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Noname manuscript No. (will be inserted by the editor)

Summary: Noname manuscript No.
(will be inserted by the editor)
The hydra effect, bubbles, and chaos in a simple discrete
population model with constant effort harvesting
Eduardo Liz · Alfonso Ruiz-Herrera
October 26, 2011
Abstract We analyze the effects of a strategy of constant effort harvesting in
the global dynamics of a one-dimensional discrete population model that in-
cludes density-independent survivorship of adults and overcompensating den-
sity dependence. We discuss the phenomenon of bubbling (which indicates
that harvesting can magnify fluctuations in population abundance) and the
hydra effect, which means that the stock size gets larger as harvesting rate in-
creases. Moreover, we show that the system displays chaotic behaviour under
the combination of high per capita recruitment and small survivorship rates.
Keywords discrete population model · harvesting · bubbles · hydra effect ·
Mathematics Subject Classification (2000) 92D25, 39A11, 39A33
1 Introduction
One dimensional maps have been very often used as models of population
dynamics. Despite its apparent simplicity, it is well known that they can exhibit


Source: Arias, Cristina M. - Departamento de Matemática Aplicada, Universidad de Granada


Collections: Mathematics