TITLE:
A Theory of Ratio Selection—Lattice Model for Obligate Mutualism
AUTHORS:
Kei-Ichi Tainaka, Tsuyoshi Hashimoto
KEYWORDS:
Obligate Mutualism, Population Dynamics, Ratio Selection, Allee Effect, Lattice Model, Sex-Ratio Selection, Endosymbiosis
JOURNAL NAME:
Open Journal of Ecology,
Vol.6 No.6,
May
13,
2016
ABSTRACT: Mutualisms are cooperative interactions between members of different
species. We focus on obligate mutualism, where each species cannot survive
without the other. From a theoretical aspect, obligate mutualism is similar to
the relationship between male and female. Empirical data indicate a sex-ratio
selection: male and female have a specific ratio in their population sizes. In
the present paper, we apply lattice model to obligate mutualism between two
species, and present a theory of “ratio selection” which is a generalization of
sex-ratio selection. Computer simulations are carried out by two methods: local
and global interactions. In the former, interactions occur between neighbouring
cells, while in the latter they occur between any pair of cells. Simulations in
both interactions show the so-called Allee effect: both species can survive,
when both densities are large in some extent. However, we find a large difference
between local and global simulations. In the case of local interaction,
restriction for survival is found to be extremely severe compared to global
interaction. Both species require a proper ratio for their sustainability. This
result leads to the theory of ratio selection: when interaction occurs locally,
the ratio of both species is uniquely determined. We discuss that the ratio
selection explains not only the evolution of endosymbionts
from free-living ancestors but also the evolution from endosymbionts
to organelles.