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Mathematical Models for Society and Biology, 2nd Edition by Edward Beltrami

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Chapter 1

Crabs and Criminals

1.1 Background

A hand reaches into the still waters of the shallow lagoon and gently places a shell on the sandy bottom. We watch. A little later a tiny hermit crab scurries out of a nearby shell and takes possession of the larger one just put in. This sets off a chain reaction in which another crab moves out of its old quarters and scuttles over to the now-empty shell of the previous owner. Other crabs do the same, until at last some barely habitable shell is abandoned by its occupant for a better shelter, and it remains unused.

One day the president of a corporation decides to retire. After much fanfare and maneuvering within the firm, one of the vice presidents is promoted to the top job. This leaves a vacancy, ...

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