Punctuated equilibrium, recently regarded as the power law distribution of lifespan, is estimated with respect to self-organized criticality. Previous explanations were based on a global property, such as the selection of species depending on their fitness, however a particular entity defined through such global property cannot be relevant to the notion of "self". Here, we introduce local ambiguity of a niche with respect to function and define a function network by using two types of maps. Due to the local complex structure of the function network, motif and lateral connections, some species are easily replaced by others, and other species have long lives. Punctuated equilibrium can, therefore, be explained by local ambiguous interaction, which suggests the notion of self and supports the idea of self-organized criticality.
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