2013/04/03 by W. Felder, William Felder, Edward C. Waymire +2
Biochemistry, Genetics and Molecular Biology · Mathematics · #Diffusion and Search Dynamics #FOS: Mathematics #Probability (math.PR) #math.PR
paper · pdf · doi:10.48550/arxiv.1304.1208
arxiv created 2013/04/03 · openalex publication_date 2013/04/03 · arxiv updated 2013/04/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This note is motivated by the article by F. Lutscher, E. Pachepsky, and M. Lewis (2005), The Effect of Dispersal Patterns on Stream Populations SIAM Rev. Vol. 47 No. 4 pp. 749-772 on the drift paradox. We consider the case of a regime switching probabilistic model for a population of organisms living in a one dimensional environment with drift towards an absorbing boundary of the type introduced by Lutscher et al. (2005). In particular, the two regimes consist of birth/death style demographics governing the evolution of the immobile regime, and some form of advection-dispersion governing the evolution of the mobile regime, together with a regime-switching mechanism linking the two. In the present note it is shown for the regime-switching model, and in contrast to the results in the afore cited work, for any finite advection speed, no matter how large, there is a finite critical length of the domain above which the population can persist.