Growth with regulation in fluctuating environments. I. Alternative logistic-like diffusion models
type: Item
instance of: scholarly article
title: Growth with regulation in fluctuating environments. I. Alternative logistic-like diffusion models
zbMATH Open document ID: 0553.92016
DOI: 10.1007/BF00334464
published in: Biological Cybernetics
publication date: 1984-01-01T00:00:00Z
review text: The authors consider a third order logistic-like growth model. In order to account for environmental fluctuations, the idea of growth in a random environment is introduced, by substituting the intrinsic fertility parameter of the population with a normal stationary delta-correlated random process whose mean is identified with the population's fertility. Stochastic differential equations are thus obtained whose solutions X(t) are stationary diffusion processes. By means of a monotone transformation, such processes become Wiener processes Y(t). The different features of the processes X(t) and Y(t) are discussed and compared with the Gompertz growth process and the logistic model. Finally the first passage time T through a state is introduced for the processes X(t) and Y(t) and the Laplace transform of its p.d.f. is calculated. This is useful to acquire further information; e.g. it allows the evaluation of moments of the time necessary for a population to attain an assigned size for the first time.
Mathematics Subject Classification ID: 92D25
Mathematics Subject Classification ID: 60J70
Mathematics Subject Classification ID: 92D40
zbMATH DE Number: 3882255
zbMATH Keywords: third order logistic-like growth model
zbMATH Keywords: environmental fluctuations
zbMATH Keywords: random environment
zbMATH Keywords: normal stationary delta-correlated random process
zbMATH Keywords: Stochastic differential equations
zbMATH Keywords: stationary diffusion processes
zbMATH Keywords: monotone transformation
zbMATH Keywords: Wiener processes
zbMATH Keywords: Gompertz growth process
zbMATH Keywords: first passage time
zbMATH Keywords: Laplace transform
author: Amelia G. Nobile
author: L. M. Ricciardi
MaRDI profile type: Publication
Wikidata QID: Q63434488
cites work: A diffusion model for population growth in random environment
cites work: Growth with regulation in random environment
cites work: Q5528194
cites work: Q5820721
cites work: A population's stationary distribution and chance of extinction in a stochastic environment with remarks on the theory of species packing
cites work: Diffusion Processes in One Dimension
cites work: Q4275389
cites work: Stochastic processes and filtering theory
cites work: Q5671822
cites work: Q4127741
cites work: On the First Passage Time Probability Problem
cites work: Q5545093
cites work: Q3230522
cites work: A study of some diffusion models of population growth
description: scientific article; zbMATH DE number 3882255