Elementary models for population growth and distribution analysis

John C. Hudson*

*Corresponding author for this work

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

A version of the Lotka-Volterra interaction model is adapted to describe population growth and migration processes in a two-region system. The regions are identified as a metropolis and its non-metropolitan hinterland. Several conditions on growth and migration regimes are imposed. The time behavior of the systems are analyzed, noting especially situations where total depopulation or population explosion eventually occur in one or both populations. Neither growth control nor migration control alone results in a condition of long-run stability in both regions. If at least a momentary condition of zero growth is achieved in both regions, it is possible to maintain finite populations if each population follows a logistic natural growth process and migration flow is proportional to the volume of interaction. It is necessary also that the natural increase limitation is strong relative to migration rates. This result holds even if one population has a net migration advantage over the other.

Original languageEnglish (US)
Pages (from-to)361-368
Number of pages8
JournalDemography
Volume7
Issue number3
DOIs
StatePublished - Aug 1 1970

Fingerprint

population growth
migration
zero-growth
population migration
migration policy
metropolis
interaction
logistics

ASJC Scopus subject areas

  • Demography

Cite this

@article{8a686089de0b48feb1ae5257d710adee,
title = "Elementary models for population growth and distribution analysis",
abstract = "A version of the Lotka-Volterra interaction model is adapted to describe population growth and migration processes in a two-region system. The regions are identified as a metropolis and its non-metropolitan hinterland. Several conditions on growth and migration regimes are imposed. The time behavior of the systems are analyzed, noting especially situations where total depopulation or population explosion eventually occur in one or both populations. Neither growth control nor migration control alone results in a condition of long-run stability in both regions. If at least a momentary condition of zero growth is achieved in both regions, it is possible to maintain finite populations if each population follows a logistic natural growth process and migration flow is proportional to the volume of interaction. It is necessary also that the natural increase limitation is strong relative to migration rates. This result holds even if one population has a net migration advantage over the other.",
author = "Hudson, {John C.}",
year = "1970",
month = "8",
day = "1",
doi = "10.2307/2060155",
language = "English (US)",
volume = "7",
pages = "361--368",
journal = "Demography",
issn = "0070-3370",
publisher = "Springer New York",
number = "3",

}

Elementary models for population growth and distribution analysis. / Hudson, John C.

In: Demography, Vol. 7, No. 3, 01.08.1970, p. 361-368.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Elementary models for population growth and distribution analysis

AU - Hudson, John C.

PY - 1970/8/1

Y1 - 1970/8/1

N2 - A version of the Lotka-Volterra interaction model is adapted to describe population growth and migration processes in a two-region system. The regions are identified as a metropolis and its non-metropolitan hinterland. Several conditions on growth and migration regimes are imposed. The time behavior of the systems are analyzed, noting especially situations where total depopulation or population explosion eventually occur in one or both populations. Neither growth control nor migration control alone results in a condition of long-run stability in both regions. If at least a momentary condition of zero growth is achieved in both regions, it is possible to maintain finite populations if each population follows a logistic natural growth process and migration flow is proportional to the volume of interaction. It is necessary also that the natural increase limitation is strong relative to migration rates. This result holds even if one population has a net migration advantage over the other.

AB - A version of the Lotka-Volterra interaction model is adapted to describe population growth and migration processes in a two-region system. The regions are identified as a metropolis and its non-metropolitan hinterland. Several conditions on growth and migration regimes are imposed. The time behavior of the systems are analyzed, noting especially situations where total depopulation or population explosion eventually occur in one or both populations. Neither growth control nor migration control alone results in a condition of long-run stability in both regions. If at least a momentary condition of zero growth is achieved in both regions, it is possible to maintain finite populations if each population follows a logistic natural growth process and migration flow is proportional to the volume of interaction. It is necessary also that the natural increase limitation is strong relative to migration rates. This result holds even if one population has a net migration advantage over the other.

UR - http://www.scopus.com/inward/record.url?scp=0014826574&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0014826574&partnerID=8YFLogxK

U2 - 10.2307/2060155

DO - 10.2307/2060155

M3 - Article

VL - 7

SP - 361

EP - 368

JO - Demography

JF - Demography

SN - 0070-3370

IS - 3

ER -