Chaos and population disappearances in simple ecological models

Area of Science:

• Ecology
• Mathematical Biology
• Population Dynamics

Background:

• Discrete-time single-species models are crucial for understanding population dynamics.
• Some models exhibit complex behaviors where low or high densities lead to extinction.

Purpose of the Study:

• To classify the dynamics of truncated unimodal discrete-time single-species models.
• To identify bifurcations leading to sudden population disappearances.

Main Methods:

• Analysis of truncated unimodal discrete-time single-species models.
• Classification of population dynamics into five types: extinction, semistability, bistability, chaotic semistability, and essential extinction.
• Application to Logistic, Ricker, and generalized Beverton-Holt maps with constant harvesting.

Main Results:

• A five-type classification of population dynamics was proven.
• Two specific bifurcations, saddle node and chaotic blue sky catastrophe, were identified as drivers of sudden population extinction.
• These bifurcations transition populations from bistability to extinction or essential extinction.

Conclusions:

• The study provides a comprehensive classification of population dynamics in discrete-time models.
• Sudden population disappearances are linked to specific bifurcation events.
• Understanding these dynamics is vital for ecological management and conservation efforts.