Catastrophe-dispersion models in random and varying environments across generations
Lucas R. de Lima, Fábio P. Machado
TLDR
This paper analyzes branching processes with catastrophe and dispersal in varying environments, showing survival is tied to the log-mean process.
Key contributions
- Introduces branching processes with offspring laws derived from growth, catastrophe, and dispersal cycles.
- Demonstrates survival and extinction are determined by the log-mean process, mirroring classical theory.
- Analyzes four dispersal mechanisms, establishing a universal ordering of induced offspring means.
- Provides explicit extinction/survival thresholds for Poissonian growth with binomial survival.
Why it matters
This paper extends classical branching process theory to complex, realistic scenarios involving environmental variability and catastrophic events. It offers a robust framework for understanding population dynamics, with practical ecological applications for survival and extinction predictions.
Original Abstract
We study a class of branching processes in which the offspring distribution is not specified directly but is induced by a cycle of internal colony growth, catastrophic reduction and structured dispersal. The parameters governing growth, survival and dispersal are allowed to vary deterministically or randomly from one generation to the next, giving rise to branching processes in varying and random environments with implicitly defined offspring laws. We show that survival and extinction are governed entirely by the associated log-mean process, exactly as in the classical theory. The paper treats four qualitatively different dispersal mechanisms and establishes a universal ordering of the induced offspring means. For Poissonian growth with binomial survival, explicit thresholds are obtained that determine extinction or survival uniformly over all four mechanisms. A series of ecologically motivated examples with Yule-Simon growth illustrates the versatility of the framework.
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