Tropical Tevelev degrees

We define the tropical Tevelev degrees, ${\mathsf{T}\mathsf{e}\mathsf{v}}_g^{trop}$, as the degree of a natural finite morphism between certain tropical moduli spaces, in analogy to the algebraic case. We develop an explicit combinatorial construction that computes ${\mathsf{T}\mathsf{e}\mathsf{v}}_g^{trop}=2^g$. We prove that these tropical enumerative invariants agree with their algebraic counterparts, giving an independent tropical computation of the algebraic degrees $Te{v}_g$.