Hughes Aircraft. He has written numerous publications on on a variety of topics ranging from evolutionary game theory, natural selection and darwinian dynamics through to neural networks.



For more information see http://www.ame.arizona.edu/faculty/vincent/vincent.php#pubÂ

For More Information: Graham Keen, AMSI Ph. 8344-1772