Consistency and fluctuation theorems for discrete time structured population models having demographic stochasticity

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5 Citations (Scopus)

Abstract

In this paper we prove a consistency theorem (law of large numbers) and a fluctuation theorem (central limit theorem) for structured population processes. The basic assumptions for these theorems are that the individuals have no statistically distinguishing features beyond their class and that the interaction between any two individuals is not too high. We apply these results to density dependent models of Leslie type and to a model for flour beetle dynamics.

Original languageEnglish (US)
Pages (from-to)253-271
Number of pages19
JournalJournal of Mathematical Biology
Volume41
Issue number3
StatePublished - Sep 2000

Fingerprint

Fluctuation Theorem
Structured Populations
Stochasticity
Beetles
Flour
Population Model
Discrete-time
demographic statistics
Demography
Law of large numbers
Tenebrionidae
Theorem
Central limit theorem
Population
Dependent
Interaction
Model
Class

Keywords

  • Central limit theorem
  • Conditional exchangeability
  • Demographic stochasticity
  • Law of large numbers
  • Structured population models

ASJC Scopus subject areas

  • Agricultural and Biological Sciences (miscellaneous)
  • Mathematics (miscellaneous)

Cite this

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abstract = "In this paper we prove a consistency theorem (law of large numbers) and a fluctuation theorem (central limit theorem) for structured population processes. The basic assumptions for these theorems are that the individuals have no statistically distinguishing features beyond their class and that the interaction between any two individuals is not too high. We apply these results to density dependent models of Leslie type and to a model for flour beetle dynamics.",
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