Left: predicted relation between f_esc, Lyα and Lyα EW₀ for our toy model, which shows little to no correlation by sampling all physical parameters independently (see Table A.1). We also show the observed range (≈ ± 0.05) which is well constrained at z ∼ 0−2.6. We use simulated sources that are consistent with observations of LAEs to explore the potential reason behind the observed tight f_esc, Lyα-EW₀ correlation for LAEs. Right: by restricting our toy model to the observed relation and its scatter, we find a relatively tight ξ_ion − E(B − V) anti-correlation for LAEs (EW₀ >  25 Å): log₁₀(ξ_ion/Hz erg⁻¹) ≈ −1.85 × E(B − V) + 25.6 (shown as grey dot-dashed line). This is in good agreement with the family of best fits using Eq. (6) (we show the 1, 2 and 3σ contours) which yields log₁₀(ξ_ion/Hz erg⁻¹) ≈ −1.71 × E(B − V) + 25.6, with only a small difference in the slope. The highest observed EW₀ correspond to the highest ξ_ion and the lowest E(B − V), while lower EW₀ leads to a lower ξ_ion and a higher E(B − V). Our results thus show that the observed f_esc, Lyα-EW₀ correlation for LAEs at z ∼ 0−2.6 only allows a well defined ξ_ion − E(B − V) sequence that may be related with important physics such as the age of the stellar populations, their metallicity, dust production and how those evolve together.