Tropical pseudostable curves

We study the tropical version of the contraction morphism 𝒯 between moduli spaces of stable and pseudostable curves. By promoting 𝒯 to a logarithmic morphism, we obtain a piecewise linear function between the generalized cone complexes parameterizing tropical stable and pseudostable curves. The ray corresponding to the contracted divisor δ_1 is not contracted to the cone point but mapped onto a ray of ℳ_g,n^ trop, ps, with a slope reflecting the geometry of the desingularization of a plane cusp. We explore in detail the situation of g=1, where the tautological geometry of both spaces is fully described by piecewise polynomial functions on the tropical moduli spaces.