Arbitrarily many population maxima under uniform global dispersal

Unrefereed research candidate. Individuals leave their location at rate d and resettle anywhere in the habitat with equal probability. Bai and Li (arXiv:2108.01826) proved that the total equilibrium population has a single peak in d when habitat quality varies by less than a factor of about 1.618, and asked whether several peaks are possible. This package answers yes. For every budget and every N there are smooth increasing resources, converging to a constant in every finite Lp, whose population curve has at least N strict local maxima: a tiny patch of very rich habitat adds a population bump at a dispersal rate comparable to its richness. An exact three-level example has a certified minimum at d = 3; two resource levels always give a single peak; and a three-level example with contrast about 14.17 is certified exactly and by two interval traps. Effect sizes: the peaks are real but tiny. In the 14.17 example the left maximum lies within 10-4 of d0, is about 10-32 high, and vanishes under tiny parameter changes. The result is qualitative. Priority caveat: Liang and Zhang (2021) and Bai, Li and Shi (2024) were read only as abstracts; the former's equal-patch model contains our rational examples. The archive contains the 16-page manuscript (PDF and LaTeX), exact standard-library certificates with receipts, numerical scripts with pinned dependencies, semantic negative controls, CI and SHA-256 sums. Assurance: written proofs; exact rational and interval certificates; internal AI-assisted review only (not peer review, independent reproduction or formal verification). Creator: Anonymous. Text and data CC0-1.0; code MIT.

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-10-27
DOI
https://doi.org/10.5281/zenodo.23687851
Primary Topic
Mathematical and Theoretical Epidemiology and Ecology Models
Type
preprint
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preprint

Arbitrarily many population maxima under uniform global dispersal

Zenodo (CERN European Organization for Nuclear Research)
Mathematical and Theoretical Epidemiology and Ecology Models
preprint

Arbitrarily many population maxima under uniform global dispersal

preprint en

Abstract

Unrefereed research candidate. Individuals leave their location at rate d and resettle anywhere in the habitat with equal probability. Bai and Li (arXiv:2108.01826) proved that the total equilibrium population has a single peak in d when habitat quality varies by less than a factor of about 1.618, and asked whether several peaks are possible. This package answers yes. For every budget and every N there are smooth increasing resources, converging to a constant in every finite Lp, whose population curve has at least N strict local maxima: a tiny patch of very rich habitat adds a population bump at a dispersal rate comparable to its richness. An exact three-level example has a certified minimum at d = 3; two resource levels always give a single peak; and a three-level example with contrast about 14.17 is certified exactly and by two interval traps. Effect sizes: the peaks are real but tiny. In the 14.17 example the left maximum lies within 10-4 of d0, is about 10-32 high, and vanishes under tiny parameter changes. The result is qualitative. Priority caveat: Liang and Zhang (2021) and Bai, Li and Shi (2024) were read only as abstracts; the former's equal-patch model contains our rational examples. The archive contains the 16-page manuscript (PDF and LaTeX), exact standard-library certificates with receipts, numerical scripts with pinned dependencies, semantic negative controls, CI and SHA-256 sums. Assurance: written proofs; exact rational and interval certificates; internal AI-assisted review only (not peer review, independent reproduction or formal verification). Creator: Anonymous. Text and data CC0-1.0; code MIT.

Zenodo (CERN European Organization for Nuclear Research)
Mathematical and Theoretical Epidemiology and Ecology Models
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Arbitrarily many population maxima under uniform global dispersal · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS