Diffusion rate determines balance between extinction and proliferationin birth-death processes

We here study spatially extended catalyst induced growth processes.This type of process exists in multiple domains of biology, rangingfrom ecology (nutrients and growth), through immunology (antigensand lymphocytes) to molecular biology (signaling molecules initiatingsignaling cascades). Such system...

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Main Authors: Hilla Behar, Alexandra Agranovich, Yoram Louzoun
Format: Article
Language:English
Published: AIMS Press 2013-03-01
Series:Mathematical Biosciences and Engineering
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Online Access:https://www.aimspress.com/article/doi/10.3934/mbe.2013.10.523
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author Hilla Behar
Alexandra Agranovich
Yoram Louzoun
author_facet Hilla Behar
Alexandra Agranovich
Yoram Louzoun
author_sort Hilla Behar
collection DOAJ
description We here study spatially extended catalyst induced growth processes.This type of process exists in multiple domains of biology, rangingfrom ecology (nutrients and growth), through immunology (antigensand lymphocytes) to molecular biology (signaling molecules initiatingsignaling cascades). Such systems often exhibit an extinction-proliferationtransition, where varying some parameters can lead to either extinctionor survival of the reactants.   When the stochasticity of the reactions, the presence of discretereactants and their spatial distribution is incorporated into theanalysis, a non-uniform reactant distribution emerges, even when allparameters are uniform in space.   Using a combination of Monte Carlo simulation and percolation theorybased estimations; the asymptotic behavior of such systems is studied.In all studied cases, it turns out that the overall survival of thereactant population in the long run is based on the size and shapeof the reactant aggregates, their distribution in space and the reactantdiffusion rate. We here show that for a large class of models, thereactant density is maximal at intermediate diffusion rates and lowor zero at either very high or very low diffusion rates. We give multipleexamples of such system and provide a generic explanation for thisbehavior. The set of models presented here provides a new insighton the population dynamics in chemical, biological and ecologicalsystems.
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spelling doaj-art-f24258d02dfb472f836898590ddbe59d2025-01-24T02:26:12ZengAIMS PressMathematical Biosciences and Engineering1551-00182013-03-0110352355010.3934/mbe.2013.10.523Diffusion rate determines balance between extinction and proliferationin birth-death processesHilla Behar0Alexandra Agranovich1Yoram Louzoun2Department of Mathematics, Bar Ilan University, Ramat GanDepartment of Mathematics, Bar Ilan University, Ramat GanDepartment of Mathematics, Bar Ilan University, Ramat GanWe here study spatially extended catalyst induced growth processes.This type of process exists in multiple domains of biology, rangingfrom ecology (nutrients and growth), through immunology (antigensand lymphocytes) to molecular biology (signaling molecules initiatingsignaling cascades). Such systems often exhibit an extinction-proliferationtransition, where varying some parameters can lead to either extinctionor survival of the reactants.   When the stochasticity of the reactions, the presence of discretereactants and their spatial distribution is incorporated into theanalysis, a non-uniform reactant distribution emerges, even when allparameters are uniform in space.   Using a combination of Monte Carlo simulation and percolation theorybased estimations; the asymptotic behavior of such systems is studied.In all studied cases, it turns out that the overall survival of thereactant population in the long run is based on the size and shapeof the reactant aggregates, their distribution in space and the reactantdiffusion rate. We here show that for a large class of models, thereactant density is maximal at intermediate diffusion rates and lowor zero at either very high or very low diffusion rates. We give multipleexamples of such system and provide a generic explanation for thisbehavior. The set of models presented here provides a new insighton the population dynamics in chemical, biological and ecologicalsystems.https://www.aimspress.com/article/doi/10.3934/mbe.2013.10.523localization.ab modellogistic growthdirected percolationadaption
spellingShingle Hilla Behar
Alexandra Agranovich
Yoram Louzoun
Diffusion rate determines balance between extinction and proliferationin birth-death processes
Mathematical Biosciences and Engineering
localization.
ab model
logistic growth
directed percolation
adaption
title Diffusion rate determines balance between extinction and proliferationin birth-death processes
title_full Diffusion rate determines balance between extinction and proliferationin birth-death processes
title_fullStr Diffusion rate determines balance between extinction and proliferationin birth-death processes
title_full_unstemmed Diffusion rate determines balance between extinction and proliferationin birth-death processes
title_short Diffusion rate determines balance between extinction and proliferationin birth-death processes
title_sort diffusion rate determines balance between extinction and proliferationin birth death processes
topic localization.
ab model
logistic growth
directed percolation
adaption
url https://www.aimspress.com/article/doi/10.3934/mbe.2013.10.523
work_keys_str_mv AT hillabehar diffusionratedeterminesbalancebetweenextinctionandproliferationinbirthdeathprocesses
AT alexandraagranovich diffusionratedeterminesbalancebetweenextinctionandproliferationinbirthdeathprocesses
AT yoramlouzoun diffusionratedeterminesbalancebetweenextinctionandproliferationinbirthdeathprocesses