Bounding biomass in the Fisher equation

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dc.creatorBirch, Daniel A.
dc.creatorTsang, Yue-Kin
dc.creatorYoung, William R.
dc.date2007-03-17
dc.date.accessioned2026-07-07T08:27:21Z
dc.date.available2026-07-07T08:27:21Z
dc.descriptionThe FKPP equation with a variable growth rate and advection by an incompressible velocity field is considered as a model for plankton dispersed by ocean currents. If the average growth rate is negative then the model has a survival-extinction transition; the location of this transition in the parameter space is constrained using variational arguments and delimited by simulations. The statistical steady state reached when the system is in the survival region of parameter space is characterized by integral constraints and upper and lower bounds on the biomass and productivity that follow from variational arguments and direct inequalities. In the limit of zero-decorrelation time the velocity field is shown to act as Fickian diffusion with an eddy diffusivity much larger than the molecular diffusivity and this allows a one-dimensional model to predict the biomass, productivity and extinction transitions. All results are illustrated with a simple growth and stirring model.
dc.description32 Pages, 13 Figures
dc.identifierhttps://arxiv.org/abs/q-bio/0703039
dc.identifierhttp://arxiv.org/abs/q-bio/0703039
dc.identifierPhysical Review E 75, 066304 (2007)
dc.identifierdoi:10.1103/PhysRevE.75.066304
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/137245
dc.subjectPopulations and Evolution
dc.subjectChaotic Dynamics
dc.subjectChemical Physics
dc.titleBounding biomass in the Fisher equation
dc.typetext

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