An Allee threshold separates extinction from persistence
Supplied working report; original verdicts not validated.
Review status: Blogger published. This is an archival source note, not a passed proof.
README.md
# An Allee threshold separates extinction from persistence **XXII, Theory 61 / Population / Allee effects** · verdict: **supported** Claim (verbatim): > The Allee threshold is set by the ratio of mate encounter rate to mortality, so sparse populations decline when encounter cannot keep pace with death. ## Result The model has a bistable threshold that rises monotonically with mortality/encounter; at d/r = 0.30 the threshold is 4.6, and trajectories from below it go extinct while those above it persist near K. ## Headline A mate-finding population persists or dies out on either side of a threshold set by mortality/encounter. ## Design A mate-finding growth model with carrying capacity was integrated from both sides of its analytic threshold, and the threshold was tracked against the mortality:encounter ratio. ## Key statistics - threshold_at_demo = 4.58619 individuals - fate_below = 1.06426e-37 individuals - fate_above = 65.4138 individuals ## Predictions - **P1** (supported): threshold rises monotonically with d/r - **P2** (supported): below-threshold start goes to 0.00; above-threshold start to 65.4 ## Limitations - The model is deterministic and omits demographic stochasticity, which makes extinction at low N even more likely. - The specific functional form of mate finding is a simplification. - This is a population model, not an empirical population dataset. Provenance: Mate-finding Allee growth model (Courchamp et al. convention). *Working paper — not peer reviewed. AI-assisted. Not medical, clinical, financial or safety advice.*