Thinking Inside the Box: An Advection-Diffusion Model of Animal Movement in an Enclosed Region

2019/09/17 by Stephen Tennenbaum, Tennenbaum, Stephen, John V. Gatto +3
Environmental Science · Mathematics · #Analysis of PDEs (math.AP) #Ecosystem dynamics and resilience #FOS: Biological sciences #FOS: Mathematics #Mathematical Biology Tumor Growth #Quantitative Methods (q-bio.QM)

paper · pdf · doi:10.48550/arxiv.1909.07625

openalex publication_date 2019/09/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We develop simple diffusion-advection models to estimate the average time it takes fish to reach one of the boundaries of an enclosure and the population distribution over time moving in the enclosure (such as a lake or slough). We start with a combination of random walks and directed movement and then, from these, proceeding to the associated Partial Differential Equations and their solution. We also find the evolution of the population distribution and communities composition over time moving in the enclosure. Although this model was developed with fish movements in mind it has wide-ranging applicability scaling from the molecular to human and action from inert to deliberate.

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