Energy dependence of particle ratio fluctuations in central<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi mathvariant="normal">Pb</mml:mi><mml:mo>+</mml:mo><mml:mi mathvariant="normal">Pb</mml:mi></mml:mrow></mml:math>collisions from<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msqrt><mml:mrow><mml:msub><mml:mi>s</mml:mi><mml:mrow><mml:msub><mml:mi/><mml:mrow><mml:mi mathvariant="italic">NN</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:msub></mml:mrow></mml:msqrt><mml:mo>=</mml:mo><mml:mn>6</mml:mn><mml:mo>.</mml:mo><mml:mn>3</mml:mn></mml:mrow></mml:math>to 17.3 GeV

We present measurements of the energy dependence of event-by-event fluctuations in the $K/\ensuremath{\pi}$ and $(p+\overline{p})/\ensuremath{\pi}$ multiplicity ratios in heavy-ion collisions at the CERN SPS. The particle ratio fluctuations were obtained for central $\mathrm{Pb}+\mathrm{Pb}$ collisions at five collision energies, $\sqrt{{s}_{\mathit{NN}}}$, between 6.3 and 17.3 GeV. After accounting for the effects of finite-number statistics and detector resolution, we extract the strength of nonstatistical fluctuations at each energy. For the $K/\ensuremath{\pi}$ ratio, larger fluctuations than expected for independent particle production are found at all collision energies. The fluctuations in the $(p+\overline{p})/\ensuremath{\pi}$ ratio are smaller than expectations from independent particle production, indicating correlated pion and proton production from resonance decays. For both ratios, the deviation from purely statistical fluctuations shows an increase toward lower collision energies. The results are compared to transport model calculations, which fail to describe the energy dependence of the $K/\ensuremath{\pi}$ ratio fluctuations.