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.
Highlights
In recent years, the concern for mutualism is growing, since almost all species have mutualistic relationship withHow to cite this paper: Tainaka, K.-I. and Hashimoto, T. (2016) A Theory of Ratio Selection—Lattice Model for Obligate Mutualism
Tainaka et al (2006) have explained the evolution of 1:1 sex ratio on the basis of sustainability [8]. We extend this idea to obligate mutualism
Lattice models have been applied to ecological problems, where simulations have been carried out by two methods: local and global interactions [20] [21]
Summary
The concern for mutualism is growing, since almost all species have mutualistic relationship with. Lattice models have been applied to ecological problems, where simulations have been carried out by two methods: local and global interactions [20] [21]. In the former, interactions occur between neighboring sites, whereas in the latter they occur between any pair of lattice sites. The most famous model of population dynamics in ecology is Lotka-Volterra equations (LVEs) [24] [25] They have a flaw, when we apply them to mutualism [4] [25]. Iwata et al [9] introduced a simple population model for mutualism, applying the lattice gas model They assume that all interactions occur between any pair of cells. We present an idea of “ratio selection” which is an extension of the sex-ratio selection [12]-[15]
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