Size-selective sex-allocation and host feeding in a parasitoid-host model

W.W. Murdoch, R.M. Nisbet, R.F. Luck, H.C.J. Godfray, William Gurney

Research output: Contribution to journalArticle

44 Citations (Scopus)

Abstract

1. Hymenopterous parasitoids frequently exhibit (a) size-selective sex-allocation, laying predominantly male eggs in smaller host individuals and female eggs in larger hosts, and (b) size-selective host-feeding, i.e. feeding on and killing, but not parasitizing, smaller host individuals. We abbreviate size-selective sex-allocation and host-feeding by SSH. We analyse a parasitoid--host model incorporating SSH that recognizes the following: overlapping generations, an invulnerable adult host stage, a young immature stage, an old immature host stage, and only the female parasitoid. We assume that young immature hosts are attacked by the parasitoids, die as a consequence, but do not contribute to the juvenile female parasitoid population; each attack on an old immature host produces a juvenile female parasitoid. 2. SSH leads to delayed pseudo-density-dependence in recruitment to the parasitoid population because the current attack rate on young immatures, which is a function of parasitoid density, influences the future number of old immatures and hence the future per head rate of recruitment of searching parasitoids. SSH has two effects on the model's stability properties. (a) It is potentially stabilizing because it tends to suppress the inherent long-period host-parasitoid cycles. This stabilizing propensity is enhanced when the adult host stage lasts about as long as or langer than the entire immature stage, the immature parasitoid stage is short-lived, and the young immature host stage is not too long-lived or the attack rate on it is not too high. (b) SSH can also destabilize the model by creating a region of instability in which cycles occur with a period related to the total length of the host immature stages. These shorter-period cycles are promoted by the same features that tend to suppress the underlying parasitoid--host cycles. 3. Small perturbations from equilibrium in the locally stable region of parameter space are followed by damped oscillations. However, because of the presence of a multiple attractor, in much of the locally stable region large perturbations may be followed by limit cycles, commonly of the type seen in the new unstable region.
Original languageEnglish
Pages (from-to)533-541
Number of pages9
JournalJournal of Animal Ecology
Volume61
Issue number3
Publication statusPublished - Oct 1992

Fingerprint

sex allocation
parasitoid
immatures
parasitoids
perturbation
egg
density dependence

Keywords

  • parasitoid--host cycles
  • size-selective host-feeding
  • parasitoids

Cite this

Murdoch, W. W., Nisbet, R. M., Luck, R. F., Godfray, H. C. J., & Gurney, W. (1992). Size-selective sex-allocation and host feeding in a parasitoid-host model. Journal of Animal Ecology, 61(3), 533-541.
Murdoch, W.W. ; Nisbet, R.M. ; Luck, R.F. ; Godfray, H.C.J. ; Gurney, William. / Size-selective sex-allocation and host feeding in a parasitoid-host model. In: Journal of Animal Ecology. 1992 ; Vol. 61, No. 3. pp. 533-541.
@article{320dbffbc846409297b32e577c88d982,
title = "Size-selective sex-allocation and host feeding in a parasitoid-host model",
abstract = "1. Hymenopterous parasitoids frequently exhibit (a) size-selective sex-allocation, laying predominantly male eggs in smaller host individuals and female eggs in larger hosts, and (b) size-selective host-feeding, i.e. feeding on and killing, but not parasitizing, smaller host individuals. We abbreviate size-selective sex-allocation and host-feeding by SSH. We analyse a parasitoid--host model incorporating SSH that recognizes the following: overlapping generations, an invulnerable adult host stage, a young immature stage, an old immature host stage, and only the female parasitoid. We assume that young immature hosts are attacked by the parasitoids, die as a consequence, but do not contribute to the juvenile female parasitoid population; each attack on an old immature host produces a juvenile female parasitoid. 2. SSH leads to delayed pseudo-density-dependence in recruitment to the parasitoid population because the current attack rate on young immatures, which is a function of parasitoid density, influences the future number of old immatures and hence the future per head rate of recruitment of searching parasitoids. SSH has two effects on the model's stability properties. (a) It is potentially stabilizing because it tends to suppress the inherent long-period host-parasitoid cycles. This stabilizing propensity is enhanced when the adult host stage lasts about as long as or langer than the entire immature stage, the immature parasitoid stage is short-lived, and the young immature host stage is not too long-lived or the attack rate on it is not too high. (b) SSH can also destabilize the model by creating a region of instability in which cycles occur with a period related to the total length of the host immature stages. These shorter-period cycles are promoted by the same features that tend to suppress the underlying parasitoid--host cycles. 3. Small perturbations from equilibrium in the locally stable region of parameter space are followed by damped oscillations. However, because of the presence of a multiple attractor, in much of the locally stable region large perturbations may be followed by limit cycles, commonly of the type seen in the new unstable region.",
keywords = "parasitoid--host cycles, size-selective host-feeding, parasitoids",
author = "W.W. Murdoch and R.M. Nisbet and R.F. Luck and H.C.J. Godfray and William Gurney",
year = "1992",
month = "10",
language = "English",
volume = "61",
pages = "533--541",
journal = "Journal of Animal Ecology",
issn = "0021-8790",
number = "3",

}

Murdoch, WW, Nisbet, RM, Luck, RF, Godfray, HCJ & Gurney, W 1992, 'Size-selective sex-allocation and host feeding in a parasitoid-host model', Journal of Animal Ecology, vol. 61, no. 3, pp. 533-541.

