The systematic formulation of population models for insects with dynamically varying instar duration

R.M. Nisbet, William Gurney

Research output: Contribution to journalArticle

120 Citations (Scopus)

Abstract

We develop a formalism for insect population dynamics which covers the situation where maturation from one instar to its successor is triggered by weight gain and not by chronological age. We specify assumptions which result in the instantaneous “subpopulations” of various instars obeying delay-defferential equations with time delays (representing instar duration) which are themselves dynamic variables, changing in response to the availability of food. We demonstrate the stabilizing potential of variable time delays by studying an idealised two-stage model in which maturation to the adult stage occurs after absorption of a given (fixed) quantity of food.
LanguageEnglish
Pages114-135
Number of pages22
JournalTheoretical Population Biology
Volume23
Issue number1
DOIs
Publication statusPublished - Feb 1983

Fingerprint

insect models
maturation
instars
insect
duration
food
subpopulation
population dynamics
food availability
weight gain
insects

Keywords

  • insect population dynamics
  • dynamic variables
  • instar duration

Cite this

@article{44f3c2269aa340189c1824be8ffcb4c7,
title = "The systematic formulation of population models for insects with dynamically varying instar duration",
abstract = "We develop a formalism for insect population dynamics which covers the situation where maturation from one instar to its successor is triggered by weight gain and not by chronological age. We specify assumptions which result in the instantaneous “subpopulations” of various instars obeying delay-defferential equations with time delays (representing instar duration) which are themselves dynamic variables, changing in response to the availability of food. We demonstrate the stabilizing potential of variable time delays by studying an idealised two-stage model in which maturation to the adult stage occurs after absorption of a given (fixed) quantity of food.",
keywords = "insect population dynamics, dynamic variables, instar duration",
author = "R.M. Nisbet and William Gurney",
year = "1983",
month = "2",
doi = "10.1016/0040-5809(83)90008-4",
language = "English",
volume = "23",
pages = "114--135",
journal = "Theoretical Population Biology",
issn = "0040-5809",
number = "1",

}

The systematic formulation of population models for insects with dynamically varying instar duration. / Nisbet, R.M. ; Gurney, William.

In: Theoretical Population Biology, Vol. 23, No. 1, 02.1983, p. 114-135.

Research output: Contribution to journalArticle

TY - JOUR

T1 - The systematic formulation of population models for insects with dynamically varying instar duration

AU - Nisbet, R.M.

AU - Gurney, William

PY - 1983/2

Y1 - 1983/2

N2 - We develop a formalism for insect population dynamics which covers the situation where maturation from one instar to its successor is triggered by weight gain and not by chronological age. We specify assumptions which result in the instantaneous “subpopulations” of various instars obeying delay-defferential equations with time delays (representing instar duration) which are themselves dynamic variables, changing in response to the availability of food. We demonstrate the stabilizing potential of variable time delays by studying an idealised two-stage model in which maturation to the adult stage occurs after absorption of a given (fixed) quantity of food.

AB - We develop a formalism for insect population dynamics which covers the situation where maturation from one instar to its successor is triggered by weight gain and not by chronological age. We specify assumptions which result in the instantaneous “subpopulations” of various instars obeying delay-defferential equations with time delays (representing instar duration) which are themselves dynamic variables, changing in response to the availability of food. We demonstrate the stabilizing potential of variable time delays by studying an idealised two-stage model in which maturation to the adult stage occurs after absorption of a given (fixed) quantity of food.

KW - insect population dynamics

KW - dynamic variables

KW - instar duration

U2 - 10.1016/0040-5809(83)90008-4

DO - 10.1016/0040-5809(83)90008-4

M3 - Article

VL - 23

SP - 114

EP - 135

JO - Theoretical Population Biology

T2 - Theoretical Population Biology

JF - Theoretical Population Biology

SN - 0040-5809

IS - 1

ER -