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Mathematical Biosciences and Engineering

2007, Volume 4, Issue 1: 47-65. doi: 10.3934/mbe.2007.4.47
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Insect development under predation risk, variable temperature, and variable food quality

  • 1.
    Department of Mathematics, University of Nebraska, Lincoln, NE 68588-0130
  • 2.
    Program in Mathematics, College of St. Mary, Omaha, NE 68134
  • 3.
    Division of Biology, Kansas State University, Manhattan, KS 66506
  • Received: 01 November 2005 Accepted: 29 June 2018 Published: 01 November 2006

  • MSC : 92D25, 92D40,92D50.

  • We model the development of an individual insect, a grasshopper, through its nymphal period as a function of a trade-off between prey vigilance and nutrient intake in a changing environment. Both temperature and food quality may be variable. We scale up to the population level using natural mortality and a predation risk that is mass, vigilance, and temperature dependent. Simulations reveal the sensitivity of both survivorship and development time to risk and nutrient intake, including food quality and temperature variations. The model quantifies the crucial role of temperature in trophic interactions and development, which is an important issue in assessing the effects of global climate change on complex environmental interactions.

    Citation: J. David Logan, William Wolesensky, Anthony Joern. Insect development under predation risk, variable temperature, and variable food quality[J]. Mathematical Biosciences and Engineering, 2007, 4(1): 47-65. doi: 10.3934/mbe.2007.4.47

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  • We model the development of an individual insect, a grasshopper, through its nymphal period as a function of a trade-off between prey vigilance and nutrient intake in a changing environment. Both temperature and food quality may be variable. We scale up to the population level using natural mortality and a predation risk that is mass, vigilance, and temperature dependent. Simulations reveal the sensitivity of both survivorship and development time to risk and nutrient intake, including food quality and temperature variations. The model quantifies the crucial role of temperature in trophic interactions and development, which is an important issue in assessing the effects of global climate change on complex environmental interactions.


  • This article has been cited by:

    1. A.N. Laws, A. Joern, Density mediates grasshopper performance in response to temperature manipulation and spider predation in tallgrass prairie, 2017, 107, 0007-4853, 261, 10.1017/S0007485316000894
    2. Julia L. Moore, Justin V. Remais, Developmental Models for Estimating Ecological Responses to Environmental Variability: Structural, Parametric, and Experimental Issues, 2014, 62, 0001-5342, 69, 10.1007/s10441-014-9209-9
    3. J. David Logan, William Wolesensky, An index to measure the effects of temperature change on trophic interactions, 2007, 246, 00225193, 366, 10.1016/j.jtbi.2006.11.014
    4. J. David Logan, Phenologically-Structured Predator-Prey Dynamics with Temperature Dependence, 2008, 70, 0092-8240, 1, 10.1007/s11538-007-9237-6
    5. J. DAVID LOGAN, WILLIAM WOLESENSKY, ACCOUNTING FOR TEMPERATURE IN PREDATOR FUNCTIONAL RESPONSES, 2008, 20, 08908575, 549, 10.1111/j.1939-7445.2007.tb00220.x
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  • © 2007 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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