Neutrino oscillation data versus three light neutrino flavors

Assuming oscillations of solar and LSND neutrinos to explain the corresponding data, we explore how much of the observed atmospheric neutrino anomaly can be accommodated by the hypothesis of only three light neutrino flavors. Standard Model interactions, considered exclusively, are found to allow a universal survival probability, equal to the ratio of ratios $R$, down to a best-fit value of about 0.58 for both the sub-GeV and the multi-GeV data, but no variation of this ratio with the zenith angle. Mild variations of the latter kind may be admitted by postulating large anomalous diagonal $\nu_\tau$-quark interactions, but $R$ can never be less than 0.5.