Deep Extragalactic VIsible Legacy Survey (DEVILS): The sSFR-M$_{\star}$plane part I: The recent SFH of galaxies and movement through the plane

In a recent paper we parameterised the evolution of the star-formation rate dispersion ($\sigma_{SFR}$) across the specific star-formation rate - stellar mass plane (sSFR-M$_{\star}$) using the Deep Extragalactic VIsible Legacy Survey (DEVILS) - suggesting that the point at which the minimum in the dispersion occurs (M$^{*}_{\sigma-min}$) defines a boundary between different physical mechanisms affecting galaxy evolution. Here we expand upon that work to determine the movement of galaxies through the sSFR-M$_{\star}$ plane using their recent star-formation histories (SFHs) and explore how this leads to the observed $\sigma_{SFR}$-M$_{\star}$ relation. We find that galaxies in sub-regions of the sSFR-M$_{\star}$ plane show distinctly different SFHs, leading to a complex evolution of the sSFR-M$_{\star}$ plane and star-forming sequence (SFS). However, we find that selecting galaxies based on stellar mass and position relative to SFS alone (as is traditionally the case), may not identify sources with common recent SFHs, and therefore propose a new selection methodology. We then use the recent SFH of galaxies to measure the evolution of the SFS, showing that it has varying contributions from galaxies with different SFHs that lead to the observed changes in slope, normalisation and turnover stellar mass. Finally, we determine the overall evolution of the sSFR-M$_{\star}$ plane from $z\sim1$ to today. In the second paper in this series we will discuss physical properties of galaxies with common recent SFHs and how these lead to the observed $\sigma_{SFR}$-M$_{\star}$ relation and evolution of the sSFR-M$_{\star}$ plane.