We present a critical analysis of aspects of cosmic ray (CR) generation and propagation in the Galaxy, relevant for the interpretation of recent positron and anti-proton measurements. We give model independent expressions for the secondary p flux, and an upper limit for the secondary e⁺ flux, obtained by neglecting e⁺ radiative losses, e⁺/(e⁺ + e^-)<0.2±0.1 up to ~300 GeV. These expressions are completely determined by the rigidity dependent grammage, measured from stable CR secondaries up to ~150 GeV/nuc, and by nuclear cross sections measured in the laboratory.
p and e⁺ measurements, available up to ~100 GeV, are consistent with these estimates, implying that there is no need for new, non-secondary, p or e⁺ sources. The radiative loss suppression of the e⁺ flux depends on the e⁺ propagation in the Galaxy, which is not understood theoretically. A rough, model independent estimate can be obtained from unstable secondary decay and is found to be consistent with the positron fraction measured by PAMELA. We show that models, that agree with compositional CR data, agree with our simple expressions for the e⁺ and p flux. The claims that the positron fraction measured by PAMELA requires new primary e⁺ sources are therefore based on assumptions, that are not supported by observations. We argue that measurements of the e⁺ to p ratio are more useful for challenging secondary production models than the e⁺/(e⁺ + e^-) fraction.