"Diversity dynamics in large complex biological networks"
One of the goals of ecology is to find a mechanism to stabilize large-scale complex ecological systems with many species interacting each other, universally observed on the earth, e.g. in tropical forrests and coral reefs. Field ecologists in 1960's suggested that complex ecosysmtems were stable because of their complexity itself. This view was challenged by theoretical studies on simple mathematical models in 1970's and the problem of the complexity and stability has been considered a paradox. Theoretical studies so far have supported that high diversity is never maintained and ecosystems with small number of species is barely survived if the interaction matrix is randomly asymmetric (no correlation between the matrix elements) or symmetric (mutualistic or competitive) in the limit of strong complexity. Here we show that half of initial diversity is maintained if the interaction matrix is skew-symmetric (prey-predator relationships). It is revealed that the survived subsystem is characterised by its hierarchically ordered interactions, e.g. pyramidal food web. The present study on the problem of the diversity and stability is not connected only to ecology but also to polymorphisms at major histocompatibility complex, large-scale metabolic networks and initial evolution of life.