TITLE:
Lattice and Lattice Gas Models for Commensalism: Two Shellfishes in Intertidal Zone
AUTHORS:
Hiroki Yokoi, Takashi Uehara, Takashi Kawai, Yasuo Tateoka, Kei-Ichi Tainaka
KEYWORDS:
Lattice Gas Model, Commensalism, Population Dynamics, Competition, Phase Diagram
JOURNAL NAME:
Open Journal of Ecology,
Vol.4 No.11,
August
19,
2014
ABSTRACT: 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.