We consider unfavoured light quark/antiquark to D meson fragmentation. We discuss nonperturbative effects for small transverse momenta. The asymmetry for D + and D − production measured by the LHCb collaboration provides natural constraints on the parton (quark/antiquark) fragmentation functions. We find that already a fraction of q/q → D fragmentation probability is sufficient to account for the measured asymmetry. We make predictions for similar asymmetry for neutral D mesons. Large D-meson production asymmetries are found for large x F which is related to dominance of light quark/antiquark q/q → D fragmentation over the standard c → D fragmentation. As a consequence, prompt atmospheric neutrino flux at high neutrino energies can be much larger than for the conventional c → D fragmentation. The latter can constitute a sizeable background for the cosmic neutrinos claimed to be observed recently by the IceCube Observatory. Large rapidity-dependent D + /D − and D 0 /D 0 asymmetries are predicted for low ( √ s = 20 -100 GeV) energies. The q/q → D fragmentation leads to enhanced production of D mesons at low energies. At √ s = 20 GeV the enhancement factor with respect to the conventional contribution is larger than a factor of five. In the considered picture the large-x F D mesons are produced dominantly via fragmentation of light quarks/antiquarks. Predictions for fixed target p + 4 He collisions relevant for a fixed target LHCb experiment are presented. PACS numbers:were found to be extremely small, consistent with zero (see e.g. Refs.[4-6] and references therein). The LHCb result was obtained for D ± → K 0 s K ± decays. Can perturbative effects lead to any asymmetry? Higher-order pQCD and electroweak effects on cc asymmetry (both quark and antiquark registered) was studied in Ref. [7] for E T > 20 GeV. The predicted effect was, however, rather small (< 1 %), at least for the LHCb (pseudo)rapidity coverage 2 < η < 4.The production asymmetries were interpreted in Refs. [8,9] as due to meson cloud mechanism and specific structure of the proton Fock components. The string model approach to the problem of heavy meson production and asymmetries in the production of heavy mesons was discussed in extent in Ref. [10]. The LHCb asymmetry was discussed also in the framework of heavy-quark recombination approach [11] (for earlier work see e.g. Ref.[12]). Here there are four unknown parameters responsible for formation of D mesons. It was shown that with some combination of parameters one can describe the LHCb data [11].The conventional D meson production mechanism leads to symmetry in D + /D − or D 0 /D 0 production, i.e. σ(D + ) = σ(D − ) and σ(D 0 ) = σ(D 0 ). As will be discussed in the present paper, only a subtle isospin-violating effect in vector D meson decays (D * → DX) leads to a significant effect of σ(D + /D − ) < σ(D 0 /D 0 ).Here we consider a simple alternative phenomenological explanation using so-called unfavored fragmentation functions responsible for light quark/antiquark fragmentation to D mesons. Such un...