We study constraints on the population of neutrino emitting blazars imposed by the absence of doublets in astrophysical muon neutrino signal and z>0.3 redshift of nearest identified neutrino-emitting blazar (an order of magnitude further away than the nearest gamma-ray emitting blazar). We show that in spite of the absence of correlation of neutrino arrival directions with positions of gamma-ray emitting blazars, cumulative blazar flux could explain most of astrophysical neutrino flux measured in muon neutrino channel. This is possible if the population of neutrino emitting blazars has experienced rapid positive evolution at least as (1+z)^5 at z< 1. Such a model avoids previously derived constraint on the low level of blazar contribution to extragalactic neutrino flux because gamma-ray and neutrino fluxes are dominated by different sets of blazars. Rapid evolution of neutrino emitting blazars could be explained by the fact that only high luminosity blazars hosting radiatively efficient accretion flows are efficient neutrino sources.
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