Organisms do not live alone but interact with each other, through, for example, resource competition, symbiosis and parasitism. How does the interaction between species the evolutionary and ecological outcome? In this presentation, I will talk about three topics on theoretical study of the coevolutionary dynamics.

The first topic is the effect of mortality enhancement on the coexistence of strains of infectious disease. Dengue virus has four major serotypes that characterized by a large genetic and immunological distance. Antibody dependent enhancement (ADE) results from a new infection with one serotype in an individual with acquired immunity to a different serotype. A mathematical model is presented that describes the epidemiological dynamics of two serotypes of a pathogen where there is the possibility of coinfection and reinfection by a different serotype, along with increased mortality due to enhancement. I show that if there is no or little increased mortality for reinfections (enhancement), serotypes with even a negligibly small immunological distance can stably coexist. In contrast, if the enhancement is sufficiently large, a substantial immunological distance is necessary in order for two serotypes to stably coexist in the population. Therefore high mortality due to enhancement leads to an evolutionarily stable viral community constituting of a set of distantly separated serotypes.

The second topic is malaria control under the threat of counter evolution of vector insect. 　Strategies to eradicate the vector-borne infectious diseases (e.g. malaria and Japanese encephalitis) are often directed to control vectors by insecticides. Spraying insecticide, however, opens a way for the development of the insecticide-resistance in vectors that may lead to the failure in disease control. In this study, I examine if the combined use of insecticide spray with zooprophylaxis can resolve the problem of insecticide-resistant mosquito. Zooprophylaxis refers to a control strategy of an infectious disease by attracting vectors to domestic animal in which the pathogen cannot amplify (a dead-end host). The human malaria parasite Plasmodium spp. has a closed transmission cycle between human and mosquito, and hence cattle can serve as a dead-end livestock. The model reveals that by a suitable choice of insecticide spray rate and cattle density, malaria can be controlled without allowing the development of insecticide-resistance in mosquito.

The last topic is Mullerian mimicry system. Sibling species of tropical butterflies, Heliconius erato and H. melepomene is one of the best known example of Mullerian mimicry, in which many different kinds of locally comimicking morphs are distributed over the Central-South America, forming a patchwork of mimicry rings in a large geographical scale with sharp boundaries (intergradation zones) dividing each piece of mosaic. I here analyze the reaction diffusion system that describes two-species Mullerian mimicry in one and two-dimensional habitats. I analyze the interfacial dynamics of the boundaries to find whether a stable cline is maintained, and to obtain the wave speed if the cline is unstable. The results are: (1) In a spatially uniform habitat the morph with greater base fitness spreads both in one and two species system. (2) In spatial heterogeneous habitats, stable clines can be maintained due to the balance between base fitness gradient and the biased gene flow by negative curvature of boundary. This allows the persistence of spatial mosaic even if one of the morphs is everywhere advantageous over the other. A balanced cline is also maintained if there is gradient in population density.