  The supernova explosion which deposited $^{60}$Fe isotopes on Earth 2-3
million years ago should have also produced cosmic rays which contribute to the
locally observed cosmic ray flux. We show that the contribution of this "local
source" explains the "anomalies" observed in the positron and antiproton fluxes
and explains why their spectral shape agrees with that of the proton flux. At
the same time, this local source component accounts for the difference in the
slopes of the spectra of cosmic ray nuclei as the result of the slightly
varying relative importance of the "local" and the average component for
distinct CR nuclei. Such a "local supernova" model for the spectra of nuclei
can be tested via a combined measurement of the energy dependence of the
boron-to-carbon (primary-to-secondary cosmic rays) ratio and of the antiproton
spectrum: While the antiproton spectrum is predicted to extend approximately as
a power law into the TeV range without any softening break, the B/C ratio is
expected to show a "plateau" at a level fixed by the observed positron excess
in the 30-300 GeV range. We discuss the observability of such a plateau with
dedicated experiments for the measurement of the cosmic ray composition in 10
TeV energy range (NUCLEON, ISS-CREAM).
