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

摘要

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.