Infrared-to-radio flux ratios, using the observed 24 μm (q₂₄; top) and 100 μm flux densities (q₁₀₀; bottom); the radio-excess sources in our sample (q < 1.68) are highlighted by open circles. The shaded regions in the two plots represent the q₂₄ and q₁₀₀ ratios predicted for our range of star-forming galaxies as a function of redshift. The horizontal line in the top plot is the q₂₄ = 0 selection used by Donley et al. (2005) to define their radio-excess sample. In the bottom panel we identified q₁₀₀ = 1.5 as an easy selection of radio-excess sources (dashed line), with reasonable completeness (≈60–80%) at least out to z ≈ 2.