Size-selective sex-allocation and host feeding in a parasitoid-host model. / Murdoch, W.W.; Nisbet, R.M.; Luck, R.F.; Godfray, H.C.J.; Gurney, William.

In: Journal of Animal Ecology, Vol. 61, No. 3, 10.1992, p. 533-541.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Size-selective sex-allocation and host feeding in a parasitoid-host model

AU - Murdoch, W.W.

AU - Nisbet, R.M.

AU - Luck, R.F.

AU - Godfray, H.C.J.

AU - Gurney, William

PY - 1992/10

Y1 - 1992/10

N2 - 1. Hymenopterous parasitoids frequently exhibit (a) size-selective sex-allocation, laying predominantly male eggs in smaller host individuals and female eggs in larger hosts, and (b) size-selective host-feeding, i.e. feeding on and killing, but not parasitizing, smaller host individuals. We abbreviate size-selective sex-allocation and host-feeding by SSH. We analyse a parasitoid--host model incorporating SSH that recognizes the following: overlapping generations, an invulnerable adult host stage, a young immature stage, an old immature host stage, and only the female parasitoid. We assume that young immature hosts are attacked by the parasitoids, die as a consequence, but do not contribute to the juvenile female parasitoid population; each attack on an old immature host produces a juvenile female parasitoid. 2. SSH leads to delayed pseudo-density-dependence in recruitment to the parasitoid population because the current attack rate on young immatures, which is a function of parasitoid density, influences the future number of old immatures and hence the future per head rate of recruitment of searching parasitoids. SSH has two effects on the model's stability properties. (a) It is potentially stabilizing because it tends to suppress the inherent long-period host-parasitoid cycles. This stabilizing propensity is enhanced when the adult host stage lasts about as long as or langer than the entire immature stage, the immature parasitoid stage is short-lived, and the young immature host stage is not too long-lived or the attack rate on it is not too high. (b) SSH can also destabilize the model by creating a region of instability in which cycles occur with a period related to the total length of the host immature stages. These shorter-period cycles are promoted by the same features that tend to suppress the underlying parasitoid--host cycles. 3. Small perturbations from equilibrium in the locally stable region of parameter space are followed by damped oscillations. However, because of the presence of a multiple attractor, in much of the locally stable region large perturbations may be followed by limit cycles, commonly of the type seen in the new unstable region.

AB - 1. Hymenopterous parasitoids frequently exhibit (a) size-selective sex-allocation, laying predominantly male eggs in smaller host individuals and female eggs in larger hosts, and (b) size-selective host-feeding, i.e. feeding on and killing, but not parasitizing, smaller host individuals. We abbreviate size-selective sex-allocation and host-feeding by SSH. We analyse a parasitoid--host model incorporating SSH that recognizes the following: overlapping generations, an invulnerable adult host stage, a young immature stage, an old immature host stage, and only the female parasitoid. We assume that young immature hosts are attacked by the parasitoids, die as a consequence, but do not contribute to the juvenile female parasitoid population; each attack on an old immature host produces a juvenile female parasitoid. 2. SSH leads to delayed pseudo-density-dependence in recruitment to the parasitoid population because the current attack rate on young immatures, which is a function of parasitoid density, influences the future number of old immatures and hence the future per head rate of recruitment of searching parasitoids. SSH has two effects on the model's stability properties. (a) It is potentially stabilizing because it tends to suppress the inherent long-period host-parasitoid cycles. This stabilizing propensity is enhanced when the adult host stage lasts about as long as or langer than the entire immature stage, the immature parasitoid stage is short-lived, and the young immature host stage is not too long-lived or the attack rate on it is not too high. (b) SSH can also destabilize the model by creating a region of instability in which cycles occur with a period related to the total length of the host immature stages. These shorter-period cycles are promoted by the same features that tend to suppress the underlying parasitoid--host cycles. 3. Small perturbations from equilibrium in the locally stable region of parameter space are followed by damped oscillations. However, because of the presence of a multiple attractor, in much of the locally stable region large perturbations may be followed by limit cycles, commonly of the type seen in the new unstable region.

KW - parasitoid--host cycles

KW - size-selective host-feeding

KW - parasitoids

UR - http://www.jstor.org/stable/5608

M3 - Article

VL - 61

SP - 533

EP - 541

JO - Journal of Animal Ecology

JF - Journal of Animal Ecology

SN - 0021-8790

IS - 3

ER -

Murdoch WW, Nisbet RM, Luck RF, Godfray HCJ, Gurney W. Size-selective sex-allocation and host feeding in a parasitoid-host model. Journal of Animal Ecology. 1992 Oct;61(3):533-541.