Extinction risk of a meta-population

Aggregation approach

Hiroshi Hakoyama, Yoh Iwasa

Research output: Contribution to journalArticle

12 Citations (Scopus)

Abstract

Aggregation of variables of a complex mathematical model with realistic structure gives a simplified model which is more suitable than the original one when the amount of data for parameter estimation is limited. Here we explore use of a formula derived for a single unstructured population (canonical model) in predicting the extinction time for a population living in multiple habitats. In particular we focus multiple populations each following logistic growth with demographic and environmental stochasticities, and examine how the mean extinction time depends on the migration and environmental correlation. When migration rate and/or environmental correlation are very large or very small, we may express the mean extinction time exactly using the formula with properly modified parameters. When parameters are of intermediate magnitude, we generate a Monte Carlo time series of the population size for the realistic structured model, estimate the "effective parameters" by fitting the time series to the canonical model, and then calculate the mean extinction time using the formula for a single population. The mean extinction time predicted by the formula was close to those obtained from direct computer simulation of structured models. We conclude that the formula for an unstructured single-population model has good approximation capability and can be applicable in estimating the extinction risk of the structured meta-population model for a limited data set.

Original languageEnglish
Pages (from-to)203-216
Number of pages14
JournalJournal of Theoretical Biology
Volume232
Issue number2
DOIs
Publication statusPublished - Jan 21 2005

Fingerprint

Extinction Time
Metapopulation
Extinction
Aggregation
extinction
Agglomeration
Population Model
Canonical Model
Population
Migration
Time series
Logistic Growth
time series analysis
Stochasticity
Population Size
Parameter Estimation
Express
Computer Simulation
Population Density
Model

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Modelling and Simulation
  • Biochemistry, Genetics and Molecular Biology(all)
  • Immunology and Microbiology(all)
  • Agricultural and Biological Sciences(all)
  • Applied Mathematics

Cite this

Extinction risk of a meta-population : Aggregation approach. / Hakoyama, Hiroshi; Iwasa, Yoh.

In: Journal of Theoretical Biology, Vol. 232, No. 2, 21.01.2005, p. 203-216.

Research output: Contribution to journalArticle

Hakoyama, Hiroshi ; Iwasa, Yoh. / Extinction risk of a meta-population : Aggregation approach. In: Journal of Theoretical Biology. 2005 ; Vol. 232, No. 2. pp. 203-216.
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