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Population dynamics models based on cumulative density dependent feedback: A link to the logistic growth curve and a test for symmetry using aphid data

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  • Matis, James H.
  • Kiffe, Thomas R.
  • van der Werf, Wopke
  • Costamagna, Alejandro C.
  • Matis, Timothy I.
  • Grant, William E.

Abstract

Density dependent feedback, based on cumulative population size, has been advocated to explain and mathematically characterize “boom and bust” population dynamics. Such feedback results in a bell-shaped population trajectory of the population density. Here, we note that this trajectory is mathematically described by the logistic probability density function. Consequently, the cumulative population follows a time trajectory that has the same shape as the cumulative logistic function. Thus, the Pearl–Verhulst logistic equation, widely used as a phenomenological model for density dependent population growth, can be interpreted as a model for cumulative rather than instantaneous population. We extend the cumulative density dependent differential equation model to allow skew in the bell-shaped population trajectory and present a simple statistical test for skewness. Model properties are exemplified by fitting population trajectories of the soybean aphid, Aphis glycines. The linkage between the mechanistic underpinnings of the logistic probability density function and cumulative distribution function models could open up new avenues for analyzing population data.

Suggested Citation

  • Matis, James H. & Kiffe, Thomas R. & van der Werf, Wopke & Costamagna, Alejandro C. & Matis, Timothy I. & Grant, William E., 2009. "Population dynamics models based on cumulative density dependent feedback: A link to the logistic growth curve and a test for symmetry using aphid data," Ecological Modelling, Elsevier, vol. 220(15), pages 1745-1751.
    • Handle: RePEc:eee:ecomod:v:220:y:2009:i:15:p:1745-1751
    DOI: 10.1016/j.ecolmodel.2009.04.026
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    References listed on IDEAS

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    1. Matis, James H. & Kiffe, Thomas R. & Matis, Timothy I. & Jackman, John A. & Singh, Harvir, 2007. "Population size models based on cumulative size, with application to aphids," Ecological Modelling, Elsevier, vol. 205(1), pages 81-92.
    2. Matis, James H. & Kiffe, Thomas R. & Matis, Timothy I. & Jackman, John A. & Grant, William E. & Singh, Harvir, 2008. "On the use of growth rate parameters for projecting population sizes: Application to aphids," Ecological Modelling, Elsevier, vol. 213(1), pages 133-142.
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    Cited by:

    1. Piyaratne, M.K.D.K. & Zhao, Huiyan & Meng, Qingxiang, 2013. "APHIDSim: A population dynamics model for wheat aphids based on swallowtail catastrophe theory," Ecological Modelling, Elsevier, vol. 253(C), pages 9-16.
    2. Dong Yang & Mengyuan Dang & Lingwen Sun & Feng Han & Feng Shi & Hongbo Zhang & Hongjun Zhang, 2021. "A System Dynamics Model for Urban Residential Building Stock towards Sustainability: The Case of Jinan, China," IJERPH, MDPI, vol. 18(18), pages 1-23, September.
    3. Thakur, Tiesta & Hurley, Terrance M., 2020. "Will Farmers adopt Remote Sensing for Soybean Aphid Management? An Economic Perspective," 2020 Annual Meeting, July 26-28, Kansas City, Missouri 304267, Agricultural and Applied Economics Association.
    4. Wang, Hsiao-Hsuan & Grant, William E. & Koralewski, Tomasz E. & Brewer, Michael J. & Elliott, Norman C., 2021. "Simulating migration of wind-borne pests: “Deconstructing” representation of the emigration process," Ecological Modelling, Elsevier, vol. 460(C).
    5. Yuheng Yang & Xi Zhang & Leran Chang & Yufei Cheng & Shengle Cao, 2018. "A Method of Evaluating Ecological Compensation Under Different Property Rights and Stages: A Case Study of the Xiaoqing River Basin, China," Sustainability, MDPI, vol. 10(3), pages 1-14, February.

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