  We present an analytical model of the relation between the surface density of
gas and star formation rate in galaxies and clouds, as a function of the
presence of supersonic turbulence and the associated structure of the
interstellar medium. The model predicts a power-law relation of index 3/2,
flattened under the effects of stellar feedback at high densities or in very
turbulent media, and a break at low surface densities when ISM turbulence
becomes too weak to induce strong compression. This model explains the
diversity of star formation laws and thresholds observed in nearby spirals and
their resolved regions, the Small Magellanic Cloud, high-redshift disks and
starbursting mergers, as well as Galactic molecular clouds. While other models
have proposed interstellar dust content and molecule formation to be key
ingredients to the observed variations of the star formation efficiency, we
demonstrate instead that these variations can be explained by interstellar
medium turbulence and structure in various types of galaxies.
