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Contributed Talk 5: Uptake levelling in chemotactic bacteria measured by the Gini index

Date: 
Friday 12th September 2014 - 10:40 to 10:55
Venue: 
INI Seminar Room 1
Abstract: 
Co-author: Raymond E. Goldstein (University of Cambridge)

Classic experiments on the accumulation of ducks around distinct food sources found consistency with the `ideal free' distribution in which the local population is proportional to the local supply rate: the animal behaviour smoothes the individual uptake over the population. Motivated by this, we examine the analogous problem in the microbial world: the distribution of chemotactic bacteria around multiple nearby food sources and their associated uptake. Through a series of simple models we illustrate how chemotaxis, nutrient consumption, and diffusion of both bacteria and nutrients conspire to produce spatial distributions with unequal resource uptake. It is suggested that the Gini index, well known in theoretical economics, provides a useful quantification of these effects.
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons