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Lattice and Lattice Gas Models for Commensalism: Two Shellfishes in Intertidal Zone

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The study of mutual interactions in an intertidal zone is important. We are interested in two sessile shellfishes, mussel (Septifer virgatus: species X) and goose barnacle (Capitulum mitella: species Y). Both species X and Y have similar body sizes, and live in an intertidal zone. Their relation is known to be a kind of commensalism: the survival rate of X increases near the location of Y. In contrast, Y receives no gain from X. In the present paper, we present lattice and lattice gas models for commensalism. The latter is mean-field theory of the former. It is found that the relation of commensalism is not stable. Under certain conditions, the competition prevails between both species; if the density of Y is high, the species X receives a damage originated in the limiting space. Moreover, we find that the basic equation derived by lattice gas model well explains the population dynamics for lattice model.
Cite this paper
Yokoi, H. , Uehara, T. , Kawai, T. , Tateoka, Y. and Tainaka, K. (2014) Lattice and Lattice Gas Models for Commensalism: Two Shellfishes in Intertidal Zone. Open Journal of Ecology, 4, 671-677. doi: 10.4236/oje.2014.411057. 
 

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