Stage-specificity and the synchronisation of life-cycles to periodic environmental variations

E.P.M. Grist, William Gurney

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

Previous work has shown that life-histories consisting of a contiguous series of stages all with density independent development rates exhibiting the same dependence on time cannot synchronise to a periodic environmental variation. This work also examined models representing both dormancy and quiescence at specific points in the life cycle and showed that both could produce strong synchronising effects. In this paper we examine a very general strategic model of an organism with a two-stage life-cycle each stage having a density independent development rate with a characteristic (periodic) time-dependence. We develop a compact representation of this model in terms of a circle map composed from two simple rotations and the ldquointerphase maprdquo representing the relationship between the physiological times for the two life-history stages. We derive a series of analytic results relating the behaviour of systems whose interphase maps are interrelated and give analytic conditions for a broad class of two-stage circle maps to have a fixed point (that is for the systems they describe to reach the critical life-history stage at the same point in each environmental cycle). Finally we report the results of a numerical investigation of the relationship between the biological characteristics of the development functions and the fine-scale details of the locking behaviour of the systems they define.
LanguageEnglish
Pages123-147
Number of pages25
JournalJournal of Mathematical Biology
Volume34
Issue number2
DOIs
Publication statusPublished - Jan 1995

Fingerprint

Life Cycle Stages
Life Cycle
Specificity
Life cycle
Circle Map
life cycle (organisms)
Synchronization
life history
Dormancy
Series
Time Dependence
Locking
Numerical Investigation
interphase
dormancy
Interphase
Fixed point
developmental stages
Model
Cycle

Keywords

  • life-cycle
  • synchronisation
  • periodic
  • environment
  • stage-specific

Cite this

@article{a9dd07d324504583abda5103d5dbdcce,
title = "Stage-specificity and the synchronisation of life-cycles to periodic environmental variations",
abstract = "Previous work has shown that life-histories consisting of a contiguous series of stages all with density independent development rates exhibiting the same dependence on time cannot synchronise to a periodic environmental variation. This work also examined models representing both dormancy and quiescence at specific points in the life cycle and showed that both could produce strong synchronising effects. In this paper we examine a very general strategic model of an organism with a two-stage life-cycle each stage having a density independent development rate with a characteristic (periodic) time-dependence. We develop a compact representation of this model in terms of a circle map composed from two simple rotations and the ldquointerphase maprdquo representing the relationship between the physiological times for the two life-history stages. We derive a series of analytic results relating the behaviour of systems whose interphase maps are interrelated and give analytic conditions for a broad class of two-stage circle maps to have a fixed point (that is for the systems they describe to reach the critical life-history stage at the same point in each environmental cycle). Finally we report the results of a numerical investigation of the relationship between the biological characteristics of the development functions and the fine-scale details of the locking behaviour of the systems they define.",
keywords = "life-cycle, synchronisation, periodic , environment , stage-specific",
author = "E.P.M. Grist and William Gurney",
year = "1995",
month = "1",
doi = "10.1007/BF00178770",
language = "English",
volume = "34",
pages = "123--147",
journal = "Journal of Mathematical Biology",
issn = "0303-6812",
number = "2",

}

Stage-specificity and the synchronisation of life-cycles to periodic environmental variations. / Grist, E.P.M.; Gurney, William.

In: Journal of Mathematical Biology, Vol. 34, No. 2, 01.1995, p. 123-147.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Stage-specificity and the synchronisation of life-cycles to periodic environmental variations

AU - Grist, E.P.M.

AU - Gurney, William

PY - 1995/1

Y1 - 1995/1

N2 - Previous work has shown that life-histories consisting of a contiguous series of stages all with density independent development rates exhibiting the same dependence on time cannot synchronise to a periodic environmental variation. This work also examined models representing both dormancy and quiescence at specific points in the life cycle and showed that both could produce strong synchronising effects. In this paper we examine a very general strategic model of an organism with a two-stage life-cycle each stage having a density independent development rate with a characteristic (periodic) time-dependence. We develop a compact representation of this model in terms of a circle map composed from two simple rotations and the ldquointerphase maprdquo representing the relationship between the physiological times for the two life-history stages. We derive a series of analytic results relating the behaviour of systems whose interphase maps are interrelated and give analytic conditions for a broad class of two-stage circle maps to have a fixed point (that is for the systems they describe to reach the critical life-history stage at the same point in each environmental cycle). Finally we report the results of a numerical investigation of the relationship between the biological characteristics of the development functions and the fine-scale details of the locking behaviour of the systems they define.

AB - Previous work has shown that life-histories consisting of a contiguous series of stages all with density independent development rates exhibiting the same dependence on time cannot synchronise to a periodic environmental variation. This work also examined models representing both dormancy and quiescence at specific points in the life cycle and showed that both could produce strong synchronising effects. In this paper we examine a very general strategic model of an organism with a two-stage life-cycle each stage having a density independent development rate with a characteristic (periodic) time-dependence. We develop a compact representation of this model in terms of a circle map composed from two simple rotations and the ldquointerphase maprdquo representing the relationship between the physiological times for the two life-history stages. We derive a series of analytic results relating the behaviour of systems whose interphase maps are interrelated and give analytic conditions for a broad class of two-stage circle maps to have a fixed point (that is for the systems they describe to reach the critical life-history stage at the same point in each environmental cycle). Finally we report the results of a numerical investigation of the relationship between the biological characteristics of the development functions and the fine-scale details of the locking behaviour of the systems they define.

KW - life-cycle

KW - synchronisation

KW - periodic

KW - environment

KW - stage-specific

U2 - 10.1007/BF00178770

DO - 10.1007/BF00178770

M3 - Article

VL - 34

SP - 123

EP - 147

JO - Journal of Mathematical Biology

T2 - Journal of Mathematical Biology

JF - Journal of Mathematical Biology

SN - 0303-6812

IS - 2

ER -