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A simple population theory for mutualism by the use of lattice gas model

Author

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  • Iwata, Shigehide
  • Kobayashi, Kazuyuki
  • Higa, Shinichiro
  • Yoshimura, Jin
  • Tainaka, Kei-ichi

Abstract

The population dynamics of species interactions provides valuable information for life sciences. Lotka–Volterra equations (LVEs) are known to be the most popular model, and they are mainly applied to the systems of predation and competition. However, LVEs often fail to catch the population dynamics of mutualism; the population sizes of species increase infinitely under certain condition (divergence problem). Furthermore, LVEs never predicts the Allee effect in the systems of obligate mutualism. Instead of LVEs, several models have been presented for mutualism; unfortunately, they are rather complicated. It is, therefore, necessary to introduce a simpler theory for mutualism. In the present paper, we apply the lattice gas model which corresponds to the mean-field theory of the usual lattice model. The derived equations are cubic and contain only essential features for mutualism. In the case of obligate mutualism, the dynamics exhibits the Allee effect, and it is almost the same as in the male–female systems. In our model, the population sizes never increase infinitely, because our model contains not only intra- but also interspecific competitions. If the density of one species increases disproportionately in respect of its mutual partners, then this might imply downward pressure on the population abundance of the mutual partner species and such feedback would eventually act as a controlling influence on the population abundance of either species. We discuss several assumptions in our model; in particular, if both species can occupy in each cell simultaneously, then the interspecific competition disappears.

Suggested Citation

  • Iwata, Shigehide & Kobayashi, Kazuyuki & Higa, Shinichiro & Yoshimura, Jin & Tainaka, Kei-ichi, 2011. "A simple population theory for mutualism by the use of lattice gas model," Ecological Modelling, Elsevier, vol. 222(13), pages 2042-2048.
    • Handle: RePEc:eee:ecomod:v:222:y:2011:i:13:p:2042-2048
    DOI: 10.1016/j.ecolmodel.2011.04.009
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    References listed on IDEAS

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    1. Francesca Fiegna & Yuen-Tsu N. Yu & Supriya V. Kadam & Gregory J. Velicer, 2006. "Evolution of an obligate social cheater to a superior cooperator," Nature, Nature, vol. 441(7091), pages 310-314, May.
    2. Unknown, 1986. "Letters," Choices: The Magazine of Food, Farm, and Resource Issues, Agricultural and Applied Economics Association, vol. 1(4), pages 1-9.
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    1. Aliyu, Murtala Bello & Mohd, Mohd Hafiz, 2021. "The interplay between mutualism, competition and dispersal promotes species coexistence in a multiple interactions type system," Ecological Modelling, Elsevier, vol. 452(C).

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