Lattice and Lattice Gas Models for Commensalism: Two Shellfishes in Intertidal Zone
- 1 Graduate School of Science and Technology, Shizuoka University, Naka-ku, Hamamatsu, Japan
- 2 Graduate School of Science and Technology, Shizuoka University, Naka-ku, Hamamatsu, Japan
- 3 Faculty of Science, University of Ryukyus, 1-Senbaru, Nishihara, Nakagami, Okinawa, Japan
- 4 Graduate School of Science and Technology, Shizuoka University, Naka-ku, Hamamatsu, Japan
- 5 Graduate School of Science and Technology, Shizuoka University, Naka-ku, Hamamatsu, Japan
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.
- Neumann, D. (1976) Adaptations of Chironomids to Intertidal Environments. Annual Review of Entomology, 21, 387- 414. http://dx.doi.org/10.1146/annurev.en.21.010176.002131
- Lent, C.M. (1969) Adaptations of the Ribbed Mussel, Modiolus demissus (Dillvvyn), to the Intertidal Habitat. American Zoologist, 9, 283-292. http://dx.doi.org/10.1093/icb/9.2.283
- Reese, E.S. (1969) Behavioral Adaptations of Intertidal Hermit Grabs. American Zoologist, 9, 343-355. http://dx.doi.org/10.1093/icb/9.2.343
- Faubel, A., Sluys, R. and Reid, D.G. (2007) A New Genus Species of Polyclad Flatworm Found in the Mantle Cavities of Gastropod Molluscs in the High-Intertidal Zone of the Pacific Coast of Central America. Journal of the Marine Biological Association of the United Kingdom, 87, 429-434. http://dx.doi.org/10.1017/S0025315407055245
- Fujiwara, Y., Urabe, J. and Takeda, S. (2014) Host Preference of a Symbiotic Flatworm in Relation to the Ecology of Littoral Snails. Marine Biology, 161, 1873-1882. http://dx.doi.org/10.1007/s00227-014-2469-8
- Kawai, T. and Tokeshi, M. (2004) Variable Modes of Facilitation in the Upper Intertidal: Goose Barnacles and Mussels. Marine Ecology Progress Series, 272, 203-213. http://dx.doi.org/10.3354/meps272203
- Kawai, T. and Tokeshi, M. (2006) Asymmetric Coexistence: Bidirectional Abiotic and Biotic Effects between Goose Barnacles and Mussels. Journal of Animal Ecology, 75, 928-941. http://dx.doi.org/10.1111/j.1365-2656.2006.01111.x
- Kawai, T. and Tokeshi, M. (2007) Testing the Facilitation-Competition Paradigm under the Stress-Gradient Hypothesis: Decoupling Multiple Stress Factors. Proceedings of the Royal Society B: Biological Sciences, 274, 2503-2508. http://dx.doi.org/10.1098/rspb.2007.0871
- Lotka, A.J. (1925) Elements of Physical Biology. Williams and Wilkins, Baltimore.
- Volterra, V. (1926) Pages 409-448 in Chapman R.N. 1931. Animal Ecology. McGraw-Hill, New York.
- Begon, M., Townsend, C.R. and Harper, J.L. (2006) Ecology: From Individuals to Ecosystems. Wiley, New York.
- Takeuchi, Y. (1996) Global Dynamical Properties of Lotka-Volterra Systems. World Scientific, Singapore City.
- Tainaka, K. (1988) Lattice Model for the Lotka-Volterra System. Journal of the Physical Society of Japan, 57, 2588- 2590. http://dx.doi.org/10.1143/JPSJ.57.2588