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The classical clutching and gluing maps between the moduli stacks of stablemarked algebraic curves are not logarithmic, i.e. they do not induce morphismsover the category of logarithmic schemes, since they factor through theboundary. Using insight from tropical geometry, we enrich the category oflogarithmic schemes to include so-called sub-logarithmic morphisms and showthat the clutching and gluing maps are naturally sub-logarithmic. Building onthe recent framework developed by Cavalieri, Chan, Wise, and the third author,we further develop a stack-theoretic counterpart of these maps in the tropicalworld and show that the resulting maps naturally commute with the process oftropicalization.

Clutching and gluing in tropical and logarithmic geometry