## Abstract

We model the evolution of two competing populations* *by a two-dimensional size-dependent branching process of Ricker type. For a small force of inhibition by the present population (modeling, e.g., scarcity of food) the process typically follows the corresponding deterministic Ricker competition model closely, for a very long time. Under some conditions, notably a mutual invasibility condition, the deterministic model has a coexistence fixed point in the open first quadrant. The asymptotic behaviour is studied through the quasi-stationary distribution of the process. We initiate a study of those distributions as the inhibitive force approach 0.

Original language | Undefined/Unknown |
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Title of host publication | Difference Equations, Discrete Dynamical Systems and Applications |

Editors | Lluís Alsedà i Soler, Jim M. Cushing, Saber Elaydi, Alberto Adrego Pinto |

Publisher | Springer |

Pages | 135–144 |

ISBN (Electronic) | 978-3-662-52927-0 |

ISBN (Print) | 978-3-662-52926-3 |

Publication status | Published - 2016 |

MoE publication type | A4 Article in a conference publication |

Event | 18th International Conference on Difference Equations and Applications - 18th International Conference on Difference Equations and Applications Duration: 23 Jul 2012 → 27 Jul 2012 |

### Conference

Conference | 18th International Conference on Difference Equations and Applications |
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Period | 23/07/12 → 27/07/12 |