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Individual abundances in the Milky Way disc record stellar birth properties(e.g. age, birth radius ($R_{\rm birth}$)) and capture the diversity of thestar-forming environments over time. Assuming an analytical relationshipbetween ([Fe/H], [$\alpha$/Fe]) and $R_{\rm birth}$, we examine thedistributions of individual abundances [X/Fe] of elements C, O, Mg, Si, Ca($\alpha$), Al (odd-z), Mn (iron-peak), Y, and Ba (neutron-capture) for starsin the Milky Way. We want to understand how these elements might differentiateenvironments across the disc. We assign tracks of $R_{\rm birth}$ in the[$\alpha$/Fe] vs. [Fe/H] plane as informed by expectations from simulations for$\sim 59,000$ GALAH stars in the solar neighborhood ($R\sim7-9$ kpc) which alsohave inferred ages. Our formalism for $R_{\rm birth}$ shows that older stars($\sim$10 Gyrs) have a $R_{\rm birth}$ distribution with smaller mean values(i.e., $\bar{R}_{\mbox{birth}}$$\sim5\pm0.8$ kpc) compared to younger stars($\sim6$ Gyrs; $\bar{R}_{\mbox{birth}}$$\sim10\pm1.5$ kpc), for a given [Fe/H],consistent with inside-out growth. The $\alpha$-, odd-z, and iron-peak elementabundances decrease as a function of $R_{\rm birth}$, whereas theneutron-capture abundances increase. The $R_{\rm birth}$-[Fe/H] gradient wemeasure is steeper compared to the present-day gradient (-0.067 dex/kpc vs-0.058 dex/kpc), which we also find true for $R_{\rm birth}$-[X/Fe] gradients.These results (i) showcase the feasibility of relating the birth radius ofstars to their element abundances, (ii) the abundance gradients across $R_{\rmbirth}$ are steeper than those over current radius, and (iii) offer anobservational comparison to expectations on element abundance distributionsfrom hydrodynamical simulations.

The individual abundance distributions of disc stars across birth radii in GALAH