Population growth as a nonlinear process

dc.citation.issue11-13
dc.citation.volume38
dc.contributor.authorSoboleva TK
dc.contributor.authorPleasants T
dc.date.available2003-12-01
dc.date.issued2003-12-01
dc.description.abstractThe evolution of the probability density of a biological population is described using nonlinear stochastic differential equations for the growth process and the related Fokker-Planck equations for the time-dependent probability densities. It is shown that the effect of the initial conditions disappears rapidly from the evolution of the mean of the process. But the behaviour of the variance depends on the initial condition. It may monotonically increase, reaching its maximum in the steady state, or have a rather complicated evolution reaching the maximum near the point where growth rates (not population size) is maximal. The variance then decreases to its steady-state value. This observation has implications for risk assessments associated with growing populations, such as microbial populations, which cause food poisoning if the population size reaches a critical level.
dc.description.confidentialfalse
dc.description.publication-statusPublished
dc.format.extent1437 - 1442 (6)
dc.identifier.citationMathematical and Computer Modelling, 2003, 38 (11-13), pp. 1437 - 1442 (6)
dc.identifier.doi10.1016/S0895-7177(03)90147-6
dc.identifier.elements-id281170
dc.identifier.harvestedMassey_Dark
dc.identifier.issn1872-9479
dc.relation.isPartOfMathematical and Computer Modelling
dc.relation.urihttps://www.sciencedirect.com/science/article/pii/S0895717703901476?via=ihub
dc.rightsUnder an Elsevier user license
dc.subjectNonlinear stochastic processes
dc.subjectPopulation growth
dc.subjectFokker-Planck equations
dc.subjectMean evolution
dc.subjectRisk assessments
dc.subject.anzsrc0102 Applied Mathematics
dc.subject.anzsrc0103 Numerical and Computational Mathematics
dc.subject.anzsrc0802 Computation Theory and Mathematics
dc.titlePopulation growth as a nonlinear process
dc.typeJournal article
pubs.notesNot known
pubs.organisational-group/Massey University
pubs.organisational-group/Massey University/College of Sciences
pubs.organisational-group/Massey University/College of Sciences/Institute of Vet, Animal & Biomed Science
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